Composite material physical property estimation method, composite material physical property estimation device, and program

Abstract

To provide a composite material physical property estimation method, a composite material physical property estimation device, and a program for highly accurately estimating physical properties of a composite material in which a plurality of fillers have been dispersed in its base material.SOLUTION: A composite material physical property estimation method includes the steps of: calculating an equivalent natural electric field vector<E*Ω>Ω which indicates a volume average of an equivalent natural electric field in a heterogeneous inclusion Ω resulting from a difference in conductivity between a base material D and the heterogeneous inclusion Ω, for a composite material containing a double-inclusion V constituted of the heterogenous inclusion Ω and an inclusion Γ having the same dielectric constant as the base material D, on the basis of a dielectric constant tensor C, CΩ, an Eshelby tensor SΩ, SV, a natural electric field vector<EpΩ>Ω, <EpΓ>Γ, a working electric flux density vector D0, a working electric field vector E0, and a volume content f, fV; and a step for estimating thermal and electromagnetic physical properties of a composite material by using the equivalent natural electric field vector<E*Ω>Ω.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a composite material property estimation method, a composite material property estimation device, and a program. [Background technology]

[0002] A method for estimating physical properties that estimates the physical properties representing the thermal and electromagnetic properties of a composite material in which one type of filler different from the matrix is ​​dispersed in the matrix based on Eshelby's equivalent inclusion method and Mori-Tanaka's theorem has been proposed (see, for example, Non-Patent Document 1). In this method, the physical properties of a composite material in which a plurality of finite ellipsoidal fillers different from the matrix are present in a matrix that is uniform and isotropic and infinite are estimated. Specifically, the volume fraction of the filler in the matrix of the composite material is used to derive a relational expression between the electric flux density field and the electric field in the composite material when an external electric flux density is applied to the composite material, taking into consideration the mutual interference between the filler and the matrix, and the permittivity of the composite material is estimated based on the derived relational expression. In addition, the electric conductivity of the composite material is estimated by replacing the electric flux density with the current density. In addition, the magnetic permeability of the composite material is estimated by replacing the electric flux density with the magnetic flux density and the electric field with the magnetic field. In addition to these electromagnetic problems, the thermal conductivity of the composite material is estimated by replacing the electric flux density with the heat flow velocity and the electric field with the temperature gradient. In the following, we will explain using the relationship between the electric flux density, the electric field, and the dielectric constant. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Minoru Taya, "Fundamentals and Applications of Micro-Mechanics Models for Estimating the Physical Properties of Composite Materials (1)", Materia, Vol. 33, No. 4, p276-p288, 1994. Summary of the Invention [Problem to be solved by the invention]

[0004] However, when a filler is dispersed in a composite material, a plurality of fillers may be locally unevenly distributed in the matrix to form clusters, and the formation of these clusters may cause the magnitude of the electric field in the vicinity of the fillers present inside and outside the cluster to differ. Therefore, in the method of estimating physical properties described in Non-Patent Document 1, the structure of the actual composite material is not sufficiently reflected in the model, and there is a risk that the physical properties of the composite material cannot be accurately estimated.

[0005] The present invention has been made in consideration of the above-mentioned reasons, and aims to provide a composite material property estimation method, a composite material property estimation device, and a program that can estimate the properties of a composite material in which a plurality of fillers are dispersed in a base material with high accuracy. [Means for solving the problem]

[0006] In order to achieve the above object, a composite material property value estimation method according to the present invention includes: A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material, and a plurality of double inclusions including a first inhomogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second inclusion having a dielectric constant equal to that of the base material and surrounding the first inhomogeneous inclusion, comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion and a dual inclusion shape parameter indicating a shape of the dual inclusion; calculating a first inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the first inhomogeneous inclusion, based on the first inhomogeneous inclusion shape parameters, and generating a double inclusion Eshelby tensor, which is the Eshelby tensor of the double inclusion, based on the double inclusion shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion; acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; Obtaining a volume fraction of the first heterogeneous inclusion in the dual inclusion and a volume fraction of the dual inclusion in a base material; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the first inhomogeneous inclusion and a volume average of an equivalent intrinsic electric field in the double inclusion based on the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the double inclusion Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector and the two volume contents; and estimating thermal and electromagnetic properties of the composite material using the equivalent eigenelectric field vector. Effect of the Invention

[0007] According to the present invention, an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the first inhomogeneous inclusion and the cluster is calculated based on the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, and the volume content. Then, the calculated equivalent intrinsic electric field vector is used to estimate the thermal and electromagnetic properties of the composite material. The estimation result includes the volume content of the first inhomogeneous inclusion in the cluster, and by combining this size with the effect of the local uneven distribution of the first inhomogeneous inclusion, the thermal and electromagnetic properties of the composite material can be estimated using a model that is closer to the actual state of the composite material in which these first inhomogeneous inclusions are dispersed in the matrix, thereby improving the estimation accuracy of the thermal and electromagnetic properties of the composite material. [Brief description of the drawings]

[0008] [Figure 1]1 shows models of a composite material according to an embodiment, in which (A) is a schematic diagram showing a model in which one ellipsoidal inhomogeneous inclusion is present in the base material, (B) is a schematic diagram showing a model in which multiple inhomogeneous inclusions arranged in one direction are present in the base material, and (C) is a schematic diagram showing a model in which multiple double inhomogeneous inclusions arranged in one direction are present in the base material. [Diagram 2] FIG. 2 is a schematic diagram showing a first-type mixed double heterogeneous inclusion model according to the embodiment. [Diagram 3] FIG. 2A is a schematic diagram showing a high-level cluster model of a composite material according to an embodiment, and FIG. 2B is a schematic diagram showing a first-type mixed dual inclusion model thereof. [Figure 4] FIG. 2A is a schematic diagram showing a low-level cluster model of a composite material according to an embodiment, and FIG. 2B is a schematic diagram of another low-level cluster model of a composite material according to an embodiment. [Diagram 5] FIG. 2A is a schematic diagram showing a multi-type high-level cluster model of a composite material according to an embodiment, and FIG. 2B is a schematic diagram showing a multi-type low-level cluster model of a composite material according to an embodiment. [Figure 6] FIG. 2 is a schematic diagram showing a first-type mixed triple heterogeneous inclusion model according to the embodiment. [Figure 7] FIG. 1 is a schematic diagram showing a dual heterogeneous inclusion low-level cluster model according to an embodiment. [Figure 8] 1A and 1B show models of a composite material according to an embodiment, in which (A) is a schematic diagram showing a high-level cluster model of dual inhomogeneous inclusions, and (B) is a schematic diagram showing a low-level cluster model of dual inhomogeneous inclusions. [Figure 9] 1 is a block diagram showing a hardware configuration of a composite material property estimation apparatus according to an embodiment. FIG. [Figure 10] 1 is a block diagram showing a functional configuration of a composite material property estimation apparatus according to an embodiment; [Figure 11] 10 is a flowchart showing an example of a flow of a composite material property estimation process according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the composite material property estimation method according to the present embodiment, the thermal and electromagnetic properties of a composite material in which reinforcing base materials (fillers) such as particles, fibers, and flakes other than woven or knitted fibers are dispersed in a matrix are estimated. In this composite material property estimation method, the structure of the composite material is approximated by one of ten types of models, and the thermal and electromagnetic properties of the composite material are estimated using the adopted model. The ten types of models include a mixed double inclusion model, a unidirectionally oriented high-level cluster model, a unidirectionally oriented low-level cluster model, a multi-type high-level cluster model, a multi-type low-level cluster model, a mixed triple inclusion model, a unidirectionally oriented double heterogeneous inclusion high-level cluster model, a unidirectionally oriented double heterogeneous inclusion low-level cluster model, a multi-type double heterogeneous inclusion high-level cluster model, and a multi-type double heterogeneous inclusion low-level cluster model, which will be described later. First, the Eshelby equivalent inclusion method and the Mori-Tanaka theorem, which are the basis of these models, will be briefly described.

[0010] In Eshelby's equivalent inclusion method, first, as shown in Figure 1(A), a composite material can be approximated by a model in which an isotropic and homogeneous matrix D contains an inhomogeneous inclusion Ω of ellipsoidal shape. Here, the inhomogeneous inclusion Ω has a dielectric constant e different from that of the matrix D. D* ij and has a specific electric field E p i and is completely bonded to the base material D. In the model shown in FIG. 1(A), the equivalent equation (1) below is derived from Eshelby's equivalent inclusion method.

[0011]

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[0012] Here, e D denotes the dielectric constant of the base material D. Also, E 0 j is the electric flux density D in the composite material. 0 i (=e D E0 i ) is applied to the electric field, and H ij denotes the Eshelby tensor of the inhomogeneous inclusion Ω. Also, E * i is the equivalent specific electric field representing the difference between the dielectric constant of the base material D and the dielectric constant of the inhomogeneous inclusion Ω, and is an unknown quantity that can be obtained by solving the equivalent equation (1). Here, the Eshelby tensor H ij When the inhomogeneous inclusion Ω is an ellipsoid, it is expressed as a function with the shape factor of the inhomogeneous inclusion Ω as an argument, and the shape factor is expressed as a function of the aspect ratio of the ellipsoid. Specifically, it is expressed by formulas (6) to (14) described in the literature by Araki (Araki Hidetoshi et al., "Micromechanics Analysis of Macroscopic Dielectric Constant and Macroscopic Linear Expansion Coefficient of Composite Material Containing Ellipsoidal Reinforcement Substrate", Proceedings of the Japan Society of Mechanical Engineers (Series A), Vol. 74, No. 745, September 2008, pp. 37-44).

[0013] Also, the electric flux density in the inhomogeneous inclusion Ω is D i Then, the following relational expression (2) can be derived from the expression (22.13.1) described in the document Mura (T. Mura, “Micromechanics of Defect in Solids Second, revised edition”, Kluwer Academic Publishers, (1987), pp.178-187.).

[0014]

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[0015] Therefore, using the relational expression (1), the equivalent specific electric field E is calculated from the dielectric constants of the base material D and the inhomogeneous inclusion Ω, the electric flux density acting on the composite material and the electric field generated by it, and the inhomogeneous inclusion Ω. * i The specific electric flux density generated in the inhomogeneous inclusion Ω can be calculated from the calculated equivalent specific electric field, the aforementioned Eshelby tensor, and the specific electric field using the relational expression (2).

[0016] Also, assume that the composite material can be approximated by a model in which a large number of inhomogeneous inclusions Ω are randomly present in a matrix D so that the principal axes of the inhomogeneous inclusions Ω are aligned in the same direction, as shown in FIG. 1(B). In this case, an interaction electric flux density occurs due to the interaction between the large number of inhomogeneous inclusions Ω contained in the composite material or between the inhomogeneous inclusions Ω and the matrix D. The volume average of this interaction electric flux density is expressed by the following relational expression (3) based on the expressions (9) and (10) showing the Mori-Tanaka theorem described in the literature Mori (T. Mori and K. Tanaka, "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions", Acta Metallurgica, Vol. 21 (1973), pp. 571-574.) and the above-mentioned expression (2).

[0017]

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[0018] Here, D ~ i represents the volume average of the interaction electric flux density, and f Ω indicates the volume content of the inhomogeneous inclusion Ω in the base material D. The equivalent formula (4) below is derived from formula (2) or formula (6) and formula (1) described in the literature by Taya (M. Taya and TW Chou, Internal Journal of Solids and Structures, 17 (1981), pp. 553-563.) and the above formula (3).

[0019]

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[0020] Therefore, by substituting equation (3) into the equivalent equation (4), we obtain D ~ i Using the formula with the above eliminated, the equivalent specific electric field E * iAfter calculating, the specific electric flux density generated in the inhomogeneous inclusion Ω can be calculated from the calculated equivalent specific electric field and the aforementioned Eshelby tensor and specific electric field using the relational expression (2). Then, the volume average of the interacting electric flux density in the composite material can be calculated from the calculated specific electric flux density or equivalent specific electric field using the aforementioned expression (3).

[0021] In addition, for the above equation (4), the electric flux density and the electric field are expressed as row vectors D and E with 3 rows and 1 column, respectively, and the Eshelby tensor H ij and dielectric constant e D* ij are 3-by-3 matrices H and e D* and the superscript Ω is added. The specific electric field and the equivalent specific electric field are expressed by the symbol < > which indicates the volume average within Ω. Ω Using the above formula and adding the superscript Ω, this is expressed as the equivalent formula (5) below.

[0022]

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[0023] Here, I represents a unit matrix. From equations (4) and (3), the following relational expression (6) is derived.

[0024]

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[0025] The relation between the electric flux density acting on the composite material and the corresponding electric field satisfies the following formula (7).

[0026]

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[0027] Then, from equations (5) and (6), the equivalent equation of equation (8) below is derived.

[0028]

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[0029] Here, from the left of both sides of equation (8), (e D*Ω -e D ) -1 By multiplying by, the final equivalent equation of this model becomes equation (9) below.

[0030]

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[0031] Here, the specific electric flux density is expressed by the symbol < >, which indicates the volume average in Ω. Ω Using the above and adding the superscript ∞ for identification purposes, the following relational expression (10) can be derived from the above expression (2).

[0032]

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[0033] From the Mori-Tanaka theorem (3) mentioned above, the relational expression (11) below holds.

[0034]

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[0035] Furthermore, by solving the equivalent equation (9), the volume average of the sum of the specific electric field and the equivalent specific electric field is given by the following equation (12).

[0036]

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[0037] Then, by substituting equation (12) into equation (10), the specific electric flux density is obtained, as shown in equation (13) below.

[0038]

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[0039] Therefore, the volume average of the specific electric flux density generated in the inhomogeneous inclusion Ω can be obtained using the relational expression (13). Furthermore, by substituting the specific electric flux density obtained using the relational expression (13) into the expression (11), the volume average of the interacting electric flux density in the composite material can be obtained.

[0040] In addition, in the above formula (9), the volume fraction f Ω The term multiplied by is the interaction electric field E that occurs throughout the composite material. ~ Considering that the above is due to the above, the equivalent equation (9) can be rewritten as the following equivalent equation (14).

[0041]

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[0042] Furthermore, it is assumed that the composite material can be approximated by a double heterogeneous model in which there are many double heterogeneous objects V in the matrix D, each of which is composed of a heterogeneous object Ω and a heterogeneous object Γ that surrounds the heterogeneous object Ω and has a dielectric constant different from that of the heterogeneous object Ω, as shown in Figure 1(C). The heterogeneous object has a dielectric constant different from that of the matrix D, but has no inherent electric field and is completely bonded to the matrix. If there is only one double heterogeneous object in the matrix D, the equivalent equations (15) and (16) below can be derived for the heterogeneous objects Ω and Γ, respectively, from equation (10.4.24) described in the literature Nemat (S. Nemat-Nasser and M. Hori, micromechanics: overall properties of heterogeneous materials, North-Holland Publishers, (1993), pp.340-357.).

[0043]

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[0044]

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[0045] Here, e D is the dielectric constant of the base material D, and e D*Ω is the dielectric constant of the inner inhomogeneity Ω of the double inhomogeneity V, and e D*Γ denotes the dielectric constant of the inhomogeneous material Γ. Also, H Ω denotes the Eshelby tensor of the inhomogeneity Ω, and H V denotes the Eshelby tensor of the double inhomogeneity V, and f denotes the volume fraction of the inhomogeneity Ω in the double inhomogeneity V. If the inner inhomogeneity Ω of the double inhomogeneity V and the inhomogeneity Γ surrounding it are inhomogeneous inclusions that also have intrinsic electric fields, the equivalent equation of the inhomogeneity inclusions Ω and Γ can be derived from equations (15), (16-1), and (16-2).

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[0046]

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[0047] Then, from equations (16-1) and (16-2) and the aforementioned Mori-Tanaka theorem, using the same approach as in deriving the aforementioned equation (5), the equivalent equations of equations (17) and (18) below can be derived for the case where a large number of double heterogeneous inclusions are present in the base material D.

[0048]

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[0049]

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[0050] Then, using the same idea as in deriving equation (14), the final equivalent equations of this model are given by equations (19) and (20) from equations (17) and (18).

[0051]

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[0052]

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[0053] The relationship between the equivalent specific electric field and the specific electric field in the double inhomogeneous inclusion V is expressed by the following equation (21):

[0054]

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[0055] Moreover, in a manner similar to the derivation of equation (10), the following relational expressions (22) and (23) are derived from equations (19) and (20).

[0056]

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[0057]

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[0058] Moreover, from equations (22) and (23), the following relational equation (24) can be obtained.

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[0059] From the above-mentioned Mori-Tanaka theorem (11), the relational expression (25) below is established using the volume fraction fv of the double heterogeneous inclusion V in the base material D.

[0060]

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[0061] Therefore, the equivalent intrinsic electric field of the inhomogeneous inclusions Ω and Γ can be calculated using the above-mentioned relational expressions (19) and (20), and the volume average of the intrinsic electric flux density generated in each of the inhomogeneous inclusions Ω and Γ and the double inhomogeneous inclusion V can be obtained from the calculated equivalent intrinsic electric field using the relational expressions (22) to (24). Furthermore, the volume average of the interacting electric flux density in the composite material can be obtained from the equivalent intrinsic electric field of the inhomogeneous inclusions Ω and Γ obtained using the relational expressions (19) and (20) using the above-mentioned relational expressions (25) and (24).

[0062] Next, a case will be described where a composite material can be approximated by the above-mentioned first type mixed double inclusion model. As shown in Fig. 2, the first type mixed double inclusion model is a model in which a matrix D contains a large number of mixed double inclusions V, each consisting of a heterogeneous inclusion Ω and an inclusion Γ that surrounds the heterogeneous inclusion Ω and has the same dielectric constant and intrinsic electric field as the matrix D. In other words, it corresponds to a model in which the dielectric constant of the heterogeneous inclusion Γ is made equal to that of the matrix D in the model explained using Fig. 1(C). In this case, since the dielectric constants of the heterogeneous inclusion Γ and the matrix D are equal, the equivalent intrinsic electric field at the heterogeneous inclusion Γ in the above-mentioned equation (19) can be expressed as <E *Γ > Γ can be set to 0, and the equivalent equation (26) below holds.

[0063]

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[0064] Here, after substituting the above equation (24) into equation (25), the equivalent specific electric field at the inclusion Γ is <E *Γ > Γ If we set it to 0, we obtain the following relational expression (27).

[0065]

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[0066] Then, by substituting the relational expression (27) into the relational expression (26), the final equivalent equation of this model becomes the following equation (28).

[0067]

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[0068] Here, by solving the equivalent equation (28), the volume average of the sum of the intrinsic electric field and the equivalent intrinsic electric field is given by the following equation (29).

[0069]

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[0070] The specific electric flux density is expressed by the specific electric field in the region Γ in each of the above-mentioned equations (22) to (24). <E *Γ > Γ By setting to 0, it is expressed as the following equations (30) to (32).

[0071]

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[0072]

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[0073]

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[0074] In addition, in the above equivalent equation (28), f V = 0, D 0 D 0 +D ~ Substituting this, we get the interaction electric flux density D ~The equivalent equation of this model when is unknown is the following equation (33).

[0075]

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[0076] Therefore, the equivalent intrinsic electric field of the inhomogeneous inclusion Ω can be calculated using the result of the above-mentioned equation (29), and the volume average of the intrinsic electric flux density generated in each of the inhomogeneous inclusion Ω, the inclusion Γ, and the mixed double inclusion V can be obtained from the calculated equivalent intrinsic electric field using the relational expressions (30) to (32). Furthermore, the volume average of the interacting electric flux density in the composite material can be obtained from the equivalent intrinsic electric field of the inhomogeneous inclusion Ω calculated using the relational expression (29) using the relational expressions (25) and (32) above.

[0077] Next, we will explain the case where a composite material can be approximated by the unidirectionally oriented high-level cluster model mentioned above. The unidirectionally oriented high-level cluster model is a model in which multiple inhomogeneous inclusions Ω gather together to form a cluster V, as shown in Figure 3(A). The main semi-axial directions of the inhomogeneous inclusions Ω and cluster V are aligned in one direction within the cluster V. Furthermore, there are no inhomogeneous inclusions Ω outside the cluster V in the base material D. In this case, the volume fraction of each inhomogeneous inclusion Ω within cluster V is defined as f, and the volume fraction of the inhomogeneous inclusions Ω within cluster V is defined as f. total In this case, the volume fraction f of all the inhomogeneous inclusions Ω in the base material D is Ω is the volume fraction of cluster V, f V Using this, the relation is expressed by the following equation (34).

[0078]

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[0079] Here, the region of the base material D in the cluster V is defined as the Γ region, and its intrinsic electric field is <E pΓ > ΓThen, as shown in FIG. 3(B), the cluster V can be regarded as a first type mixed double inclusion consisting of one inhomogeneous inclusion Ω and an inclusion Γ that surrounds the inhomogeneous inclusion Ω and has the same dielectric constant and intrinsic electric field as the base material D. The intrinsic electric field of the Γ region is <E pΓ > Γ Let the sum of the intrinsic electric field of the inhomogeneous inclusion other than the inhomogeneous inclusion Ω mentioned above and the equivalent intrinsic electric field, which is the volume average in the Γ region, be <E p(V-Ω) > V-Ω Then, the relational expression (35) below is established.

[0080]

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[0081] Therefore, in the case of the model shown in FIG. 3(B), <E pΓ > Γ of <E p(V-Ω) > V-Ω Therefore, for equation (28), <E pΓ > Γ of <E p(V-Ω) > V-Ω and then substituting the relationship in equation (35), the final equivalent equation for this model is given by equation (36) below.

[0082]

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[0083] Here, by solving the equivalent equation (36), the volume average of the sum of the specific electric field and the equivalent specific electric field is given by equation (37).

[0084]

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[0085] Here, the volume average of the specific electric flux density in each cluster V is expressed by the following equations (30) and (32): <E Γ > Γof, <E p(V-Ω) > V-Ω and then substituting the relational expression in equation (35), the equation can be derived as the relational expressions shown in the following equations (38) and (39).

[0086]

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[0087]

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[0088] In addition, the volume average of the specific electric flux density in the Γ region, which is the base material region in cluster V, <D ∞ > Γ is expressed by the following relational expression (40).

[0089]

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[0090] Also, the interaction electric flux density D ~ is expressed by the following relational expression (41) by substituting the relational expression (39) into the expression (25).

[0091]

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[0092] Therefore, the equivalent intrinsic electric field of the inhomogeneous inclusion Ω can be calculated using the result of the above-mentioned formula (37), and the volume average of the intrinsic electric flux density generated in the inhomogeneous inclusion Ω, the region Γ outside the inhomogeneous inclusion Ω in the cluster V, and the cluster V can be obtained from the calculated equivalent intrinsic electric field using the relational expressions (38) to (40). Furthermore, the volume average of the interacting electric flux density in the composite material can be obtained from the intrinsic electric flux density of the cluster V calculated using the relational expression (39) using the relational expression (41) above.

[0093] In addition, in the above-mentioned equivalent equation (36), f V = 0, D 0 D 0 +D ~ Substituting this, we get the interaction electric flux density D ~ The equivalent equation of this model when is unknown is the following equation (42).

[0094]

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[0095] Next, we will explain the case where a composite material can be approximated by the unidirectionally oriented low-level cluster model mentioned above. The unidirectionally oriented low-level cluster model is a model in which, as shown in Fig. 4(A), multiple inhomogeneous inclusions Ω gather in a matrix D to form a cluster V, and inhomogeneous inclusions Ω are also present outside the cluster V in the matrix D. Here, the principal semi-axial directions of the inhomogeneous inclusions Ω and cluster V are aligned in one direction within the cluster V. Here, the inhomogeneous inclusions that exist outside the cluster V and are aligned in one direction are defined as Ω(0), and their volume fraction is f (0) Then, the volume fraction f of all inhomogeneous inclusions in the base material D is Ω If the positions of the clusters V in the base material D are random, then is expressed by the following relational expression (42).

[0096]

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[0097] Here, for the unidirectionally oriented low-level cluster model, as shown in Fig. 4(B), the shape of cluster V(i) contained in the base material D and the volume fraction f V(i) and the volume fraction f of the inhomogeneous inclusion Ω contained in cluster V(i) total(i) The clusters are n V In this case, the volume fraction f of the inhomogeneous inclusion Ω in the base material D is Ωis expressed by the following relational expression (44).

[0098]

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[0099] The unidirectionally oriented low-level cluster model is formed by adding cluster V(i) to the inhomogeneous inclusion Ω(0) dispersed throughout the entire region of the base material D. In this case, the sum of the intrinsic electric field and the equivalent intrinsic electric field of the inhomogeneous inclusion Ω(0) is <E *Ω(0) > Ω(0) + <E pΩ(0) > Ω(0) is averaged over the entire region of D. <E Γ(0) > Γ(0) is given by the following equation (45-1).

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[0100] And, on the right hand side of equation (42), <E pΓ > Γ is shown in the above equation (45-1). <E Γ(0) > Γ(0) Furthermore, the average intrinsic electric field due to Ω(0) distributed over the entire region of the matrix D for cluster V(i) is <E Γ(0) > Γ(0) Therefore, the left side of equation (42) <E pΩ > Ω + <E *Ω > Ω From the characteristic electric field of <E Γ(0) > Γ(0) Also, on the right hand side, < L E pΩ > Ω =L Ω <E pΩ > Ω The same is true for <E pΩ > Ω from <E Γ(0) > Γ(0)After making these modifications to equation (42), substituting equation (45-1) above and rearranging, the final equivalent equation for this model is given by equation (45-2) below.

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[0101] Here, f(i) is the volume fraction of one inhomogeneous inclusion Ω in cluster V(i). Also, the sum of the intrinsic electric field and the equivalent intrinsic electric field of the inhomogeneous inclusion Ω(0) is <E *Ω(0) > Ω(0) + <E pΩ(0) > Ω(0) In equation (12), Ω is replaced by Ω(0) and f Ω f (0) and the interaction electric flux density D in cluster V ~ Considering that the influence of extends to the entire base material D, D 0 D 0 +D ~ By substituting this, the following relational expression (46) is obtained.

[0102]

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[0103] Furthermore, by solving the equivalent equation (45-2), the volume average of the sum of the intrinsic electric field and the equivalent intrinsic electric field is given by the following equation (47).

[0104]

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[0105] Also, the equivalent specific electric field of cluster V <E * > V(i) + <E p > V(i) is expressed by the following relational expression (48).

[0106]

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[0107] Here, the volume average of the specific electric flux density of the heterogeneous inclusions Ω and Γ in each cluster V(i) and the entire cluster is expressed by the following equations with respect to the above-mentioned equations (38) to (40): <E pΓ > Γ is shown in the above equation (45-1). <E Γ(0) > Γ(0) Replace with <E pΩ > Ω + <E *Ω > Ω and <E p > V + <E * > V from <E Γ(0) > Γ(0) Subtracting this, the following relations are expressed by the following equations (49) to (51).

[0108]

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[0109]

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[0110]

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[0111] Furthermore, similarly to the above-mentioned equation (41), the interaction electric flux density is expressed by the relational expression shown in the following equation (51-2).

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[0112] Therefore, the equivalent intrinsic electric field of each of the inhomogeneous inclusions Ω(0) present outside the cluster V(i), the inhomogeneous inclusions Ω(i) in the cluster V(i), and the cluster V(i) can be calculated using the above-mentioned relational expressions (46) to (48). Then, the volume average of the intrinsic electric flux density generated in each of the inhomogeneous inclusions Ω(i) in the cluster V(i), the cluster V(i), and the region Γ(i) other than Ω(i) in the cluster V(i) can be calculated from the calculated equivalent intrinsic electric field using the relational expressions (49) to (51-1). Furthermore, the volume average of the interaction electric flux density in the composite material can be calculated from the intrinsic electric flux density of the cluster V calculated using the relational expression (50) using the above-mentioned relational expression (51-2).

[0113] Next, we will explain the case where a composite material can be approximated by the above-mentioned multi-type high-level cluster model. As shown in Figure 5(A), the multi-type high-level cluster model is a cluster of multiple inhomogeneous inclusions Ω(ijk) with different dielectric constants, specific electric fields, shapes, and orientation angles, which are grouped together to form n V In this model, a cluster V(i) of a certain type is formed. Here, j is an index indicating the dielectric constant, the specific electric field, and the shape, and n Ω There are three types, k is the index indicating the orientation angle, and n k Here, the major axis directions of the clusters V(i) are all the same. The global coordinate system is G x, and the local coordinate system of the inhomogeneous inclusion Ω(ijk) is L(k) If x, the following relational expression (52) holds.

[0114]

number

[0115] Here, in the above equation (33), f is replaced by f(ij) and the Eshelby tensor H M(1) H M(1)(ijk)Furthermore, if anything that can be expressed in the global coordinate system is expressed in the global coordinate system using the relation in equation (52), the equivalent equation in equation (53) below is obtained.

[0116]

number

[0117] Also, H V(i) is the global coordinate system, H Ω(j) Considering that is expressed in the local coordinate system, the following relational expression (54) holds.

[0118]

number

[0119] Then, taking into consideration the relational expression (54), the relational expression shown in the following formula (55) is derived from the above-mentioned formula (28).

[0120]

number

[0121] Here, the equivalent intrinsic electric field of all the inhomogeneous inclusions present in the cluster V(i) and the volume average of the intrinsic electric field in the cluster V(i) are expressed by the relational expression shown in the following formula (56).

[0122]

number

[0123] Then, using the relation in Eq. (56), the equivalent intrinsic electric field of the inhomogeneous inclusion existing in the region Γ(ij) (=V(i)-Ω(ij)) excluding the inhomogeneous inclusion Ω(ij) in the cluster V(i) and the volume average of the intrinsic electric field in the cluster V(i) are calculated. <E pΓ(ij) > Γ(ij) is expressed by the following equation (57).

[0124]

number

[0125] Now, substituting (57) into the equivalent equation (53), G E pΩ(ij) > Ω(ijk) +< G E *Ω(ijk) > Ω(ijk) By transforming to the local coordinate system, the final equivalent equation of this model becomes (58) below.

[0126]

number

[0127] Here, for equation (58), by approximating that f(ij) is sufficiently smaller than 1, we can obtain from equation (55): L(k) H S(ijk) ≒H Ω(j) , L(k) B S(ijk) ≒B Ω(j) Therefore, by using this approximation in the above-mentioned equivalent equation (58), and then solving this to find the volume average of the sum of the equivalent specific electric field and the specific electric field, we obtain the following equation (59).

[0128]

number

[0129] The specific electric flux density is expressed by each of the above-mentioned formulas (30) to (32). <E pΓ > Γ is expressed by equation (57). <E pΓ(ijk) > Γ(ijk) After replacing with, substitute equation (57), and further, approximate that f(ij) is sufficiently small compared to 1, L(k) H S(ijk) ≒H Ω(j) , L(k) B S(ijk) ≒B Ω(j) By approximating the above, the following relational expressions (60) to (62) are obtained.

[0130]

number

[0131]

number

[0132]

number

[0133] Therefore, the equivalent intrinsic electric field of the inhomogeneous inclusion Ω(i) can be calculated using the result of the above-mentioned formula (59), and the volume average of the intrinsic electric flux density generated in each of the inhomogeneous inclusion Ω(i) in the cluster V(i) and in the region Γ(i) other than the inhomogeneous inclusion Ω(i) in the cluster V(i) and the inhomogeneous inclusion Ω(i) in the cluster V(i) can be calculated from the calculated equivalent intrinsic electric field using the relational expressions (60) to (62). Furthermore, the volume average of the interacting electric flux density in the composite material can be calculated from the intrinsic electric flux density of the cluster V calculated using the relational expression (61) using the relational expression (51-1) above.

[0134] Next, we will explain the case where a composite material can be approximated by the above-mentioned multi-type low-level cluster model. As shown in Fig. 5(B), the multi-type low-level cluster model is a model in which multiple types of inhomogeneous inclusions Ω(ijk) gather together in a base material D to form a cluster V(i), and inhomogeneous inclusions Ω(0jk) also exist outside the cluster V(i) in the base material D. Here, j is an index indicating the type of dielectric constant, specific electric field, and shape, and n Ω There are three types, k is the index indicating the orientation angle, and n k Here, the directions of the principal semi-axis of the cluster V(i) are all the same. If the volume fraction of the inhomogeneous inclusion Ω(0jk) is f(0jk) and the volume fraction in the region Ω(0j) is f(0j), the following relational expression (63) is established.

[0135]

number

[0136] Then, from the specific electric field on both sides of equation (58), we obtain the following equation (63): G E *Ω(0) > ΣΩ(0) +< G E pΩ(0) > ΣΩ(0) After subtracting and rearranging, the final equivalent equation for this model is given by equation (64) below.

[0137]

number

[0138] Here, for equation (64), by approximating that f(ij) is sufficiently smaller than 1, we can obtain from equation (55): L(k) H S(ijk) ≒H Ω(j) , L(k) B S(ijk) ≒B Ω(j) Therefore, by using this approximation in the above-mentioned equivalent equation (64), and then solving this to find the sum of the equivalent intrinsic electric field and the intrinsic electric field, we obtain the following equation (65).

[0139]

number

[0140] Then, by substituting equation (65) into equation (56), the following relational equations (66) and (67) are obtained.

[0141]

number

[0142]

number

[0143] Based on the above equations (12) and (13), the interaction electric flux density in cluster V(i) is D ~ Let D be the interaction electric flux density when only the region Ω(0j) exists. ~ Ω(0) Then, the following relational expressions (68) and (69) are obtained.

[0144]

number

[0145]

number

[0146] Then, by substituting equation (68) into equation (63), the following relational equation (70) is obtained.

[0147]

number

[0148] Also, from the Mori-Tanaka theorem mentioned above, the interaction electric flux density D ~ Ω(0) is expressed by the following equation (71).

[0149]

number

[0150] Then, by substituting equation (69) into equation (71), the following relational equation (72) is derived.

[0151]

number

[0152] Moreover, by substituting equation (72) into equation (70), the volume average of the sum of the equivalent intrinsic electric field and the intrinsic electric field of all the inhomogeneous inclusions Ω(0j) distributed in the region Γ(0) is expressed by the following equation (73).

[0153]

number

[0154] Then, by subtracting the volume average of the sum of the equivalent intrinsic electric field and the intrinsic electric field of all the inhomogeneous inclusions Ω(0j) distributed in the region Γ(0) from the intrinsic electric field on the right-hand side of the above-mentioned relational expressions (60) to (62), the following relational expressions (74) to (76) are obtained.

[0155]

number

[0156]

number

[0157]

number

[0158] And the interaction electric flux density D ~ is expressed by the relational expression shown in the following expression (77) from expressions (75), (67), and (73).

[0159]

number

[0160] Therefore, the relation of the above formula (67) can be calculated by formula (77) D ~ By substituting the above, the volume average of the intrinsic electric field and the equivalent intrinsic electric field in cluster V(i) can be calculated. Furthermore, by substituting D, which can be calculated by equation (77), into the relational equation (73) mentioned above, ~By substituting the above, the equivalent intrinsic electric field of all the inhomogeneous inclusions Ω(0j) distributed in the region Γ(0) outside the cluster V(i) can be calculated. Using the relational expressions (74) to (76), the volume average of the intrinsic electric flux density generated in the inhomogeneous inclusions Ω(ijk) in the cluster V(i) and in the region Γ(i) other than the inhomogeneous inclusions Ω(ijk) in the cluster V(i) and in the cluster V(i) can be calculated from the calculated equivalent intrinsic electric field. Furthermore, using the relational expression (77), the volume average of the interaction electric flux density in the composite material can be calculated.

[0161] In addition, the orientation angle distribution f total(ijk) / f total(ij) and the orientation angle distribution f of Ω(0jk) (0jk) / f (0j) Once this is obtained, the coefficient related to the orientation angle distribution (hereinafter referred to as the “orientation angle distribution coefficient”) can be found using the relation between equations (66) and (70).

[0162] Here, the macroscopic total electric field, which represents the deformation of the entire composite material, G E - corresponds to the sum of the acting electric field acting on the entire composite material and the volume average of the sum of the equivalent intrinsic electric field and the intrinsic electric field, and is expressed by the following relational expression (78).

[0163]

number

[0164] The macroscopic dielectric constant of the composite material is e D- Then, the total macroscopic electric field G E - and the acting electric flux density G D 0 is expressed by the following relational expression (78-2).

number

[0165] Substituting equations (67) and (73) into equation (78-1), and further substituting the interaction electric flux density D~ Substituting this, we obtain the following relational equation (78-3).

number

[0166] Equating equation (78-2) and equation (78-3), the intrinsic electric field < G E p(i) > V(i) and G E pΩ(0) > ΣΩ(0)) If we set to 0, then from equations (67), (70), (72), (77), and (78-1), Σ A^ p = Σ P^ p = 0, and by further substituting these relationships, the macroscopic dielectric constant e D- is calculated, resulting in the following equation (78-4).

number

[0167] From equation (78-4), the macroscopic dielectric constant of this composite material model can be estimated.

[0168] For all the models described so far, the equivalent specific electric field, the specific electric flux density, and the interaction electric flux density have been obtained, so the macroscopic dielectric constant can be estimated by following the same procedures as those described in paragraphs

[0162] to

[0167] .

[0169] Next, a case will be described in which a composite material can be approximated by the above-mentioned first type mixed triple inclusion model. The first type mixed triple inclusion model will be described as being represented by a model in which a large number of first type mixed triple inclusions V2, each consisting of the above-mentioned double heterogeneous inclusion V1 and an inclusion Γ2 that surrounds the double heterogeneous inclusion V1 and has an intrinsic electric field, are present in a matrix D, as shown in Fig. 6. Comparing the above-mentioned equivalent equation (14) with equivalent equation (26) which holds for the first type mixed double heterogeneous inclusion model, equation (26) has the following inclusion in equation (14): a term (H V -HΩ ) <E pΓ > Γ From this, for the first type mixed triple inclusion model, in each of equations (19) and (20), f is the volume fraction of the heterogeneous inclusion Ω in the double heterogeneous inclusion V1, and the term due to the intrinsic electric field in region Γ2 (H V2 -H V1 ) <E pΓ2 > Γ2 The following relational expressions (81) and (82) are established by adding the above.

[0170]

number

[0171]

number

[0172] Here, the volume average of the specific electric field and the equivalent specific electric field in the double inhomogeneous inclusion V1 is <E p > V1 , <E * > V1 is expressed by the following equation (83).

[0173]

number

[0174] Here, the relational expression (84) below is defined.

[0175]

number

[0176] Then, by substituting equations (83) and (84) into equations (81) and (82) and then taking the difference between the two, the equivalent equation for the difference, equation (85) below, is established.

[0177]

number

[0178] Also, solve the equivalent equation (85) and find the L of equations (84) and (85). S1 Substituting the above, the volume average of the sum of the specific electric field and the equivalent specific electric field is given by the following equation (86).

[0179]

number

[0180] Moreover, by multiplying both sides of equation (81) by f and multiplying both sides of equation (82) by 1-f, taking the sum of the two, and substituting the relational expressions of equations (83) and (84), we obtain the equivalent equation (87) below, which holds for the double heterogeneous inclusion V1.

[0181]

number

[0182] Here, by substituting the intrinsic electric field of equation (86) into equation (87), we obtain the average equivalent equation of equation (88) below.

[0183]

number

[0184] In addition, when the volume content of the double heterogeneous inclusions V1 relative to the first type mixed triple inclusions V2 is taken as f1, the relational expression (89) below is established.

[0185]

number

[0186] Moreover, the following relational expression (90) holds for the interaction electric flux density of the first type mixed triple inclusions V2.

[0187]

number

[0188] Then, by substituting equations (89) and (90) into the equivalent equation (88), the final equivalent equation for this model becomes equation (91) below.

[0189]

number

[0190] Then, by solving the equivalent equation (91), the equivalent specific electric field at the double inhomogeneous inclusion V1 is given by the following equation (92).

[0191]

number

[0192] In addition, the volume average of the equivalent specific electric field in the first type mixed triple inclusion V2 <E * > V2 + <E p > V2 is expressed by the following relational expression (93).

[0193]

number

[0194] The specific electric flux density in the first type mixed triple inclusion V2 is calculated by subtracting the electric flux density -(B V1 -B V2 ) <E pΓ2 > Γ2 By adding the term, the following relations are expressed by the following equations (94) to (96).

[0195]

number

[0196]

number

[0197]

number

[0198] Furthermore, the following relational expression (97) is obtained.

number

[0199] Therefore, the equivalent specific electric fields of the double heterogeneous inclusion V1 and the first type mixed triple inclusion V2 can be calculated using the results of the above-mentioned formulas (92) and (93), and the volume average of the specific electric flux densities generated in the heterogeneous inclusion Ω, the double heterogeneous inclusion V1, the region Γ1 of the first type mixed triple inclusion V2 other than the double heterogeneous inclusion V1, and the first type mixed triple inclusion V2 can be obtained from the calculated equivalent specific electric fields using the relational expressions (94) to (97). The interaction electric flux density can be obtained from the above-mentioned formula (90) using the specific electric flux density of the first type mixed triple inclusion V2.

[0200] Next, we will explain the case where a composite material can be approximated by the unidirectionally oriented double heterogeneous inclusion low-level cluster model described above. As shown in Figure 7, the unidirectional double heterogeneous inclusion low-level cluster model is a model in which multiple types of double heterogeneous inclusions V1(i) are oriented in one direction and gather together in the base material D to form a cluster V2(i), and double heterogeneous inclusions V1(0) are also present outside the cluster V2(i) in the base material D. In this unidirectional double heterogeneous inclusion low-level cluster model, the above-mentioned first type mixed triple inclusion can be regarded as the cluster V2(i), and the double heterogeneous inclusion inside the first type mixed triple inclusion can be regarded as the double heterogeneous inclusion V1(i) inside the cluster V2(i). Based on the above-mentioned formula (45-3), the final equivalent formula of this model is the following formula (98).

[0201]

number

[0202] Then, in the same manner as in deriving the relational expressions (46) to (51) from the expression (45-3), an expression for calculating the equivalent specific electric field and the specific electric flux density can be derived from the expression (98).

[0203] Therefore, the equivalent intrinsic electric field of the double heterogeneous inclusion V1(i) and the cluster V2(i) can be calculated using the aforementioned relational equation (98-1), and the volume average of the intrinsic electric flux density generated in the double heterogeneous inclusion V1(i) and the region Γ1(i) in the cluster V2(i) other than the double heterogeneous inclusion V1(i) and in the cluster V2(i) can be found from the equivalent intrinsic electric field calculated using the relational equation (98-1).

[0204] Furthermore, similarly to the above-mentioned equation (51-2), the interaction electric flux density is expressed by the relational expression shown in the following equation (98-2).

number

[0205] Next, we will explain the case where a composite material can be approximated by the above-mentioned unidirectionally oriented double heterogeneous inclusion high-level cluster model. The unidirectionally oriented double heterogeneous inclusion high-level cluster model is the above-mentioned unidirectionally oriented double heterogeneous inclusion low-level cluster model shown in Figure 7, with the double heterogeneous inclusion V1(0) outside the cluster V2(i) removed. In the formulas (98-1) and (98-2), (0) =0.

[0206] Next, we will explain the case where a composite material can be approximated by the multi-type dual inhomogeneous inclusion high-level cluster model described above. As shown in Figure 8(A), the multi-type dual inhomogeneous inclusion high-level cluster model is a cluster of multiple dual inhomogeneous inclusions V1(ijk) with different dielectric constants, specific electric fields, shapes, and orientation directions in a base material D, which are grouped together to form n inhomogeneous inclusions with different shapes and volume contents.V2 In this model, a cluster V2(i) of a certain type is formed. Here, j is an index indicating the dielectric constant, the specific electric field, and the shape, and n V1 There are three types, k is the index indicating the orientation angle, and n k The volume fraction of the double heterogeneous inclusion V1(ijk) is f total(ijk) Let the volume fraction of the region V1(ij) be f total(ij) , the volume fraction of all double inhomogeneous inclusions contained in cluster V2(i) is f total(i) Let the volume fraction of cluster V2(i) be f V2(i) , the volume fraction of all clusters V2(i) in the matrix D is f V2 Furthermore, the volume fraction of each double heterogeneous inclusion V1(ij) contained in cluster V2(i) is f1(ij). Here, the directions of the principal semi-axes of cluster V2(i) are all the same. The global coordinate system is G x, and the local coordinate system of the dual inhomogeneous inclusion V1(ijk) is L(k) x. In this cluster model, the above-mentioned first type mixed triple inclusion can be regarded as cluster V2(i), and the double heterogeneous inclusion inside the first type mixed triple inclusion can be regarded as double heterogeneous inclusion V1(ijk) contained inside cluster V2(i). Based on the above-mentioned equivalent equation (58), the final equivalent equation of this model is the following equation (99).

[0207]

number

[0208] Here, if the volume fraction of one region V1(ij) included in cluster V2(i) is f1(ij), the following formula (100) is derived based on the above formula (55).

[0209]

number

[0210] Moreover, based on the above-mentioned equation (88), the relational expression shown in the following equation (101) is derived.

[0211]

number

[0212] Therefore, the equivalent intrinsic electric field of the double heterogeneous inclusion V1(i) and cluster V2(i) can be calculated using the equivalent equation in (99) above, and the volume average of the intrinsic electric flux density generated in the double heterogeneous inclusion V1(i), the region Γ1(i) in cluster V2(i) other than the double heterogeneous inclusion V1(i), and cluster V2(i) can be obtained from the calculated equivalent intrinsic electric field. Furthermore, the volume average of the interacting electric flux density in the composite material can be obtained using the relation in (98-2).

[0213] Next, we will explain the case where a composite material can be approximated by the aforementioned multi-type dual inhomogeneous inclusion low-level cluster model. As shown in Figure 8(B), the multi-type dual inhomogeneous inclusion low-level cluster model is a cluster of multiple dual inhomogeneous inclusions V1(ijk) with different dielectric constants, specific electric fields, shapes, and orientation directions in a base material D, which are grouped together to form n inhomogeneous inclusions with different shapes and volume contents. V2 Here, we will explain a case where a cluster model is used in which two types of clusters V2(i) are formed and a double heterogeneous inclusion V1(0jk) is present outside the cluster V2(i) in the base material D. Here, the volume fraction of the double heterogeneous inclusion V1(0jk) is expressed as f (0jk) Let the volume fraction of the region V1(0j) be f (0j) Then, based on the above equation (64), the final equivalent equation of this model is the following equation (102).

[0214]

number

[0215] Here, for equation (102), by approximating that f1(ij) is sufficiently smaller than 1, we obtain from equation (100): L(k)H S2(ijk) ≒H V1(j) It becomes.

[0216] Furthermore, the relationship of the following formula (102-2) is defined.

number

[0217] In this case, the equivalent equation (102-2) L(k) H S2(ijk) ≒H V1(j) Substituting this into equation (102-2) and solving it, the equivalent specific electric field becomes the following equation (103).

[0218]

number

[0219] Moreover, the volume-averaged sum of the equivalent intrinsic electric field and the intrinsic electric field of the region V1(ij) is expressed by the relational expression (104) below.

[0220]

number

[0221] Then, by substituting equation (103) into equation (104), the following relational equation (105) is obtained.

[0222]

number

[0223] In addition, the following relational expression (106) holds for the volume average of the sum of the equivalent specific electric field and the specific electric field of all double heterogeneous inclusions included in cluster V2(i).

[0224]

number

[0225] In addition, the volume-averaged sum of the equivalent intrinsic electric field and the intrinsic electric field of the region V1(0j) distributed outside the cluster V2(i) in the base material D is given by the following relational expression (107) based on the above-mentioned expression (73).

[0226]

number

[0227] Regarding the specific electric flux density, the following relational expressions (108) to (110) are derived based on the above-mentioned expressions (74) to (76).

[0228]

number

[0229]

number

[0230]

number

[0231] And the interaction electric flux density D ~ From equations (106) to (110), the relation shown in equation (111) below is obtained.

[0232]

number

[0233] Therefore, the volume average of the equivalent intrinsic electric field and the sum of the intrinsic electric field of all double heterogeneous inclusions contained in the cluster V2(i) and the volume average of the equivalent intrinsic electric field and the sum of the intrinsic electric field of all regions V1(0j) distributed outside the cluster V2(i) in the base material D can be calculated using the above-mentioned relational expressions (106) and (107). Then, the volume average of the intrinsic electric flux density generated in each of the double heterogeneous inclusion V1(ijk) in the cluster V2(i), the region Γ2(i) other than the double heterogeneous inclusion V1(ijk) in the cluster V2(i), and the cluster V2(i) can be calculated from the calculated volume average of the equivalent intrinsic electric field and the sum of the intrinsic electric field using the above-mentioned relational expressions (108) to (110). Furthermore, the volume average of the interaction electric flux density generated in the composite material can be calculated using the relational expression (111).

[0234] In addition, the orientation angle distribution f total(ijk) / f total(ij) and the orientation angle distribution f of V1(0jk) (0jk) / f (0j) Once this is obtained, the orientation angle distribution coefficient can be calculated using the relationship between equations (105) and (107).

[0235] Here, the macroscopic total electric field, which represents the deformation of the entire composite material, G E - Since corresponds to the sum of the acting electric field acting on the entire composite material and the volume average of the equivalent intrinsic electric field and the sum of the intrinsic electric field, it is expressed by the following relational equation (111-2).

[0236]

number

[0237] The macroscopic dielectric constant of the composite material is e D- Then, the total macroscopic electric field G E - and the acting electric flux density G D 0 is expressed by the relational expression (78-2) above.

[0238] Substituting equations (106) and (107) into equation (111-2), and further substituting the interaction electric flux density D ~ Substituting this, we obtain the following relational equation (111-3).

number

[0239] Equating equation (78-2) and equation (111-3), the intrinsic electric field < G E p(i) > V2(i) and G E pΩ(0) > ΣV1(0)) If we set to 0, then from equations (105), (106), (107), (111-1), and (111-3), Σ A^ p = Σ P^ p = 0, and by further substituting these relationships, the macroscopic dielectric constant e D- is calculated, resulting in the following equation (111-4).

number

[0240] From equation (111-4), the macroscopic dielectric constant of this composite material model can be estimated.

[0241] Since the equivalent specific electric field, specific electric flux density, and interacting electric flux density have been obtained for all the models of double inhomogeneous inclusions described so far, the macroscopic dielectric constant can be estimated by following the same procedures as those described in paragraphs

[0244] to

[0247] .

[0242] Next, a composite material property estimation device according to the present embodiment will be described. The composite material property estimation device 1 according to the present embodiment is a device for estimating thermal and electromagnetic properties of a composite material including a base material D and a heterogeneous inclusion Ω embedded in the base material D. The composite material property estimation device 1 is, for example, a personal computer, and includes a CPU (Central Processing Unit) 101, a main memory 102, an auxiliary memory 103, a display unit 104, an input unit 105, and a bus 109 connecting these to each other, as shown in FIG. 9. The main memory 102 has a volatile memory such as a RAM (Random Access Memory) and is used as a working area for the CPU 101. The main memory 102 also has an image-only memory (not shown) for temporarily storing image information to be displayed on the display unit 104. The auxiliary memory 103 is a non-volatile memory such as a semiconductor flash memory, and stores programs for the CPU 101 to execute various processes for estimating the properties of the composite material. The display unit 104 is a display device such as a liquid crystal display, an organic EL (Electro-Luminescence) display, etc. The input unit 105 is an input device such as a keyboard.

[0243] 10, the CPU 101 loads the programs stored in the auxiliary storage unit 103 into the main storage unit 102 and executes them, thereby functioning as a permittivity acquisition unit 111, a volume content acquisition unit 117, an intrinsic electric field acquisition unit 115, an orientation angle distribution acquisition unit 121, a shape parameter acquisition unit 113, an Eshelby tensor generation unit 114, an action electric flux density, action electric field acquisition unit 116, an equivalent intrinsic electric field calculation unit 118, a thermal / electromagnetic property estimation unit 119, and an estimation result output unit 114. The auxiliary storage unit 103 also has a relational equation storage unit 131 that stores information indicating a relational equation for generating an Eshelby tensor from a shape parameter such as the inhomogeneous inclusion Ω, information indicating a relational equation for calculating the equivalent intrinsic electric field in each of the above-mentioned models, information indicating a relational equation for calculating the intrinsic electric flux density from the equivalent intrinsic electric field, information for calculating an interaction electric flux density from the intrinsic electric flux density, and information indicating a relational equation for estimating the thermal / electromagnetic properties of a composite material. Here, the thermal and electromagnetic properties of a composite material include the intrinsic electric flux density generated in the inhomogeneous inclusions and clusters that make up the composite material, the interactive electric flux density in the composite material, and the macroscopic dielectric constant of the entire composite material.

[0244] The permittivity acquisition unit 111 acquires a base material permittivity tensor indicating the permittivity of the base material D and a heterogeneous inclusion permittivity tensor indicating the permittivity of the heterogeneous inclusions, both of which are input by the user via the input unit 105, according to the model selected by the user. Here, when any of the first type mixed double inclusion model, the unidirectional orientation high-level cluster model, the unidirectional orientation low-level cluster model, the multi-kind high-level cluster model, and the multi-kind low-level cluster model is selected by the user, the permittivity acquisition unit 111 acquires the base material permittivity tensor of the base material D and the heterogeneous inclusion permittivity tensors of the mixed double inclusion V or the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), and Ω(0jk) in the clusters V and V(i). On the other hand, when any of the above-mentioned first type mixed triple inclusion model, unidirectionally oriented double inhomogeneous inclusion high-level cluster model, unidirectionally oriented double inhomogeneous inclusion low-level cluster model, multi-kind double inhomogeneous inclusion high-level cluster model, and multi-kind double inhomogeneous inclusion low-level cluster model is selected by the user, the permittivity acquisition unit 111 acquires the permittivity tensor of the base material D and the permittivity tensor of the mixed triple inclusion V2 or cluster V 2、 The first inhomogeneous inclusion permittivity tensor of the inhomogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk) in the double inhomogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk) in V2(i) and the mixed triple inclusion V2 or cluster V 2、 The second inhomogeneous inclusion permittivity tensor of the inhomogeneous inclusions Γ, Γ(i), Γ(0), Γ(ijk), Γ(0jk) outside the inhomogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk) in the double inhomogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk) in V2(i), and

[0245] When the user selects any one of the above-mentioned first type mixed double inclusion model, unidirectional orientation high-level cluster model, unidirectional orientation low-level cluster model, multi-kind high-level cluster model, and multi-kind low-level cluster model, the shape parameter acquisition unit 113 acquires shape parameters indicating the shape of the mixed double inclusion V or cluster V, V(i) and shape parameters indicating the shapes of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), and Ω(0jk) in the mixed double inclusion V or cluster V, V(i) in accordance with the model selected by the user. On the other hand, when the user selects any one of the above-mentioned first type mixed triple inclusion model, unidirectional orientation double heterogeneous inclusion high-level cluster model, unidirectional orientation double heterogeneous inclusion low-level cluster model, multi-kind double heterogeneous inclusion high-level cluster model, and multi-kind double heterogeneous inclusion low-level cluster model, the shape parameter acquisition unit 113 acquires shape parameters indicating the shape of the mixed triple inclusion V2 or cluster V 2、 The shape parameters of V2(i) and V2(i) are the shape of the mixed triple inclusion V2 or cluster V 2、The shape parameters of the double heterogeneous inclusions V1, V1(i), V1(0), V1(ijk), and V1(0jk) in V2(i) and the shape parameters of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), and Ω(0jk) in the double heterogeneous inclusions V1, V1(i), V1(0), V1(ijk), and V1(0jk) are obtained. The shape parameters indicate the aspect ratios, which are the ratios of the lengths of the remaining two principal semi-axes to the principal semi-axes with the intermediate length among the three principal semi-axes, when the heterogeneous inclusion Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusion V, V1, V1(i), V1(0), V1(ijk), V1(0jk), clusters V, V(i), V2, V2(i), mixed double inclusion V, and mixed triple inclusion V2 are approximated by ellipsoids. When the above-mentioned first type mixed double inclusion model is selected by the user, the shape parameter acquisition unit 113 acquires heterogeneous inclusion shape parameters indicating the shape of the heterogeneous inclusion Ω and double inclusion shape parameters indicating the shape of the mixed double inclusion V. Furthermore, when the user selects the above-mentioned unidirectional orientation high-level cluster model, unidirectional orientation low-level cluster model, multiple-kind high-level cluster model or multiple-kind low-level cluster model, the shape parameter acquisition unit 113 acquires heterogeneous inclusion shape parameters indicating the shapes of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk) and Ω(0jk) and cluster shape parameters indicating the shapes of the clusters V and V(i). Furthermore, when the user selects the first type mixed triple inclusion model, the shape parameter acquisition unit 113 acquires heterogeneous inclusion shape parameters indicating the shape of the heterogeneous inclusion Ω, double heterogeneous inclusion shape parameters indicating the shape of the double heterogeneous inclusion V1 and triple inclusion shape parameters indicating the shape of the mixed triple inclusion V2.In addition, when the unidirectional double heterogeneous inclusion high-level cluster model, the unidirectional double heterogeneous inclusion low-level cluster model, the many-types double heterogeneous inclusion high-level cluster model or the many-types double heterogeneous inclusion low-level cluster model is selected by the user, the shape parameter acquisition unit 113 acquires heterogeneous inclusion shape parameters indicating the shapes of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusion shape parameters indicating the shapes of the double heterogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk), and cluster shape parameters indicating the shapes of the clusters V2, V2(i).

[0246] The volume content acquisition unit 117 acquires the volume content of the heterogeneous inclusions according to the model selected by the user. When the above-mentioned first type mixed double inclusion model is selected by the user, the volume content acquisition unit 117 acquires the volume content of the heterogeneous inclusion Ω in the double inclusion V and the double inclusion volume content which is the volume content of the double inclusion V in the composite material. When the above-mentioned unidirectional orientation high level cluster model is selected by the user, the volume content acquisition unit 117 acquires the heterogeneous inclusion volume content which is the volume content of one heterogeneous inclusion Ω(i) in the cluster V(i), the intra-cluster heterogeneous inclusion total volume content which is the volume content of all heterogeneous inclusions Ω(i) included in the cluster in the cluster V(i), and the cluster volume content which is the volume content of the cluster in the composite material. Furthermore, when the above-mentioned unidirectionally oriented low-level cluster model is selected by the user, the volume content acquisition unit 117 acquires the heterogeneous inclusion volume content, which is the volume content of one heterogeneous inclusion Ω(i) in the cluster V(i), the total intra-cluster heterogeneous inclusion volume content, which is the volume content in the cluster V(i) of all heterogeneous inclusions Ω(i) contained in the cluster V(i), the total extra-cluster heterogeneous inclusion volume content, which is the volume content in the composite material of all heterogeneous inclusions Ω(0) contained in the outer region of the cluster of the composite material, and the cluster volume content, which is the volume content of the cluster V in the composite material. Furthermore, when the multiple-type high-level cluster model described above is selected by the user, the volume content acquisition unit 117 acquires a heterogeneous inclusion volume content which is the volume content of each of the multiple types of heterogeneous inclusions Ω(ijk) in the cluster V(i), a total volume content of heterogeneous inclusions in a cluster which is the volume content of the heterogeneous inclusions Ω(ijk) in the cluster V(i) for each of the multiple types of heterogeneous inclusions Ω(ijk) included in the cluster V(i), and a cluster volume content which is the volume content of the cluster V(i) in the composite material.Furthermore, when the multiple-type low-level cluster model described above is selected by the user, the volume content acquisition unit 117 acquires a heterogeneous inclusion volume content which is the volume content of each of the multiple types of heterogeneous inclusions Ω(ijk) in the cluster V(i), a total intra-cluster volume content which is the volume content in the cluster V(i) of all the heterogeneous inclusions Ω(ijk) included in the cluster V(i) for each of the multiple types of heterogeneous inclusions Ω(ijk) included in the cluster V(i), a total extra-cluster volume content which is the volume content of all the heterogeneous inclusions Ω(0jk) included in the region outside the cluster V(i) of the composite material, and a cluster volume content which is the volume content of the cluster V(i) in the composite material.

[0247] In addition, when the user selects the above-mentioned first type mixed triple inclusion model, the volume content acquisition unit 117 acquires a first heterogeneous inclusion volume content which is the volume content of the heterogeneous inclusion Ω in the double heterogeneous inclusion V1, a double heterogeneous inclusion volume content which is the volume content of the double heterogeneous inclusion V1 contained in the mixed triple inclusion V2, and a mixed triple inclusion volume content which is the volume content of the mixed triple inclusion V2 in the composite material. Furthermore, when the above-mentioned unidirectional double heterogeneous inclusion high-level cluster model is selected by the user, the volume content acquisition unit 117 acquires a first heterogeneous inclusion volume content which is the volume content of the heterogeneous inclusion Ω(i) in the double heterogeneous inclusion V1(i), a double heterogeneous inclusion volume content which is the volume content of one double heterogeneous inclusion V1(i) in the cluster V2(i), a total volume content of double heterogeneous inclusions within a cluster which is the volume content in the cluster V2 of all double heterogeneous inclusions V1(i) included in the cluster V2(i), and a cluster volume content which is the volume content of the cluster V2 in the composite material. Furthermore, when the above-mentioned unidirectional double heterogeneous inclusion low-level cluster model is selected by the user, the volume content acquisition unit 117 acquires a first heterogeneous inclusion volume content which is the volume content of the heterogeneous inclusion Ω(i) in the double heterogeneous inclusion V1(i), a double heterogeneous inclusion volume content which is the volume content of one double heterogeneous inclusion V1(i) in the cluster V2(i), a total double heterogeneous inclusion volume content within the cluster which is the volume content in the cluster V2 of all double heterogeneous inclusions V1(i) included in the cluster V2(i), a total double heterogeneous inclusion volume content outside the cluster which is the volume content in the composite material of all double heterogeneous inclusions V1(0) included in the region outside the cluster V2 of the composite material, and a cluster volume content which is the volume content of the cluster V2 in the composite material.In addition, when the above-mentioned multiple-type double heterogeneous inclusion high-level cluster model is selected by the user, the volume content acquisition unit 117 acquires a first heterogeneous inclusion volume content which is the volume content of the heterogeneous inclusion Ω(ijk) in each of the multiple types of double heterogeneous inclusions V1(ijk), a double heterogeneous inclusion volume content which is the volume content of one double heterogeneous inclusion V1(ijk) in each of the multiple types of double heterogeneous inclusions V1(ijk) in the cluster V2(i), a total volume content of double heterogeneous inclusions in a cluster which is the volume content in the cluster V2 of all double heterogeneous inclusions V1(i) included in the cluster V2(i), and a cluster volume content which is the volume content of the cluster V2(i) in the composite material. Furthermore, when the above-mentioned multi-type dual heterogeneous inclusion low-level cluster model is selected by the user, the volume content acquisition unit 117 acquires a first heterogeneous inclusion volume content, which is the volume content of a heterogeneous inclusion Ω(ijk) in each of the multiple types of dual heterogeneous inclusions V1(ijk), and a dual heterogeneous inclusion volume content, which is the volume content of one dual heterogeneous inclusion V1(ijk) in each of the multiple types of dual heterogeneous inclusions V1(ijk) in the cluster V2(i). the total volume content of double heterogeneous inclusions within the cluster, which is the volume content in the cluster V2 of all double heterogeneous inclusions V1(i) contained in the cluster V2(i); the total volume content of double heterogeneous inclusions outside the cluster, which is the volume content in the composite material of all of the multiple types of double heterogeneous inclusions V1(0jk) contained in the region outside the cluster V2(i) of the composite material; and the cluster volume content, which is the volume content of the cluster V2(i) in the composite material.

[0248] The intrinsic electric field acquiring unit 115 acquires an intrinsic electric field vector indicating the intrinsic electric field in a heterogeneous inclusion or cluster input by the user via the input unit 105 according to the model selected by the user. When the first type mixed double inclusion model is selected by the user, the intrinsic electric field acquiring unit 115 acquires an intrinsic electric field vector indicating the intrinsic electric field in a heterogeneous inclusion Ω input by the user via the input unit 105, and an intrinsic electric field vector indicating the intrinsic electric field of a region Γ other than the heterogeneous inclusion Ω in the mixed double inclusion V. Furthermore, when the unidirectional orientation high-level cluster model, the unidirectional orientation low-level cluster model, the multiple-type high-level cluster model, or the multiple-type low-level cluster model is selected by the user, the intrinsic electric field acquiring unit 115 acquires an intrinsic electric field vector indicating the intrinsic electric field in the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), and Ω(0jk) input by the user via the input unit 105. Furthermore, when the first type mixed triple inclusion model is selected by the user, the intrinsic electric field acquisition unit 115 acquires an intrinsic electric field vector indicating the intrinsic electric field in the heterogeneous inclusion Ω, an intrinsic electric field vector indicating the intrinsic electric field in the heterogeneous inclusion Γ1, and an intrinsic electric field vector indicating the intrinsic electric field of the region Γ2 in the mixed triple inclusion V2 other than the double heterogeneous inclusion V1, all of which have been input by the user via the input unit 105. Furthermore, when the unidirectional double heterogeneous inclusion high-level cluster model, the unidirectional double heterogeneous inclusion low-level cluster model, the multi-kind double heterogeneous inclusion high-level cluster model, or the multi-kind double heterogeneous inclusion low-level cluster model has been selected by the user, the intrinsic electric field acquisition unit 115 acquires an intrinsic electric field vector indicating the intrinsic electric field in the heterogeneous inclusion Ω, all of which have been input by the user via the input unit 105. and an intrinsic electric field vector indicating the intrinsic electric field in the regions Γ, Γ(i), Γ(0), Γ(ijk), Γ(0jk) other than the inhomogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk) in the double inhomogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk).

[0249] The Eshelby tensor generation unit 114 generates Eshelby tensors for each of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusions V, V1, V1(i), V1(0), V1(ijk), V1(0jk), clusters V, V(i), V2, V2(i), mixed double inclusion V, and mixed triple inclusion V2 when they are approximated by ellipsoids, based on the shape parameters acquired by the shape parameter acquisition unit 113 and the volume contents acquired by the volume content acquisition unit 117 in accordance with the model selected by the user. Here, the Eshelby tensor is expressed as a function with the shape factors of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusions V, V1, V1(i), V1(0), V1(ijk), V1(0jk), clusters V, V(i), V2, V2(i), mixed double inclusion V, and mixed triple inclusion V2 as arguments, and is expressed as a function of the above-mentioned aspect ratio. When the above-mentioned first type mixed double inclusion model is selected by a user, the Eshelby tensor generating unit 114 calculates the heterogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the heterogeneous inclusion Ω, based on the shape parameters of the heterogeneous inclusion Ω, and calculates the double inclusion Eshelby tensor, which is the Eshelby tensor of the double inclusion V, based on the shape parameters of the mixed double inclusion V. Furthermore, when the above-mentioned unidirectional heterogeneous inclusion high-level cluster model, unidirectional heterogeneous inclusion low-level cluster model, multi-type heterogeneous inclusion high-level cluster model or multi-type heterogeneous inclusion low-level cluster model is selected by the user, the Eshelby tensor generation unit 114 calculates the heterogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), and the cluster Eshelby tensor, which is the Eshelby tensor of the clusters V and V(i), based on the shape parameters of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), the shape parameters of the clusters V and V(i), and the volume content acquired by the volume content acquisition unit 117.Furthermore, when the above-mentioned first type mixed triple inclusion model is selected by the user, the Eshelby tensor generating unit 114 calculates the heterogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the heterogeneous inclusion Ω, based on the shape parameters of the heterogeneous inclusion Ω, calculates the double heterogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the double heterogeneous inclusion V1, based on the shape parameters of the double heterogeneous inclusion V1, and also calculates the triple inclusion Eshelby tensor, which is the Eshelby tensor of the mixed triple inclusion V2, based on the shape parameters of the mixed triple inclusion V2. Furthermore, when the above-mentioned unidirectional dual heterogeneous inclusion high-level cluster model, unidirectional dual heterogeneous inclusion low-level cluster model, multi-kind dual heterogeneous inclusion high-level cluster model or multi-kind dual heterogeneous inclusion low-level cluster model is selected by the user, the Eshelby tensor generation unit 114 generates the Eshelby tensor of the inhomogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk) based on the shape parameters of the inhomogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk) and the volume fractions acquired by the volume fraction acquisition unit 117. The Eshelby tensor of the double inhomogeneous inclusions V1, V1(i), V1(0), V1(ijk), and V1(0jk) is calculated based on the shape parameters of the double inhomogeneous inclusions V1, V1(i), V1(0), V1(ijk), and V1(0jk), and the cluster Eshelby tensor of the clusters V2 and V2(i) is calculated based on the shape parameters of the clusters V2 and V2(i).

[0250] The action electric flux density electric field acquisition unit 116 acquires an action electric flux density vector indicating the electric flux density when a preset electric flux density is applied to the composite material input by the user via the input unit 105, and an action electric field vector indicating the electric field of the composite material when the electric flux density is applied to the composite material.

[0251] The orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of the heterogeneous inclusions according to the model selected by the user, and calculates the orientation angle coefficient. When the above-mentioned multi-type heterogeneous inclusion high-level cluster model is selected by the user, the orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of each of the multiple types of heterogeneous inclusions in the cluster, and calculates the orientation angle distribution coefficient of the heterogeneous inclusions in the cluster, which indicates the orientation angle distribution of the multiple types of heterogeneous inclusions in the cluster. When the above-mentioned multi-type heterogeneous inclusion low-level cluster model is selected by the user, the orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of each of the multiple types of heterogeneous inclusions in the cluster and outside the cluster, and calculates the orientation angle distribution coefficient of the heterogeneous inclusions in the cluster, which indicates the orientation angle distribution of the multiple types of heterogeneous inclusions in the cluster, and the orientation angle distribution coefficient of the heterogeneous inclusions outside the cluster, which indicates the orientation angle distribution of the multiple types of heterogeneous inclusions outside the cluster. Furthermore, when the user selects the above-mentioned multi-type dual heterogeneous inclusion high-level cluster model, the orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of each of the multiple types of dual heterogeneous inclusions in the cluster, and calculates the orientation angle distribution coefficient of the dual heterogeneous inclusions in the cluster, which indicates the orientation angle distribution of the multiple types of dual heterogeneous inclusions in the cluster. Furthermore, when the user selects the above-mentioned multi-type dual heterogeneous inclusion low-level cluster model, the orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of each of the multiple types of dual heterogeneous inclusions in the cluster and outside the cluster, and calculates the orientation angle distribution coefficient of the dual heterogeneous inclusions in the cluster, which indicates the orientation angle distribution of the multiple types of dual heterogeneous inclusions in the cluster, and the orientation angle distribution coefficient of the dual heterogeneous inclusions outside the cluster, which indicates the orientation angle distribution of the multiple types of dual heterogeneous inclusions outside the cluster.

[0252] The equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field caused by the difference in the dielectric constant between the base material D and the inhomogeneous inclusion, using the relational equation stored in the calculation equation storage unit 131 according to the model selected by the user. When the above-mentioned first type mixed double inclusion model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates the equivalent intrinsic electric field vector based on the base material dielectric constant tensor, the dielectric constant tensor of the inhomogeneous inclusion Ω, the inhomogeneous inclusion Eshelby tensor of the inhomogeneous inclusion Ω, the double inclusion Eshelby tensor of the mixed double inclusion V, the intrinsic electric field vector of the inhomogeneous inclusion Ω, the intrinsic electric field vector of the Γ region other than the inhomogeneous inclusion Ω in the double inclusion V, the action electric flux density vector, the action electric field vector, the volume content of the inhomogeneous inclusion Ω in the mixed double inclusion V, and the volume content of the mixed double inclusion V. Furthermore, when the above-mentioned unidirectionally oriented high-level cluster model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in cluster V based on the matrix permittivity tensor, the inhomogeneous inclusion permittivity tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω(i), the action electric flux density vector, the action electric field vector, the above-mentioned inhomogeneous inclusion volume content, the total inhomogeneous inclusion volume content, and the cluster volume content. Furthermore, when the above-mentioned unidirectionally oriented low-level cluster model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in cluster V(i) based on the matrix dielectric constant tensor, the inhomogeneous inclusion dielectric constant tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω(i), the action electric flux density vector, the action electric field vector, the inhomogeneous inclusion volume content, the total volume content of inhomogeneous inclusions within the cluster, the total volume content of inhomogeneous inclusions outside the cluster, and the cluster volume content.Furthermore, when the aforementioned multiple types high-level cluster model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in cluster V(i) based on the matrix permittivity tensor, the intrinsic inclusion permittivity tensor, the intrinsic inclusion Eshelby tensor, the cluster Eshelby tensor, the intrinsic electric field vector of the intrinsic inclusion Ω(ijk), the action electric flux density vector, the action electric field vector, the intrinsic inclusion volume content, the total volume content and cluster volume content of the intrinsic inclusions, and the orientation angle distribution coefficient of the intrinsic inclusions in the cluster V(i). Furthermore, when the above-mentioned multiple types low-level cluster model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in cluster V(i) based on the matrix dielectric constant tensor, the intrinsic inclusion dielectric constant tensor, the intrinsic inclusion Eshelby tensor, the cluster Eshelby tensor, the intrinsic electric field vector of the intrinsic inclusion Ω(ijk), the action electric flux density vector, the action electric field vector, the intrinsic inclusion volume content, the total volume content of the intrinsic inclusions in the cluster, the total volume content and cluster volume content of the intrinsic inclusions outside the cluster, the orientation angle distribution coefficient of the intrinsic inclusions in the cluster, and the orientation angle distribution coefficient of the intrinsic inclusions outside the cluster.

[0253] Furthermore, when the above-mentioned first type mixed triple inclusion model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the triple inclusion V2 based on the matrix dielectric constant tensor, the first inhomogeneous inclusion dielectric constant tensor, the second inhomogeneous inclusion dielectric constant tensor, the inhomogeneous inclusion Eshelby tensor, the double inhomogeneous inclusion Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω, the intrinsic electric field vector of the region Γ other than Ω of the double inhomogeneous inclusion V1, the intrinsic electric field vector of the region Γ2 other than the double inhomogeneous inclusion in the mixed triple inclusion V2, the action electric flux density vector, the action electric field vector, and the first inhomogeneous inclusion volume content, the double inhomogeneous inclusion volume content and the mixed triple inclusion volume content. Furthermore, when the user selects the above-mentioned unidirectionally oriented double inhomogeneous inclusion high-level cluster model, the equivalent intrinsic electric field calculation unit 118 calculates the dielectric constant tensor of the base material, the dielectric constant tensor of the first inhomogeneous inclusion, the dielectric constant tensor of the second inhomogeneous inclusion, the Eshelby tensor of the first inhomogeneous inclusion, the Eshelby tensor of the double inhomogeneous inclusion, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω, the dielectric constant tensor of the double inhomogeneous inclusion V1(i), A first equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the double heterogeneous inclusion V1(i) and a second equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the cluster V2(i) are calculated based on the intrinsic electric field vector, the acting electric flux density vector, the acting electric field vector, the volume content of the first intrinsic inclusion, the volume content of the double intrinsic inclusion, the total volume content of the double intrinsic inclusion in the cluster, and the cluster volume content of the region Γ(i) other than (i).Furthermore, when the user selects the above-mentioned unidirectionally oriented double inhomogeneous inclusion low-level cluster model, the equivalent intrinsic electric field calculation unit 118 calculates the dielectric constant tensor of the base material, the dielectric constant tensor of the first inhomogeneous inclusion, the dielectric constant tensor of the second inhomogeneous inclusion, the Eshelby tensor of the first inhomogeneous inclusion, the Eshelby tensor of the double inhomogeneous inclusion, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω, the region Γ(i) other than Ω(i) in the double inhomogeneous inclusion V1(i), ), a first equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the double heterogeneous inclusion V1(i) and a second equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the cluster V2(i) are calculated based on the intrinsic electric field vector, the acting electric flux density vector, the acting electric field vector, the volume content of the first intrinsic inclusion, the volume content of the double intrinsic inclusion, the total volume content of the double intrinsic inclusion within the cluster, the total volume content of the double intrinsic inclusion outside the cluster, and the cluster volume content. Furthermore, when the user has selected the above-mentioned multi-type double inhomogeneous inclusion high-level cluster model, the equivalent intrinsic electric field calculation unit 118 calculates the dielectric constant tensor of the base material, the dielectric constant tensor of the first inhomogeneous inclusion, the dielectric constant tensor of the second inhomogeneous inclusion, the Eshelby tensor of the first inhomogeneous inclusion, the Eshelby tensor of the double inhomogeneous inclusion, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω(ijk), the region Γ other than Ω(ijk) in the double inhomogeneous inclusion V1(ijk), A first equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the double heterogeneous inclusion V1(ijk) and a second equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the cluster V2(i) are calculated based on the intrinsic electric field vector, the acting electric flux density vector, the acting electric field vector, the volume content of the first intrinsic inclusion, the volume content of the double intrinsic inclusion, the total volume content and cluster volume content of the double intrinsic inclusion in the cluster, and the orientation angle distribution coefficient of the double intrinsic inclusion in the cluster (i).Furthermore, when the above-mentioned multi-type double inhomogeneous inclusion low-level cluster model is selected by the user, the equivalent intrinsic electric field calculation unit 118 calculates the dielectric constant tensor of the base material, the dielectric constant tensor of the first inhomogeneous inclusion, the dielectric constant tensor of the second inhomogeneous inclusion, the Eshelby tensor of the first inhomogeneous inclusion, the Eshelby tensor of the double inhomogeneous inclusion, the cluster Eshelby tensor, the intrinsic electric field vector of the inhomogeneous inclusion Ω(ijk), the intrinsic electric field vector of the region Γ(i) other than Ω(ijk) in the double inhomogeneous inclusion V1(ijk), the acting electric flux density vector, The first equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the double-heterogeneous inclusion V1(ijk) and the second equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the cluster V2(i) are calculated based on the vector, the acting electric field vector, the volume content of the first intrinsic inclusion, the volume content of the double-heterogeneous inclusion, the total volume content of the double-heterogeneous inclusion within the cluster, the total volume content and cluster volume content of the double-heterogeneous inclusion outside the cluster, the orientation angle distribution coefficient of the double-heterogeneous inclusion within the cluster, and the orientation angle distribution coefficient of the double-heterogeneous inclusion outside the cluster.

[0254] The thermal / electromagnetic property estimation unit 119 estimates the thermal / electromagnetic property of the composite material by using the relational expression stored in the calculation formula storage unit 131 and the calculated equivalent intrinsic electric field vector. Specifically, when the above-mentioned first type mixed double inclusion model is selected by the user, the thermal / electromagnetic property estimation unit 119 estimates at least one of the following by using the above-mentioned relational expression and the equivalent intrinsic electric field vector: a mixed double inclusion intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the mixed double inclusion V, an intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the heterogeneous inclusion Ω, an interactive electric flux density occurring in the entire composite material, and a macroscopic dielectric constant tensor indicating the macroscopic dielectric constant of the entire composite material. Furthermore, when the unidirectionally oriented high-level cluster model, the unidirectionally oriented low-level cluster model, the multiple-kind high-level cluster model, or the multiple-kind low-level cluster model is selected by the user, the thermal / electromagnetic property estimation unit 119 uses the relational expression and the equivalent intrinsic electric field vector described above to estimate at least one of the following: a cluster intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the cluster V(i); an intrinsic electric flux density vector inside the inhomogeneous inclusion indicating the volume average of the intrinsic electric flux density in the inhomogeneous inclusions Ω(i), Ω(0), Ω(ijk), and Ω(0ij); an intrinsic electric flux density vector outside the inhomogeneous inclusion indicating the volume average of the intrinsic electric flux density of the region Γ(i) other than the inhomogeneous inclusions Ω(i), Ω(ijk) in the clusters V and V(i); an interaction electric flux density occurring in the entire composite material; and a macroscopic dielectric constant tensor indicating the macroscopic dielectric constant of the entire composite material.Furthermore, when the above-mentioned first type mixed triple inclusion model is selected by the user, the thermal / electromagnetic property estimation unit 119 uses the above-mentioned relational expression and the above-mentioned first equivalent intrinsic electric field vector and the above-mentioned second equivalent intrinsic electric field vector to calculate a mixed triple inclusion intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the mixed triple inclusion V2, a double intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the double intrinsic inclusion V1, and a intrinsic electric flux density vector in the intrinsic electric flux density ... at least one of the following is estimated: a specific electric flux density vector inside the inhomogeneous inclusion indicating the volume average of the specific electric flux density of the inhomogeneous inclusion Ω; a specific electric flux density vector outside the inhomogeneous inclusion indicating the volume average of the specific electric flux density of the region other than the inhomogeneous inclusion Ω in the double inhomogeneous inclusion V1; a specific electric flux density vector outside the inhomogeneous inclusion indicating the volume average of the specific electric flux density of the region Γ2 in the triple inclusion V2 other than the double inhomogeneous inclusion V1; an interaction electric flux density occurring in the entire composite material; and a macroscopic dielectric constant tensor indicating the macroscopic dielectric constant of the entire composite material.Furthermore, when the above-mentioned unidirectionally oriented double inhomogeneous inclusion high-level cluster model, unidirectionally oriented double inhomogeneous inclusion low-level cluster model, multi-kind double inhomogeneous inclusion high-level cluster model, or multi-kind double inhomogeneous inclusion low-level cluster model is selected by the user, the thermal / electromagnetic property estimation unit 119 uses the above-mentioned relational expression and the above-mentioned first equivalent intrinsic electric field vector and the second equivalent intrinsic electric field vector to derive a cluster intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density in the cluster V2(i), a double inhomogeneous inclusion intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux densities in the double inhomogeneous inclusions V1(i), V1(0), V1(ijk), and V1(0jk), and a vector intrinsic electric flux density vector in the double inhomogeneous inclusions V1(i), V1(0), V1(ijk), and V1(0jk), at least one of the following is estimated: an intrinsic electric flux density vector within a heterogeneous inclusion indicating the volume average of the intrinsic electric flux density within the intrinsic electric flux density within the intrinsic inclusions Ω(i), Ω(0), Ω(ijk), Ω(0jk) within the double inhomogeneous inclusions V1(i), V1(0), V1(ijk), V1(0jk); an intrinsic electric flux density vector indicating the volume average of the intrinsic electric flux density within the regions other than the intrinsic electric flux density within the double inhomogeneous inclusions V1(i), V1(0), V1(ijk), V1(0jk); an intrinsic electric flux density vector outside the inhomogeneous inclusion indicating the volume average of the intrinsic electric flux density within the region Γ(i) within the cluster V2(i) other than the double inhomogeneous inclusions V1(i) and V1(ijk); an interaction electric flux density occurring in the entire composite material; and a macroscopic permittivity tensor indicating the macroscopic permittivity of the entire composite material.

[0255] The estimation result output unit 120 generates information indicating the properties of the composite material estimated by the thermal / electromagnetic property estimation unit 119 and causes the display unit 104 to display the information.

[0256] Next, the composite material property value evaluation process executed by the calculation processing unit 101 according to this embodiment will be described with reference to Fig. 11. First, the permittivity acquisition unit 111, the shape parameter acquisition unit 113, the Eshelby tensor generation unit 114, the intrinsic electric field acquisition unit 115, the acting electric flux density electric field acquisition unit 116, the volume content acquisition unit 117, the equivalent intrinsic electric field calculation unit 118, and the thermal / electromagnetic property estimation unit 119 identify a model selected by a user (step S1). Specifically, they identify which of the above-mentioned first type mixed double inclusion model, unidirectional orientation high-level cluster model, unidirectional orientation low-level cluster model, multi-type high-level cluster model, multi-type low-level cluster model, first type mixed triple inclusion model, unidirectional orientation double heterogeneous inclusion high-level cluster model, unidirectional orientation double heterogeneous inclusion low-level cluster model, multi-type double heterogeneous inclusion high-level cluster model, and multi-type double heterogeneous inclusion low-level cluster model has been selected.

[0257] Next, the dielectric constant acquisition unit 111 acquires a base material dielectric constant tensor indicating the dielectric constant of the base material D input by the user via the input unit 105, and a non-homogeneous inclusion dielectric constant tensor indicating the dielectric constant of the non-homogeneous inclusion, according to the model selected by the user (step S2).

[0258] Next, the shape parameter acquisition unit 113 acquires shape parameters indicating the shapes of the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk), clusters V, V(i), V2, V2(i), mixed double inclusion V, and mixed triple inclusion V2 according to the model selected by the user (step S3).

[0259] Thereafter, the volume content acquisition unit 117 acquires the volume content of the inhomogeneous inclusions according to the model selected by the user (step S4).

[0260] Next, the intrinsic electric field acquisition unit 115 acquires intrinsic electric field vectors indicating the intrinsic electric field generated in the regions Γ1, Γ1(i), Γ1(0), Γ1(ijk), Γ1(0jk) other than the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), in the double heterogeneous inclusions V, V1, V1(i), V1(0), V1(ijk), V1(0jk), and V1(0jk), in the region Γ other than the heterogeneous inclusion Ω in the mixed double inclusion V, and in the region Γ2 other than the double heterogeneous inclusion V1 in the mixed triple inclusion V2, which have been input by the user via the input unit 105 (step S5).

[0261] Next, the Eshelby tensor generation unit 114 generates Eshelby tensors for the heterogeneous inclusions Ω, Ω(i), Ω(0), Ω(ijk), Ω(0jk), double heterogeneous inclusions V1, V1(i), V1(0), V1(ijk), V1(0jk), clusters V, V(i), V2, V2(i), mixed double inclusion V, and mixed triple inclusion V2 based on the shape parameters acquired by the shape parameter acquisition unit 113 and the volume contents acquired by the volume content acquisition unit 117 in accordance with the model selected by the user (step S6).

[0262] Thereafter, the action electric flux density electric field acquisition unit 116 acquires an action electric flux density vector indicating the electric flux density when a preset electric flux density is applied to the composite material input by the user via the input unit 105, and an action electric field vector indicating the electric field of the composite material when the electric flux density is applied to the composite material (step S7).

[0263] Next, the orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit 121 acquires the orientation angle distribution of the inhomogeneous inclusions according to the model selected by the user, and calculates the orientation angle distribution coefficient of the inhomogeneous inclusions (step S8).

[0264] Next, the equivalent intrinsic electric field calculation unit 118 calculates the aforementioned equivalent intrinsic electric field vector or the first equivalent intrinsic electric field vector and the second equivalent intrinsic electric field vector using the relational equation stored in the calculation formula storage unit 131 according to the model selected by the user (step S9).

[0265] Thereafter, the thermal / electromagnetic property estimation unit 119 estimates the thermal / electromagnetic properties of the composite material using the relational equation stored in the calculation formula storage unit 131 and the calculated equivalent eigenelectric field vector or the first equivalent eigenelectric field vector and the second equivalent eigenelectric field vector (step S10).

[0266] Next, the estimation result output unit 120 generates display information indicating the thermal and electromagnetic properties of the composite material estimated by the thermal and electromagnetic property estimation unit 119, and outputs the display information to the display unit 104 (step S11).

[0267] As described above, according to the composite material property estimation method and the composite material property estimation device 100 of the present embodiment, an equivalent intrinsic electric field vector indicating the volume average of the equivalent intrinsic electric field in the first inhomogeneous inclusion and the cluster is calculated based on the base material permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, and the volume fraction. Then, the calculated equivalent intrinsic electric field vector is used to estimate the thermal and electromagnetic properties of the composite material. The estimation result includes the volume fraction of the first inhomogeneous inclusion in the cluster, and by combining the size of the volume fraction with the effect of the local uneven distribution of the first inhomogeneous inclusion, the thermal and electromagnetic properties of the composite material can be estimated using a model that is closer to the actual state of the composite material in which the first inhomogeneous inclusions are dispersed in the base material, thereby improving the estimation accuracy of the thermal and electromagnetic properties of the composite material.

[0268] Although the embodiments of the present invention have been described above, the present invention is not limited to the configurations of the above-mentioned embodiments. For example, the model representing the composite material may be fixed to any one of the first type mixed double inclusion model, unidirectional orientation high level cluster model, unidirectional orientation low level cluster model, multi-type high level cluster model, multi-type low level cluster model, first type mixed triple inclusion model, unidirectional orientation double heterogeneous inclusion high level cluster model, unidirectional orientation double heterogeneous inclusion low level cluster model, multi-type double heterogeneous inclusion high level cluster model, and multi-type double heterogeneous inclusion low level cluster model.

[0269] In addition, the various functions of the composite material property estimation apparatus 1 according to the present invention may be realized by software, firmware, or a combination of software and firmware. In this case, the software or firmware is written as a program and stored in the storage unit 32. In addition, the various functions of the control units 20, 2020, 3020 and the analysis units 30, 2030, 3030 according to the present invention can be realized by using a computer system, not a dedicated system. For example, a program for executing the above-mentioned operations may be stored in a non-transitory recording medium (flexible disk, CD-ROM (Compact Disc Read-Only Memory), DVD (Digital Versatile Disc), MO (Magneto-Optical Disc), etc.) that can be read by a computer system and distributed to a computer connected to a network, and the program may be installed in the computer system to configure the composite material property estimation apparatus 1 that executes the above-mentioned processing.

[0270] The method of providing the program to the computer is arbitrary. For example, the program may be uploaded to a server on a communication line and distributed to the computer via the communication line. The computer then starts up the program and executes it under the control of an OS (Operating System) in the same way as other applications. In this way, the computer functions as a composite material property estimation apparatus 1 that executes the above-mentioned processing.

[0271] Although the embodiment and the modified examples of the present invention have been described above, the present invention is not limited to these. The present invention includes appropriate combinations of the embodiment and the modified examples, and appropriate modifications thereto. [Industrial Applicability]

[0272] The present invention is suitable as a method for estimating the thermal and electromagnetic properties of a composite material. [Explanation of symbols]

[0273] 1: Composite material property estimation device, 101: CPU, 102: main memory unit, 103: auxiliary memory unit, 104: display unit, 105: input unit, 111: dielectric constant acquisition unit, 113: shape parameter acquisition unit, 114: Eshelby tensor generation unit, 115: intrinsic electric field acquisition unit, 116: action electric flux density electric field acquisition unit, 117: volume content acquisition unit, 118: equivalent intrinsic electric field calculation unit, 119: thermal / electromagnetic property estimation unit, 120: estimation result output unit, 121: orientation angle distribution acquisition / orientation angle distribution coefficient calculation unit, 131: relational equation storage unit

Claims

1. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material, and a plurality of double inclusions including a first inhomogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second inclusion having a dielectric constant equal to that of the base material and surrounding the first inhomogeneous inclusion, comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion and a dual inclusion shape parameter indicating a shape of the dual inclusion; calculating a first inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the first inhomogeneous inclusion, based on the first inhomogeneous inclusion shape parameters, and generating a double inclusion Eshelby tensor, which is the Eshelby tensor of the double inclusion, based on the double inclusion shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion; acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; Obtaining a volume fraction of the first heterogeneous inclusion in the dual inclusion and a volume fraction of the dual inclusion in a base metal; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the first inhomogeneous inclusion and a volume average of an equivalent intrinsic electric field in the double inclusion based on the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the double inclusion Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector and the two volume contents; and estimating thermal and electromagnetic properties of the composite material using the equivalent intrinsic electric field vector. Composite material property estimation method.

2. In the step of estimating the physical properties of the composite material, at least one of a double inclusion specific electric flux density vector indicating a volume average of the specific electric flux density in the double inclusion and a first inhomogeneous inclusion specific electric flux density vector indicating a volume average of the specific electric flux density in the first inhomogeneous inclusion is estimated. The composite material property estimation method according to claim 1 .

3. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material and inhomogeneous inclusions embedded in the base material and having a dielectric constant different from that of the base material, wherein a plurality of clusters including a plurality of the inhomogeneous inclusions are present in the base material, and the inhomogeneous inclusions are not present outside the plurality of clusters in the base material, comprising: A step of obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and an inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the inhomogeneous inclusion; acquiring a heterogeneous inclusion shape parameter indicating a shape of the heterogeneous inclusion and a cluster shape parameter indicating a shape of the cluster; calculating an inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the inhomogeneous inclusion, based on the inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor, which is the Eshelby tensor of the cluster, based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a heterogeneous inclusion volume content which is the volume content of one of the heterogeneous inclusions in the cluster, a total intra-cluster volume content which is the volume content of all of the heterogeneous inclusions contained in the cluster, and a cluster volume content which is the volume content of the cluster in the composite material; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the inhomogeneous inclusion and an equivalent intrinsic electric field in the cluster caused by a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material permittivity tensor, the inhomogeneous inclusion permittivity tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the inhomogeneous inclusion volume content, the total volume content of the inhomogeneous inclusion in the cluster, and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the equivalent intrinsic electric field vector. Composite material property estimation method.

4. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material and inhomogeneous inclusions embedded in the base material and having a dielectric constant different from that of the base material, wherein a plurality of clusters including a plurality of the inhomogeneous inclusions are present in the base material and the inhomogeneous inclusions are also present outside the plurality of clusters in the base material, the method comprising: A step of obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and an inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the inhomogeneous inclusion; acquiring a heterogeneous inclusion shape parameter indicating a shape of the heterogeneous inclusion and a cluster shape parameter indicating a shape of the cluster; calculating an inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the inhomogeneous inclusion, based on the inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor, which is the Eshelby tensor of the cluster, based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a heterogeneous inclusion volume content which is the volume content of one of the heterogeneous inclusions in the cluster, a total intra-cluster heterogeneous inclusion volume content which is the volume content in the cluster of all the heterogeneous inclusions contained in the cluster, a total extra-cluster heterogeneous inclusion volume content which is the volume content in the region outside the cluster of all the heterogeneous inclusions contained in the region outside the cluster of the composite material, and a cluster volume content which is the volume content of the cluster in the composite material; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the inhomogeneous inclusion and an equivalent intrinsic electric field in the cluster caused by a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material permittivity tensor, the inhomogeneous inclusion permittivity tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the inhomogeneous inclusion volume content, the inhomogeneous inclusion total volume content in the cluster, the inhomogeneous inclusion total volume content outside the cluster, and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the equivalent intrinsic electric field vector. Composite material property estimation method.

5. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material and a plurality of types of inhomogeneous inclusions embedded in the base material, the inhomogeneous inclusions having at least one of a dielectric constant, an intrinsic electric field, and an orientation different from each other and having a dielectric constant different from that of the base material, the base material including a plurality of clusters including the plurality of types of inhomogeneous inclusions, and the inhomogeneous inclusions not present outside the plurality of clusters in the base material, comprising: A step of obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and an inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the inhomogeneous inclusion; acquiring a heterogeneous inclusion shape parameter indicating a shape of the heterogeneous inclusion and a cluster shape parameter indicating a shape of the cluster; calculating an inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the inhomogeneous inclusion, based on the inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor, which is the Eshelby tensor of the cluster, based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a heterogeneous inclusion volume content which is a volume content of each of the plurality of types of heterogeneous inclusions in the cluster, a total volume content of heterogeneous inclusions in a cluster which is a volume content of the heterogeneous inclusions in the cluster for each of the plurality of types of heterogeneous inclusions included in the cluster, and a cluster volume content which is a volume content of the cluster in the composite material; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the cluster caused by a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material permittivity tensor, the inhomogeneous inclusion permittivity tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the inhomogeneous inclusion volume content, the inhomogeneous inclusion total volume content in the cluster, and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the equivalent intrinsic electric field vector. Composite material property estimation method.

6. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material and a plurality of types of inhomogeneous inclusions embedded in the base material, the inhomogeneous inclusions having at least one of a dielectric constant, an intrinsic electric field, and an orientation different from each other and having a dielectric constant different from that of the base material, the base material including a plurality of clusters including the plurality of types of inhomogeneous inclusions, and the inhomogeneous inclusions also existing outside the plurality of clusters in the base material, comprising: A step of obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix and an inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the inhomogeneous inclusion; acquiring a heterogeneous inclusion shape parameter indicating a shape of the heterogeneous inclusion and a cluster shape parameter indicating a shape of the cluster; calculating an inhomogeneous inclusion Eshelby tensor, which is the Eshelby tensor of the inhomogeneous inclusion, based on the inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor, which is the Eshelby tensor of the cluster, based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a heterogeneous inclusion volume content which is the volume content of one of the plurality of types of heterogeneous inclusions in the cluster, a total intra-cluster heterogeneous inclusion volume content which is the volume content in the cluster of all the heterogeneous inclusions contained in the cluster for each of the plurality of types of heterogeneous inclusions contained in the cluster, a total extra-cluster heterogeneous inclusion volume content which is the volume content in the region outside the cluster of all the heterogeneous inclusions contained in the region outside the cluster of the composite material, and a cluster volume content which is the volume content of the cluster in the composite material; calculating an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field within the cluster due to a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material permittivity tensor, the inhomogeneous inclusion permittivity tensor, the inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the inhomogeneous inclusion volume content, the inhomogeneous inclusion total volume content within the cluster, the inhomogeneous inclusion total volume content outside the cluster, and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the equivalent intrinsic electric field vector. Composite material property estimation method.

7. In the step of estimating the physical properties of the composite material, at least one of a cluster intrinsic electric flux density vector indicating a volume average of the intrinsic electric flux density in the cluster, an intrinsic electric flux density vector in a heterogeneous inclusion indicating a volume average of the intrinsic electric flux density in the intrinsic inclusion, and an outside-intrinsic electric flux density vector in a heterogeneous inclusion indicating a volume average of the intrinsic electric flux density outside the intrinsic inclusion in the cluster is estimated. The method for estimating properties of a composite material according to any one of claims 3 to 6.

8. In the step of estimating the physical properties of the composite material, at least one of an intrinsic electric flux density vector in the inhomogeneous inclusions indicating a volume average of the intrinsic electric flux density in the inhomogeneous inclusions in the composite material, an interactive electric flux density vector occurring in the composite material, and a macroscopic dielectric constant tensor indicating the macroscopic dielectric constant of the entire composite material is estimated. The method for estimating properties of a composite material according to any one of claims 3 to 6.

9. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material including a base material, a first inhomogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, a second inhomogeneous inclusion having a dielectric constant different from that of the first inhomogeneous inclusion and surrounding the first inhomogeneous inclusion, and a third inclusion having a dielectric constant equal to that of the base material and surrounding the second inhomogeneous inclusion, comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix, a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion, and a second inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the second inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion, a second inhomogeneous inclusion shape parameter indicating a shape of the second inhomogeneous inclusion, and a triple inclusion shape parameter indicating a shape of the triple inclusion; calculating a first inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the first inhomogeneous inclusion based on the first inhomogeneous inclusion shape parameters, calculating a second inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the second inhomogeneous inclusion based on the second inhomogeneous inclusion shape parameters, and calculating a triple inclusion Eshelby tensor which is the Eshelby tensor of the triple inclusion based on the triple inclusion shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion and a second intrinsic electric field vector indicating an intrinsic electric field possessed by the second inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a first heterogeneous inclusion volume content which is a volume content of the first heterogeneous inclusion in the second heterogeneous inclusion, a second heterogeneous inclusion volume content which is a volume content of the second heterogeneous inclusion in the triple inclusion, and a triple inclusion volume content which is a volume content of the triple inclusion in a composite material; calculating a second inhomogeneous inclusion equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the second inhomogeneous inclusion caused by a difference in the dielectric constant between the base material and the second inhomogeneous inclusion and a triple inclusion equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the triple inclusion based on the base material dielectric constant tensor, the first inhomogeneous inclusion dielectric constant tensor, the first inhomogeneous inclusion Eshelby tensor, the second inhomogeneous inclusion dielectric constant tensor, the second inhomogeneous inclusion Eshelby tensor, the first intrinsic electric field vector, the second intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the first inhomogeneous inclusion volume content, the second inhomogeneous inclusion volume content and the triple inclusion volume content; and estimating thermal and electromagnetic properties of the composite material using the second inhomogeneous inclusion equivalent eigenelectric field vector and the triple inclusion equivalent eigenelectric field vector. Composite material property estimation method.

10. 1. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material comprising: a base material; and a plurality of dual heterogeneous inclusions, the dual heterogeneous inclusions being composed of a first heterogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second heterogeneous inclusion having a dielectric constant different from that of the first heterogeneous inclusion and surrounding the first heterogeneous inclusion, wherein a plurality of clusters each including a plurality of the dual heterogeneous inclusions are present in the base material, and the dual heterogeneous inclusions are not present outside the plurality of clusters in the base material, Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix, a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion, and a second inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the second inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion, a double inhomogeneous inclusion shape parameter indicating a shape of the double inhomogeneous inclusion, and a cluster shape parameter indicating a shape of the cluster; calculating a first inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the first inhomogeneous inclusion based on the first inhomogeneous inclusion shape parameters, calculating a double inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the double inhomogeneous inclusion based on the double inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor which is the Eshelby tensor of the cluster based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion and a second intrinsic electric field vector indicating an intrinsic electric field possessed by the second inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a first heterogeneous inclusion volume content which is the volume content of the first heterogeneous inclusion in the dual heterogeneous inclusion, a dual heterogeneous inclusion volume content which is the volume content of one of the dual heterogeneous inclusions in the cluster, a total intra-cluster dual heterogeneous inclusion volume content which is the volume content of all the dual heterogeneous inclusions included in the cluster, and a cluster volume content which is the volume content of the cluster in the composite material; the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the second inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the double inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the second intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the first inhomogeneous inclusion volume fraction, the double inhomogeneous inclusion volume fraction, the intra-cluster double inhomogeneous inclusion calculating a first equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the first inhomogeneous inclusion resulting from differences in dielectric constant between the base material, the first inhomogeneous inclusion, and the second inhomogeneous inclusion, a double inhomogeneous inclusion equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the double inhomogeneous inclusion, and a cluster equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the cluster, based on the total inclusion volume content and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the first equivalent eigenelectric field vector, the double inhomogeneous inclusion equivalent eigenelectric field vector, and the cluster equivalent eigenelectric field vector. Composite material property estimation method.

11. 1. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material comprising: a base material; and a plurality of dual heterogeneous inclusions, the dual heterogeneous inclusions being composed of a first heterogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second heterogeneous inclusion having a dielectric constant different from that of the first heterogeneous inclusion and surrounding the first heterogeneous inclusion, wherein a plurality of clusters each including the dual heterogeneous inclusions are present in the base material and the dual heterogeneous inclusions are also present outside the plurality of clusters in the base material, the method comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix, a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion, and a second inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the second inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion, a double inhomogeneous inclusion shape parameter indicating a shape of the double inhomogeneous inclusion, and a cluster shape parameter indicating a shape of the cluster; calculating a first inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the first inhomogeneous inclusion based on the first inhomogeneous inclusion shape parameters, calculating a double inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the double inhomogeneous inclusion based on the double inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor which is the Eshelby tensor of the cluster based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion and a second intrinsic electric field vector indicating an intrinsic electric field possessed by the second inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a first heterogeneous inclusion volume content which is the volume content of one of the first heterogeneous inclusions in the dual heterogeneous inclusion, a dual heterogeneous inclusion volume content which is the volume content of one of the dual heterogeneous inclusions in the cluster, a total intra-cluster dual heterogeneous inclusion volume content which is the volume content of all the dual heterogeneous inclusions included in the cluster, a total extra-cluster dual heterogeneous inclusion volume content which is the volume content in the region outside the cluster of all the dual heterogeneous inclusions included in the region outside the cluster of the composite material, and a cluster volume content which is the volume content of the cluster in the composite material; the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the second inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the dual inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the second intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the first inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion total volume fraction in the cluster, calculating a first equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the first inhomogeneous inclusion resulting from differences in dielectric constant between the base material, the first inhomogeneous inclusion, and the second inhomogeneous inclusion, a double inhomogeneous inclusion equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the double inhomogeneous inclusion, and a cluster equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the cluster, based on the total volume content of the double inhomogeneous inclusions outside the cluster and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the first equivalent eigenelectric field vector, the double inhomogeneous inclusion equivalent eigenelectric field vector, and the cluster equivalent eigenelectric field vector. Composite material property estimation method.

12. 1. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material comprising: a base material; and a plurality of types of dual heterogeneous inclusions, the dual heterogeneous inclusions being composed of a first heterogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second heterogeneous inclusion having a dielectric constant different from that of the first heterogeneous inclusion and surrounding the first heterogeneous inclusion, the dual heterogeneous inclusions being different from each other in at least one of dielectric constant, intrinsic electric field, and orientation, wherein a plurality of clusters including the dual heterogeneous inclusions of a plurality of types are present in the base material, and the dual heterogeneous inclusions are not present outside the plurality of clusters in the base material, the method comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix, a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion, and a second inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the second inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion, a double inhomogeneous inclusion shape parameter indicating a shape of the double inhomogeneous inclusion, and a cluster shape parameter indicating a shape of the cluster; calculating a first inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the first inhomogeneous inclusion based on the first inhomogeneous inclusion shape parameters, calculating a double inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the double inhomogeneous inclusion based on the double inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor which is the Eshelby tensor of the cluster based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion and a second intrinsic electric field vector indicating an intrinsic electric field possessed by the second inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a first heterogeneous inclusion volume content which is the volume content of the first heterogeneous inclusion in each of the multiple types of dual heterogeneous inclusions, a dual heterogeneous inclusion volume content which is the volume content of one of the multiple types of dual heterogeneous inclusions in the cluster, a total intra-cluster dual heterogeneous inclusion volume content which is the volume content of all the dual heterogeneous inclusions in the cluster for each of the multiple types of dual heterogeneous inclusions included in the cluster, and a cluster volume content which is the volume content of the cluster in the composite material; the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the second inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the dual inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the second intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the first inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion in the cluster calculating a first equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in a plurality of types of first inhomogeneous inclusions resulting from differences in dielectric constant between the base material, the first inhomogeneous inclusion, and the second inhomogeneous inclusion, a double inhomogeneous inclusion equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in the double inhomogeneous inclusion, and a cluster equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in the cluster, based on the total volume content and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the first equivalent eigenelectric field vector, the double inhomogeneous inclusion equivalent eigenelectric field vector, and the cluster equivalent eigenelectric field vector. Composite material property estimation method.

13. 1. A composite material property estimation method for estimating thermal and electromagnetic properties of a composite material comprising: a base material; and a plurality of types of dual heterogeneous inclusions, each of which is composed of a first heterogeneous inclusion embedded in the base material and having a dielectric constant different from that of the base material, and a second heterogeneous inclusion surrounding the first heterogeneous inclusion and having a dielectric constant different from that of the first heterogeneous inclusion, the dual heterogeneous inclusions differing from each other in at least one of dielectric constant, intrinsic electric field, and orientation, wherein the base material contains a plurality of clusters containing the plurality of types of dual heterogeneous inclusions, and the dual heterogeneous inclusions are also present outside the plurality of clusters in the base material, the method comprising: Obtaining a matrix dielectric constant tensor indicating the dielectric constant of the matrix, a first inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the first inhomogeneous inclusion, and a second inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the second inhomogeneous inclusion; acquiring a first inhomogeneous inclusion shape parameter indicating a shape of the first inhomogeneous inclusion, a double inhomogeneous inclusion shape parameter indicating a shape of the double inhomogeneous inclusion, and a cluster shape parameter indicating a shape of the cluster; calculating a first inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the first inhomogeneous inclusion based on the first inhomogeneous inclusion shape parameters, calculating a double inhomogeneous inclusion Eshelby tensor which is the Eshelby tensor of the double inhomogeneous inclusion based on the double inhomogeneous inclusion shape parameters, and calculating a cluster Eshelby tensor which is the Eshelby tensor of the cluster based on the cluster shape parameters; acquiring a first intrinsic electric field vector indicating an intrinsic electric field possessed by the first inhomogeneous inclusion and a second intrinsic electric field vector indicating an intrinsic electric field possessed by the second inhomogeneous inclusion; A step of acquiring an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; acquiring a first heterogeneous inclusion volume content which is the volume content of the first heterogeneous inclusion in each of the multiple types of dual heterogeneous inclusions, a dual heterogeneous inclusion volume content which is the volume content of one of the multiple types of dual heterogeneous inclusions in the cluster, an intra-cluster dual heterogeneous inclusion total volume content which is the volume content of all the dual heterogeneous inclusions in the cluster for each of the multiple types of dual heterogeneous inclusions included in the cluster, an extra-cluster dual heterogeneous inclusion total volume content which is the volume content of all the dual heterogeneous inclusions included in a region outside the cluster of the composite material, and a cluster volume content which is the volume content of the cluster in the composite material; the matrix permittivity tensor, the first inhomogeneous inclusion permittivity tensor, the second inhomogeneous inclusion permittivity tensor, the first inhomogeneous inclusion Eshelby tensor, the dual inhomogeneous inclusion Eshelby tensor, the cluster Eshelby tensor, the first intrinsic electric field vector, the second intrinsic electric field vector, the action electric flux density vector, the action electric field vector, the first inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion volume fraction, the dual inhomogeneous inclusion total volume fraction in the cluster, the cluster calculating a first equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in a plurality of types of first inhomogeneous inclusions resulting from differences in dielectric constant between the base material, the first inhomogeneous inclusion, and the second inhomogeneous inclusion, a double inhomogeneous inclusion equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in the double inhomogeneous inclusion, and a cluster equivalent intrinsic electric field vector indicating a volume average of equivalent intrinsic electric fields in the cluster, based on the total volume content of double inhomogeneous inclusions outside the cluster and the cluster volume content; and estimating thermal and electromagnetic properties of the composite material using the first equivalent eigenelectric field vector, the double inhomogeneous inclusion equivalent eigenelectric field vector, and the cluster equivalent eigenelectric field vector. Composite material property estimation method.

14. A composite material property estimation device that estimates thermal and electromagnetic properties of a composite material including a base material and a heterogeneous inclusion embedded in the base material, comprising: a dielectric constant acquisition unit that acquires a base material dielectric constant tensor indicating the dielectric constant of the base material and a non-homogeneous inclusion dielectric constant tensor indicating the dielectric constant of the non-homogeneous inclusion; a shape parameter acquisition unit that acquires inhomogeneous inclusion shape parameters indicating the shape of the inhomogeneous inclusion; an Eshelby tensor generating unit that generates an Eshelby tensor of the inhomogeneous inclusion based on the inhomogeneous inclusion shape parameters; an intrinsic electric field acquisition unit that acquires an intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; an action electric flux density electric field acquisition unit that acquires an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; a volume content acquisition unit for acquiring a volume content of the heterogeneous inclusion; an equivalent intrinsic electric field calculation unit that calculates an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the inhomogeneous inclusion caused by a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material dielectric constant tensor, the inhomogeneous inclusion dielectric constant tensor, the Eshelby tensor, the intrinsic electric field vector, the action electric flux density vector, the action electric field vector, and the volume content; and a thermal / electromagnetic property estimation unit that estimates thermal / electromagnetic properties of the composite material using the equivalent eigenelectric field vector. Composite material property estimation device.

15. Computer, a dielectric constant acquisition unit that acquires a base material dielectric constant tensor indicating the dielectric constant of a base material of a composite material including a base material and a heterogeneous inclusion embedded in the base material, and an inhomogeneous inclusion dielectric constant tensor indicating the dielectric constant of the inhomogeneous inclusion; a shape parameter acquisition unit that acquires inhomogeneous inclusion shape parameters indicating the shape of the inhomogeneous inclusion; an Eshelby tensor generating unit that generates an Eshelby tensor of the inhomogeneous inclusion based on the inhomogeneous inclusion shape parameters; an intrinsic electric field acquisition unit that acquires an intrinsic electric field vector indicating an intrinsic electric field possessed by the inhomogeneous inclusion; an action electric flux density electric field acquisition unit that acquires an action electric flux density vector indicating an electric flux density when a preset electric flux density is applied to the composite material, and an action electric field vector indicating an electric field of the composite material when the electric flux density is applied to the composite material; a volume content acquisition unit that acquires the volume content of the heterogeneous inclusions; an equivalent intrinsic electric field calculation unit that calculates an equivalent intrinsic electric field vector indicating a volume average of an equivalent intrinsic electric field in the inhomogeneous inclusion due to a difference in the dielectric constant between the base material and the inhomogeneous inclusion, based on the base material dielectric constant tensor, the inhomogeneous inclusion dielectric constant tensor, the Eshelby tensor, the intrinsic electric field vector, the action electric flux density vector, the action electric field vector, and the volume content; a thermal / electromagnetic property estimation unit that estimates thermal / electromagnetic properties of the composite material using the equivalent eigenelectric field vector; A program to function as a

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