Continuous medium high-order modeling method and related device thereof

Abstract

The invention discloses a continuous medium high-order modeling method and a related device thereof. The method comprises the following steps: constructing a local constitutive model of a material according to a field variable describing a material state and an energy density; performing Taylor expansion on the local constitutive model, and performing homogenization processing on the local constitutive model after Taylor expansion on a representative volume unit to obtain a homogenized non-local constitutive model; and based on the homogenized non-local constitutive model, establishing a distribution and evolution model of field variables in any structure according to the principle of minimum action, and solving the distribution and evolution model to obtain the state and evolution process of any material point in the structure. According to the non-local constitutive model, the influence of non-uniform distribution of field variables on the constitutive model is considered, the constitutive behavior of the material on a small scale can be described more accurately, and the problem that in the prior art, material microstructure non-uniformity and physical field space distribution non-uniformity are not considered is solved. And thus, a large error exists when the state distribution in a complex structure is solved, and the like.

Description

Technical Field

[0001] The present application relates to the technical field of behavior analysis of complex structures and materials, and in particular to a continuous medium high-order modeling method and related devices. Background Art

[0002] Classical continuum theory believes that complex structures can be decomposed into a collection of infinitesimal material points. Since the material points are small enough, there is no need to consider the non-uniform state distribution inside them, and the local constitutive model (that is, the behavior of the point depends only on the state of the point) can be used to fully describe the various behaviors of the material. These assumptions lead to the fact that the classical continuum model is actually only applicable to completely homogeneous ideal materials. Since the multi-scale and non-homogeneous characteristics of the actual medium are not considered, the classical continuum model has inherent defects in describing the constitutive relations of real materials and solving non-uniformly distributed physical fields. There are errors or even mistakes that cannot be ignored when analyzing and predicting important issues such as the destruction and ultimate bearing capacity of materials and structures, the transient thermal behavior of structures under thermal pulses, and the complex flow and heat transfer behavior of fluids. The most typical example is that the classical elastic fracture mechanics theory believes that the stress / strain at the crack tip is infinite. Even for typical brittle materials such as ceramics and glass, this conclusion is unreasonable. Summary of the invention

[0003] The present application provides a continuous medium high-order modeling method and related devices, which are used to improve the problem of large errors in the prior art when using the classical continuous medium model to solve complex state distributions.

[0004] In view of this, the first aspect of the present application provides a continuous medium high-order modeling method, comprising:

[0005] Construct a local constitutive model of the material based on field variables and energy density that describe the material state;

[0006] Performing Taylor expansion on the local constitutive model, and performing homogenization processing on the local constitutive model after Taylor expansion on the representative volume unit to obtain a homogenized non-local constitutive model;

[0007] Based on the homogenized non-local constitutive model, a distribution and evolution model of field variables is established according to the principle of minimum action. The distribution and evolution model is solved to obtain the state and evolution history of any material point in the structure.

[0008] Optionally, a local constitutive model of the material is constructed based on the field variables and energy density of the material, including:

[0009] Aiming at the damage and deformation problem of materials, the damage strain energy density is used to construct the local constitutive model of the material.

[0010] Optionally, a local constitutive model of the material is constructed based on the field variables and energy density of the material, including:

[0011] Aiming at the plastic deformation problem of materials, the local constitutive model of materials is constructed by using plastic dissipative density.

[0012] Optionally, a local constitutive model of the material is constructed based on the field variables and energy density of the material, including:

[0013] Aiming at the thermal behavior problem of materials, the local constitutive model of the material is constructed using the internal energy density or conduction heat flux density.

[0014] Optionally, a local constitutive model of the material is constructed based on the field variables and energy density of the material, including:

[0015] Aiming at the electrostatic behavior of materials, the local constitutive model of the materials is constructed using the electric field energy density.

[0016] Optionally, the homogenization treatment formula of the spatial non-uniform distribution of the local constitutive model is:

[0017]

[0018] In the formula, is the energy density; is the centroid of the volume unit area; represents the volume unit area.

[0019] Optionally, the distribution and evolution model of field variables is established based on the homogenized non-local constitutive model according to the principle of minimum action, including:

[0020] The total energy functional is obtained by integrating the homogenized nonlocal constitutive model, and the distribution and evolution model of the field variables is established using the variational method based on the principle of least action.

[0021] A second aspect of the present application provides a continuous medium high-order modeling device, comprising:

[0022] A model building unit, used to build a local constitutive model of the material based on field variables and energy density describing the state of the material;

[0023] A homogenization processing unit, used for performing Taylor expansion on the local constitutive model, and performing homogenization processing on the local constitutive model after Taylor expansion on the representative volume unit to obtain a homogenized non-local constitutive model;

[0024] The model solving unit is used to establish a distribution and evolution model of field variables based on the homogenized non-local constitutive model and the principle of minimum action, solve the distribution and evolution model, and obtain the state and evolution history of any material point in the structure.

[0025] A third aspect of the present application provides an electronic device, the device comprising a processor and a memory;

[0026] The memory is used to store program code and transmit the program code to the processor;

[0027] The processor is used to execute the continuous medium high-order modeling method described in any one of the first aspects according to the instructions in the program code.

[0028] In a fourth aspect, the present application provides a computer-readable storage medium, which is used to store program code. When the program code is executed by a processor, it implements the continuous medium high-order modeling method described in any one of the first aspects.

[0029] It can be seen from the above technical solutions that this application has the following advantages:

[0030] The high-order modeling method of continuous media provided in the present application performs Taylor expansion on the local constitutive model of the constructed material, realizes the use of the gradient of the field variable to describe its non-uniform distribution in space, and then performs a homogenization operation on it on the representative volume unit to obtain an energy density form including the state variable gradient term. The homogenized non-local constitutive model takes into account the influence of the non-uniform distribution of the field variable on the constitutive model, and can more accurately describe the constitutive behavior of the material at a small scale, thereby improving the problem that the prior art does not consider the non-uniformity of the microstructure of the material and the non-uniformity of the spatial distribution of the physical field, resulting in large errors when solving the state distribution of complex structures. In addition, the homogenized non-local constitutive model in the present application only needs to introduce a scale parameter with a clear physical meaning and easy to calibrate, that is, the scale of the material representative volume unit, and does not need to introduce too many unknown parameters that are difficult to calibrate, so it is easy to apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0032] Figure 1 A schematic flow chart of a high-order modeling method for continuous media provided in an embodiment of the present application;

[0033] Figure 2 A schematic diagram of commonly used field changes for problems in mechanics, thermodynamics, and electrostatics provided in the embodiments of this application;

[0034] Figure 3A structural schematic diagram of a continuous medium high-order modeling device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0036] Classical continuum theory (such as Fourier heat conduction theory, Cauchy solid mechanics theory, classical fluid dynamics theory, and electromagnetic theory) is the basic framework of contemporary engineering science. However, due to the failure to consider the multi-scale and heterogeneous characteristics of actual media, the classical continuum model has inherent defects in describing the non-uniformly distributed physical fields and the constitutive relations of materials, resulting in the inability of these classical models to accurately solve complex physical problems that change dramatically in space and time (such as deformation concentration problems, damage and destruction of materials and structures, rapid heat conduction problems, etc.). The defects of classical continuum theory are rooted in the ideas of "reduction" and "limit". The former believes that the behavior of any complex system can be reduced to the coordinated behavior of (infinitesimal) material points; the latter believes that by infinitely scaling and extrapolating standard experimental results, the behavior of material points (i.e., constitutive behavior) can be accurately defined. However, the multi-scale and heterogeneous characteristics of real media lead to the failure of the limit idea, that is, there are no infinitesimal material points in physics. Therefore, there are also errors in using uniform physical fields to describe the complex state and behavior in a finite material micro-region. The more uneven the distribution of the physical field, the greater the error.

[0037] In order to improve the defects of the classical continuum model, the existing technology uses gradient methods and non-local methods to improve it. The gradient method believes that the state variables themselves are not enough to fully describe the true state of the material micro-region, and the first-order or second-order gradients of these state variables should be regarded as additional degrees of freedom to better describe the state in the material micro-region. However, since it is difficult to study the variation law of the gradient quantity through standard tests, how to establish a suitable constitutive relationship to describe the complex behavior of the material micro-region is the primary problem faced by the gradient method. At present, the analogy method is mostly used to introduce the gradient quantity in the form of the classical constitutive model, but this method has no strict physical basis and does not answer the fundamental question of what the real physical meaning of the gradient term is. The non-local method believes that the behavior of a certain material point is not only related to the state of the current point, but also to the state of its nearby points. Therefore, the behavior of the material point is defined by weighted average. That is, an influence zone is defined for each material point, and the state of other material points in the influence zone affects the behavior of the current point, and the degree of influence decays rapidly with the increase of the distance between the two points. Considering that the material points in the nonlocal theory are not real material particles, but still a collection of a large number of particles, there is no long-range interaction between these material points, such as electrostatic fields. Therefore, the nonlocal method also lacks a strict physical basis. The main problem of these two types of methods is that the root causes of gradient terms and nonlocal interactions have not been clarified from a physical perspective. Without clarifying this fundamental problem, the rigor of the theoretical model cannot be guaranteed, and there will be too many unknown parameters in the model that are difficult to calibrate.

[0038] To improve the above problems, please refer to Figure 1 , the present application embodiment provides a continuous medium high-order modeling method, including:

[0039] Step 110: construct a local constitutive model of the material based on the field variables and energy density that describe the state of the material.

[0040] Before constructing a local constitutive model, it is necessary to select or define appropriate field variables to describe the state of the structure for different problems. For problems such as mechanics, thermodynamics, and electrostatics, commonly used field variables are Figure 2 shown.

[0041] In the present application, field variables are used to represent the local constitutive behavior of a material point in the form of energy density, thereby constructing a local constitutive model of the material point.

[0042] Specifically, in view of the damage deformation problem of the material, the damage strain energy density is used to construct the local constitutive model of the material; wherein, the expression of the damage strain energy density is:

[0043]

[0044] In the formula, is the damage strain energy density; d is the damage factor; is the Lamé constant; is the body strain, For strain.

[0045] In view of the plastic deformation problem of the material, the local constitutive model of the material is constructed using the plastic dissipated density. The expression of the plastic dissipated density is:

[0046]

[0047] In the formula, u p is the plastic dissipation density; is the equivalent plastic strain; is the equivalent plastic strain rate, , is the plastic strain rate; SDVs is the variable describing the plastic change process and state.

[0048] Aiming at the thermal behavior of materials, the local constitutive model of materials is constructed by using internal energy density or conduction heat flux density.

[0049] The expression of internal energy density is:

[0050] u=ρc p T

[0051] Where u is the internal energy density; T is the temperature; ρ is the density of the material; c p is the specific heat of the material;

[0052] The expression of conduction heat flux is:

[0053]

[0054] Where q is the conduction heat flux density; k is the thermal conductivity of the material; is the temperature gradient.

[0055] In view of the electrostatic behavior of materials, the local constitutive model of the material is constructed using the electric field energy density. The expression of the electric field energy density is:

[0056]

[0057] In the formula, is the electric field energy density; D is the electric displacement; E is the electric field; is the dielectric constant in vacuum; is the relative dielectric constant.

[0058] Step 120: Taylor expansion is performed on the local constitutive model, and the local constitutive model after Taylor expansion is homogenized on the representative volume unit to obtain a homogenized non-local constitutive model.

[0059] Use symbol Represents the energy density of the local constitutive model, and Taylor expansion is performed on it. Its Taylor expansion form is:

[0060]

[0061] In the formula, the symbol Indicates that the corresponding parameter is a vector; is the value of the variable at the reference point, is the first-order gradient of u, is the second-order gradient of u, and “...” represents the third-order and higher-order gradients of u.

[0062] The homogenization error can be reduced by performing Taylor expansion on the energy density to represent the non-uniform distribution of the field variables and the energy density within the representative volume unit.

[0063] Due to the uneven distribution of material properties, some uniformity errors may also occur. In this case, the material properties can be further homogenized to partially eliminate the impact of the uneven distribution of material properties. In the embodiment of the present application, the local constitutive model after Taylor expansion is homogenized on the representative volume unit to obtain the energy density form containing the state variable gradient term:

[0064]

[0065] In the formula, is the centroid of the volume unit area; is the representative volume unit area; is the center of mass of the physical quantity u in the volume unit area The value of ;

[0066] For isotropic materials, choose the homogenization region as Then we have:

[0067]

[0068] In the formula, is the Laplace operator; is a biharmonic operator; ; h is the scale of the homogenized local area, that is, the scale of the volume unit, representing the size of the basic periodic unit of the actual material microstructure. If the material is relatively uniform at the microscopic level (such as metals with fine grains), then h should be small; otherwise, the h value may be large, such as polymer materials, rocks, and porous materials. The parameter h can be determined by correlation analysis with the typical length scale of the material, such as the average grain size of metals and the radius of gyration of polymer materials.

[0069] The state variables are then substituted into the homogenized energy density, which is explicitly expressed as a form containing the state variables and the gradients of the state variables. For the damage strain energy density, the final homogenized form is:

[0070]

[0071] in, , ; The symbol “=” indicates that the corresponding parameter is a tensor or matrix; the symbol “:” indicates the inner product of double contraction; U is the local strain energy density when no damage occurs; , , , , , ,

[0072] ;

[0073] For the plastically dissipated density, the final homogenized form is:

[0074]

[0075] For the internal energy density, the final homogenized form is:

[0076]

[0077] For the electric field energy density, the final homogenized form is:

[0078]

[0079] in, ; Electric field vector ; The above formula uses Einstein's notation, that is , .

[0080] Step 130: Based on the homogenized non-local constitutive model, a distribution and evolution model of field variables is established according to the principle of minimum action, and the distribution and evolution model is solved to obtain the state and evolution history of any material point in the structure.

[0081] The total energy functional is obtained by integrating the energy density in the above homogenized form. Then, according to the principle of least action, the distribution and evolution model of field variables in any structure is established by using the variational method. Solving the distribution and evolution model can obtain the state distribution and change of any material point in the structure. The distribution and evolution model contains the first-order, second-order or high-order gradient form of field variables, so it is a high-order model.

[0082] Taking the solution of the damage elasticity problem as an example, the total energy functional and damage evolution constraint equation are:

[0083]

[0084] In the formula, Is the scope Total potential energy inside is the displacement field; It is applied at the scope boundary The surface force on Damage-dependent equivalent strain The evolution function of .

[0085] According to the principle of least action, that is:

[0086]

[0087] Using the augmented Lagrangian method, we construct an equivalent energy functional:

[0088]

[0089]

[0090]

[0091] In the formula, is the Lagrange multiplier; r is the penalty parameter;

[0092] The high-order damage elastic deformation model can be obtained by using the variational method:

[0093]

[0094]

[0095]

[0096] By solving the above high-order damage elastic deformation model, the deformation of any point in the structure (i.e., u, ) and the degree of damage (i.e., d), and then the bearing capacity of the structure can be judged according to the deformation distribution and the degree of damage. The common basis for judgment is that the structure is considered to have failed when the damaged area has expanded into a macro crack. Taking the calculation of the destruction of defective structures and microelectronic multilayer film structures as an example, the high-order damage elastic deformation model in this application can not only predict the initiation and evolution process of the damaged area, but also accurately calculate the influence of defect size and film thickness on the initiation or evolution process of damage, and then optimize the design of structural parameters to improve its bearing capacity.

[0097] For heat conduction problems, heat transfer-deformation coupling problems, etc., the same method as above can also be used to construct the corresponding high-order model. The obtained high-order heat conduction model without heat source is:

[0098]

[0099] and the classic heat conduction model without heat source (i.e. ) can be found by comparison that when the temperature distribution is highly uneven (i.e. When the heat transfer coefficient is not negligible), the high-order terms will affect the transient heat transfer process. In the case of heat transfer of thermal barrier coatings under thermal shock and heat transfer of microelectronic devices, the use of the classic heat conduction model will overestimate the heat conduction rate, while the high-order heat conduction model in this application will not have this problem.

[0100] For the electrostatic field problem, the above method is used to construct a high-order model, and the high-order electrostatic field model is obtained as follows:

[0101]

[0102] For complex structures, the finite element method can be used to solve the high-order model and obtain the electric field strength at any point inside the structure. Compared with the classical model, the high-order model can calculate the complex electric field distribution more accurately, so it is very suitable for the design of miniaturized multilayer ceramic capacitors, the design of dielectric properties of composite materials, and the prediction of dielectric properties of micro-nano structures.

[0103] The high-order modeling method of continuous media provided in the present application performs Taylor expansion on the local constitutive model of the constructed material, realizes the use of the gradient of the field variable to describe its non-uniform distribution in space, and then performs a homogenization operation on it on the representative volume unit to obtain the energy density form including the state variable gradient term. The homogenized non-local constitutive model takes into account the influence of the non-uniform distribution of the field variable on the constitutive model, and can more accurately describe the constitutive behavior of the material at a small scale, thereby improving the problem that the prior art does not consider the non-uniformity of the microstructure of the material and the non-uniformity of the spatial distribution of the physical field, resulting in large errors in the calculation of complex state distribution and evolution. In addition, the homogenized non-local constitutive model in the present application only needs to introduce a scale parameter with a clear physical meaning and easy to calibrate, that is, the scale of the material representative volume unit, and does not need to introduce too many unknown parameters that are difficult to calibrate, so it is easy to apply.

[0104] The above is an embodiment of a continuous medium high-order modeling method provided by the present application, and the following is an embodiment of a continuous medium high-order modeling device provided by the present application.

[0105] Please refer to Figure 3 , a continuous medium high-order modeling device provided in an embodiment of the present application includes:

[0106] A model building unit, used to build a local constitutive model of the material based on field variables and energy density describing the state of the material;

[0107] A homogenization processing unit is used to perform Taylor expansion on the local constitutive model, and perform homogenization processing on the local constitutive model after Taylor expansion on the representative volume unit to obtain a homogenized non-local constitutive model;

[0108] The model solving unit is used to establish the distribution and evolution model of field variables based on the homogenized non-local constitutive model and the principle of minimum action, solve the distribution and evolution model, and obtain the state and evolution history of any material point in the structure.

[0109] As a further improvement, the model building unit is specifically used to construct a local constitutive model of the material using damage strain energy density for the damage deformation problem of the material;

[0110] Aiming at the plastic deformation problem of materials, the local constitutive model of materials is constructed by using plastic dissipative density.

[0111] Aiming at the thermal behavior of materials, the local constitutive model of materials is constructed by using internal energy density or conduction heat flux density.

[0112] Aiming at the electrostatic behavior of materials, the local constitutive model of the materials is constructed using the electric field energy density.

[0113] As a further improvement, the model solving unit is specifically used to integrate the homogenized non-local constitutive model to obtain the total energy functional, and based on the principle of least action, the variational method is used to establish the distribution and evolution model of the field variables; the distribution and evolution model is solved to obtain the state and evolution history of any material point in the structure.

[0114] The present application performs Taylor expansion on the local constitutive model of the constructed material, realizes the use of the gradient of the field variable to describe its non-uniform distribution in space, and then performs a homogenization operation on it on the representative volume unit to obtain the energy density form containing the state variable gradient term. The homogenized non-local constitutive model takes into account the influence of the non-uniform distribution of the field variable on the constitutive model, and can more accurately describe the constitutive behavior of the material at a small scale, thereby improving the problem that the prior art does not consider the non-uniformity of the material microstructure and the non-uniformity of the spatial distribution of the physical field, resulting in large errors in the calculation of complex state distribution and evolution. In addition, the homogenized non-local constitutive model in the present application only needs to introduce a scale parameter with a clear physical meaning and easy to calibrate, that is, the scale of the representative volume unit of the material, and does not need to introduce too many unknown parameters that are not easy to calibrate, so it is easy to apply.

[0115] The embodiment of the present application also provides an electronic device, the device comprising a processor and a memory;

[0116] The memory is used to store the program code and transmit the program code to the processor;

[0117] The processor is used to execute the continuous medium high-order modeling method in the aforementioned method embodiment according to the instructions in the program code.

[0118] An embodiment of the present application also provides a computer-readable storage medium, which is used to store program code. When the program code is executed by a processor, the continuous medium high-order modeling method in the aforementioned method embodiment is implemented.

[0119] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0120] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of this application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0121] It should be understood that in this application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0122] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0123] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0124] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0125] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a number of instructions for executing all or part of the steps of the method described in each embodiment of the present application through a computer device (which can be a personal computer, server, or network device, etc.). The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (full name in English: Read-Only Memory, English abbreviation: ROM), random access memory (full name in English: Random Access Memory, English abbreviation: RAM), disk or optical disk and other media that can store program codes.

[0126] As described above, the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A high-order modeling method for continuous media, characterized in that: include: Construct a local constitutive model of the material based on field variables and energy density that describe the material state; Performing Taylor expansion on the local constitutive model, and performing homogenization processing on the local constitutive model after Taylor expansion on the representative volume unit to obtain a homogenized non-local constitutive model; Based on the homogenized non-local constitutive model, a distribution and evolution model of field variables is established according to the principle of minimum action. The distribution and evolution model is solved to obtain the state and evolution history of any material point in the structure.

2. The continuous medium high-order modeling method according to claim 1, characterized in that: The local constitutive model of the material is constructed based on the field variables and energy density of the material, including: Aiming at the damage and deformation problem of materials, the damage strain energy density is used to construct the local constitutive model of the material.

3. The continuous medium high-order modeling method according to claim 1, characterized in that: The local constitutive model of the material is constructed based on the field variables and energy density of the material, including: Aiming at the plastic deformation problem of materials, the local constitutive model of materials is constructed by using plastic dissipative density.

4. The continuous medium high-order modeling method according to claim 1, characterized in that: The local constitutive model of the material is constructed based on the field variables and energy density of the material, including: Aiming at the thermal behavior problem of materials, the local constitutive model of the material is constructed using the internal energy density or conduction heat flux density.

5. The continuous medium high-order modeling method according to claim 1, characterized in that: The local constitutive model of the material is constructed based on the field variables and energy density of the material, including: Aiming at the electrostatic behavior of materials, the local constitutive model of the materials is constructed using the electric field energy density.

6. The continuous medium high-order modeling method according to claim 1, characterized in that: The homogenization treatment formula of the spatial non-uniform distribution of the local constitutive model is: In the formula, is the energy density; is the centroid of the volume unit area; represents the volume unit area.

7. The continuous medium high-order modeling method according to claim 1, characterized in that: The non-local constitutive model after homogenization is used to establish a distribution and evolution model of field variables according to the principle of minimum action, including: The total energy functional is obtained by integrating the homogenized nonlocal constitutive model, and the distribution and evolution model of the field variables is established using the variational method based on the principle of least action.

8. A continuous medium high-order modeling device, characterized in that: include: A model building unit, used to build a local constitutive model of the material based on field variables and energy density describing the state of the material; A homogenization processing unit, used for performing Taylor expansion on the local constitutive model, and performing homogenization processing on the local constitutive model after Taylor expansion on the representative volume unit to obtain a homogenized non-local constitutive model; The model solving unit is used to establish a distribution and evolution model of field variables based on the homogenized non-local constitutive model and the principle of minimum action, solve the distribution and evolution model, and obtain the state and evolution history of any material point in the structure.

9. An electronic device, characterized in that: The device comprises a processor and a memory; The memory is used to store program code and transmit the program code to the processor; The processor is used to execute the continuous medium high-order modeling method described in any one of claims 1-7 according to the instructions in the program code.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium is used to store program code, and when the program code is executed by a processor, the continuous medium high-order modeling method described in any one of claims 1-7 is implemented.

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