A method for constructing a mechanical constitutive model for two-dimensional woven composite materials

Abstract

The present invention discloses a method for constructing a mechanical constitutive model for two-dimensional woven composite materials, belonging to the field of mechanical property characterization and analysis of two-dimensional woven composite materials. The method is divided into two parts: geometric nonlinearity caused by fiber redirection and material nonlinearity caused by plastic behavior. The establishment of the method includes the following processes: step 1, determining the initial material constants of the orthotropic constitutive model; step 2, analyzing the transformation of material properties with applied deformation to determine the geometric nonlinear parameters; step 3, establishing a plastic constitutive model and determining the material nonlinear parameters. The method of the present invention can ensure that the two-dimensional woven composite material still has orthotropic anisotropy under finite deformation, and can accurately and reliably predict the stress-strain response of the two-dimensional woven composite material after fiber redirection under finite deformation, providing a reliable constitutive model for the characterization and analysis of the mechanical properties of two-dimensional woven composite materials.

Description

Technical Field

[0001] The present invention relates to the field of mechanical property characterization and analysis of two-dimensional woven composite materials, and in particular to a macroscopic mechanical constitutive model for two-dimensional woven composite materials under finite deformation. Background Art

[0002] The analysis of composite materials structures in engineering applications is usually based on macroscopic mechanics theory. Compared with micromechanics, macroscopic mechanics can save a lot of computing costs. Composite materials are anisotropic materials with 81 elastic constants. Through the symmetry of stress and strain and the invariance of strain energy, it can be confirmed that there are only 21 independent elastic constants among the 81 elastic constants. Based on the theory of macroscopic mechanics, the 21 independent elastic constants in anisotropic materials can be reduced to 9 independent elastic constants by finding three elastic symmetry planes that are orthogonal to each other. Therefore, the existing composite material testing standards (such as ASTM D7078, D3518, D3039, etc.) are all for orthotropic materials. The material constants obtained through the test standards are only applicable to orthotropic materials. When a material no longer has orthotropic anisotropy or for laminates with multi-angle plies, the stiffness matrix must be obtained through coordinate transformation.

[0003] In the practical application of composite materials, there are scenarios where finite deformation is used. In small deformation scenarios, the second-order terms in the Green strain tensor are ignored. This assumption is reasonable when the strain is much less than 1. Under this assumption, the differences in various strain tensors of the material (such as Green strain and Archman strain) can be ignored. At the same time, the differences in various stress tensors (such as Cauchy stress and Piola-Kirchhoff stress) can also be ignored. The constitutive model can be established under any combination; however, for large deformation scenarios, the differences between various strain and stress tensors cannot be ignored. Therefore, it is necessary to establish constitutive relations based on the energy duality between stress and strain tensors. At the same time, the geometric configuration of the structure under finite deformation has significant differences compared to the initial state. Changes in the relative positions of different components in a structure will introduce nonlinear responses of the overall structure. Therefore, studying composite materials under finite deformation has important engineering significance.

[0004] Composite structures used in practical engineering applications are typically thin-walled. To enhance the load-bearing properties of unidirectional composites perpendicular to the fiber direction, two-dimensional woven composites have emerged. When a composite is subjected to finite deformation, the fiber orientation no longer aligns with the initial fiber configuration due to matrix deformation. For unidirectional composites, since they have only one fiber direction, even if the fiber direction changes, this can be reconstructed by taking the fiber direction and two directions perpendicular to the fibers as pairwise orthogonal material axes. The planes perpendicular to these three material axes are the planes of elastic symmetry, and the three sets of elastic symmetry planes are pairwise orthogonal, satisfying the conditions for an orthotropic material. However, this approach is not feasible for two-dimensional woven composites because, under finite deformation, the fiber angles are no longer 90° due to the finite shear deformation between the fibers. Furthermore, the fiber directions are no longer orthogonal material axes due to the loss of symmetry. Therefore, treating the fiber directions of two-dimensional woven composites as orthotropic materials under finite deformation will lead to errors in the predicted stress-strain state, and these errors increase with increasing finite deformation. In order to obtain an accurate stress-strain state, if the fiber direction is used as the principal axis of the material, the two-dimensional woven composite material must be considered as an anisotropic material. If the two-dimensional woven composite material is considered as an anisotropic material, the material parameters unique to the anisotropic material must be calibrated through experiments, but the existing composite material testing standards are unable to calibrate these material parameters. At the same time, because the angle between the fibers changes continuously with finite deformation, the material parameters of the two-dimensional woven composite material also change continuously with finite deformation. Even if the anisotropic parameters are calibrated through experiments, it is impossible to confirm their changing trend with finite deformation and to perform quantitative analysis. The above problems greatly increase the complexity and difficulty of analyzing two-dimensional woven composite materials under finite deformation. Therefore, in order to improve the accuracy of the characterization and analysis of the mechanical properties of two-dimensional woven composite materials under finite deformation, it is necessary to propose a new orthotropic constitutive model under finite deformation to better predict the mechanical behavior of two-dimensional woven composite materials.

[0005] Plasticity is widely used to analyze the nonlinear response of various materials under finite deformation. Similar to unidirectional composites, two-dimensional woven composites exhibit significant nonlinear behavior when subjected to interfiber shear loads. Unlike unidirectional composites, which are generally assumed to exhibit no plastic deformation in the fiber direction, two-dimensional woven composites exhibit nonlinear behavior in this direction. In plasticity theory, the plastic behavior of a material is determined by the yield function, flow potential, and hardening law. The resulting plastic strain increment does not affect the material's stress state, which is determined solely by the elastic strain. The parameters of the yield function, flow potential, and hardening law are calibrated experimentally. Therefore, even if fiber reorientation occurs during testing, the calibrated parameters account for this effect, enabling the established plasticity model to accurately replicate experimental results. In plasticity analysis, calculation factors in the flow potential are required to obtain the plastic strain increment. This is typically done using algorithms such as back-mapping. However, these algorithms increase computational cost and are time-consuming and labor-intensive. Based on the invariance of plastic properties, an explicit expression for the plastic strain increment can be obtained, thus avoiding the use of methods such as the return mapping algorithm. The explicit expression for the plastic strain increment directly establishes the connection between the plastic strain increment and the stress increment. When calculating plastic properties, it is necessary to define the equivalent plastic strain, equivalent plastic stress, and the functional relationship between them. However, according to the above analysis, if the fiber direction is used as the principal axis of the orthotropic material, the obtained stress state is not accurate enough, and the error increases with the increase of the finite deformation. In the explicit expression for the plastic strain increment, the plastic strain increment depends on the stress increment. An inaccurate stress state will lead to inaccurate plastic behavior. Therefore, for two-dimensional woven composites, it is of great theoretical and engineering significance to develop a plastic model that takes into account the nonlinear behavior of fibers and the fiber redirection behavior. Summary of the Invention

[0006] The primary purpose of this invention is to overcome the shortcomings of existing theories, namely, that they fail to consider the fact that after fiber reorientation, the fiber orientation of two-dimensional woven composites no longer aligns with the principal axes of the orthotropic material. This method provides a macroscopic mechanical constitutive model for two-dimensional woven composites under finite deformation. This method ensures that the two-dimensional woven composite retains orthotropy under finite deformation and enables accurate and reliable prediction of the stress-strain response of the two-dimensional woven composite after fiber reorientation under finite deformation, providing a reliable constitutive model for characterizing and analyzing the mechanical properties of two-dimensional woven composites.

[0007] The present invention is implemented as follows: The nonlinearity of the macroscopic mechanical constitutive model for two-dimensional woven composite materials under finite deformation is divided into two parts: geometric nonlinearity caused by fiber reorientation and material nonlinearity caused by plastic behavior. Its establishment includes the following process:

[0008] Step 1: Determine the initial material constants of the orthotropic constitutive model;

[0009] Step 2: Analyze the transformation of material properties with applied deformation and determine the geometric nonlinear parameters;

[0010] Step 3: Establish a plastic constitutive model and determine the nonlinear parameters of the material.

[0011] The step 1 specifically includes the following steps:

[0012] Step 1.1: Determine the principal axes of the orthotropic material. For composite material models, there are three types of symmetry: reflection symmetry, rotational symmetry, and translational symmetry. Translational symmetry is defined as the coincidence of a structure of infinite size with the original structure after translation along a certain distance. Reflection symmetry is defined as the coincidence of a structure of infinite or finite size with the original structure after mirroring along a plane in space. The perpendicular axis of this plane is called the reflection symmetry axis. Rotational symmetry is defined as the coincidence of a structure of infinite or finite size with the original structure after rotation about a certain axis through a certain angle. This axis is called the rotational symmetry axis. Rotational symmetry refers to the coincidence of a structure with the original structure after rotation 180 degrees about a certain axis. The application of translational symmetry is mainly focused on the representative volume element analysis (RVE) method. The plane perpendicular to the reflection symmetry axis or rotational symmetry axis is the elastic symmetry plane of a material. A material with two orthogonal elastic symmetry planes must have a third elastic symmetry plane, and the three elastic symmetry planes are orthogonal to each other. For a two-dimensional woven composite material, when the fiber angle is 90 degrees, there are five rotational symmetry axes: the fiber direction (two), the fiber angle bisector direction (two), and the direction perpendicular to the two-dimensional plane (one); after the fiber is reoriented, there are three rotational symmetry axes: the fiber angle bisector direction (two), and the direction perpendicular to the two-dimensional plane (one). Therefore, the two fiber angle bisectors and the direction perpendicular to the two-dimensional plane can be used as the main axes of the orthotropic material.

[0013] Step 1.2: Calculate the initial material constants for the principal axes of the material determined in Step 1.1.

[0014] Since the current material constant test methods for composite materials are all based on orthotropic constitutive models with the fiber direction as the material's principal axis (ASTM D7078, D3518, D3039, etc.), additional calculations are required to obtain the material constants with the fiber angle bisector as the material's principal axis. According to tensor analysis theory, for a K-order tensor A in n-dimensional space, its components in two coordinate systems have the following conversion relationship:

[0015]

[0016] in Indicates the conversion coefficient, e' i and e r Represent the basis vectors of the two coordinate systems respectively. By transforming the elastic tensor or the flexibility tensor, the constitutive relation with the fiber angle bisector as the principal axis of the material can be obtained. However, since additional transformations are required to obtain the material constants, it is not intuitive enough. In particular, for a second-order tensor B in a 3D space, formula (1) can be expressed in the following matrix form:

[0017]

[0018] Where [B] represents the matrix composed of the components of the tensor B, and the components of the [β] matrix are the coordinate system conversion coefficients. Therefore, the components of the stress tensor σ and strain tensor ε under the fiber angle bisector as the material principal axis can be obtained by formula (2). Then, the stress vector is obtained by using the Voigt reduction representation. and strain vector The expression is:

[0019]

[0020] where σ ij and ε ij Represent the components of stress tensor σ and stress tensor ε respectively. From this, we can get the stress vector under Voigt reduction representation and strain vector The transformation matrix is ​​expressed as:

[0021]

[0022] Since the flexibility matrix [S] has the following form:

[0023]

[0024] and Therefore, the initial material constants can be obtained by converting the flexibility matrix [S] into a coordinate system with the fiber angle bisector as the material principal axis. The conversion formula is as follows:

[0025]

[0026] The material constants with the fiber angle bisector as the material principal axis can be decoupled from [S'].

[0027] Since the initial fiber angle is 90 degrees, it is only necessary to rotate the coordinate system with the fiber direction as the material principal axis 45 degrees along the three axes to obtain the coordinate system with the fiber angle bisector as the material principal axis. According to the method in step 1.1, the material constants with the fiber angle bisector as the material principal axis can be obtained.

[0028] The step 2 specifically includes the following steps:

[0029] Step 2.1: Calculate the fiber angle after deformation. Establish an RVE model with the X-axis and Y-axis as the fiber direction. Apply periodic boundary conditions:

[0030]

[0031] in is the displacement gradient. According to the theory of continuum mechanics, the deformation gradient F can be calculated by the following formula:

[0032]

[0033] The angle between the two vectors in the current configuration after deformation The cosine value can be calculated by the following formula:

[0034]

[0035] Step 2.2: Select the stress tensor and strain tensor to establish the constitutive relation. PK-II Tensor and Green's strain tensor E G It is an energy duality, so the orthogonal anisotropic basis is established between the two. The Green strain tensor E is calculated by the following formula G :

[0036] E G =1 / 2×(F T FI) (10)

[0037] The second type of Piola-Kirchhoff stress σ is calculated by the following formula PK-II :

[0038] σ PK-II =JF -1 ·σ·F -T =F -1 ·σ PK-I (11)

[0039] where σ PK-I is the first-kind Piola-Kirchhoff stress tensor, which is directly obtained from the RVE model, and J is the determinant of the deformation gradient F.

[0040] Step 2.3: Determine the variation trend and parameters of material constants with fiber reorientation behavior in the coordinate system with the fiber angle plane as the principal axis of the material. By setting the first kind of Piola-Kirchhoff stress tensor σ PK-I In the following form:

[0041]

[0042] The modulus can be calculated by applying a uniaxial tensile or compressive load to the RVE in the 1-direction coordinate system with the fiber angle plane as the material's principal axis, where a positive V indicates tension in the 1-direction and a negative V indicates compression in the 1-direction. Combining formulas (9) to (11), the trend of the modulus in the 1-direction as a function of fiber redirection behavior can be obtained, allowing the geometric nonlinear parameters to be calibrated. Since the angle between the fibers in the 2-direction is complementary to the angle between the fibers in the 1-direction, the trend of the modulus in the 2-direction as a function of fiber redirection behavior is also established.

[0043] The change trends of the remaining materials are determined based on continuum damage mechanics.

[0044] The step three specifically includes the following steps:

[0045] Step 3.1: Determine the plastic potential. The strain increment can be decomposed into the following two parts:

[0046] dε=dε el +dε pl (13)

[0047] where dε el is the elastic strain increment, and its relationship with the stress increment is determined by steps 1 and 2. pl is the plastic strain increment, which is obtained from the following formula:

[0048]

[0049] Where f is the plastic potential and dλ is the calculation factor. From formula (13), it can be seen that the plastic strain and elastic strain are decoupled, so the coordinate transformation can be performed separately. That is, the plastic strain and elastic strain in different coordinate systems can be obtained by combining formula (2).

[0050] Since plastic deformation can be divided into two parts: spherical deformation and deviatoric deformation, the plastic potential can also be divided into the spherical function f dev And the partial function f dil , the expression is:

[0051]

[0052] Since the plastic deformation in the fiber direction is very small, it is assumed that the plastic deformation in the fiber direction is caused by the partial deformation. The angle between the fiber and the 1 direction after deformation is According to formula (2), the spherical plastic strain is converted to two fiber directions and can be obtained:

[0053]

[0054] Formula (16) shows that:

[0055]

[0056] Then f dev Corrected to:

[0057]

[0058] Step 3.2: Determine the explicit expression for the plastic strain increment. Defined as:

[0059]

[0060] The expression for the calculation factor display is obtained by calculating the plastic work:

[0061]

[0062] Formula (20) shows that:

[0063]

[0064] in Represents the equivalent plastic strain, which is related to the equivalent stress There is the following relationship between them:

[0065]

[0066] According to formula (14), the explicit expression of plastic strain increment is:

[0067]

[0068] Step 3.3: Calibrate the parameters in the plasticity model. Perform an eccentric tension or compression test with the load direction as the x-direction and use formula (2) to obtain the stress components in the coordinate system with the fiber angle bisector as the material principal axis:

[0069]

[0070] According to formula (19), the equivalent stress for:

[0071]

[0072] The equivalent plastic strain is calculated by the following formula:

[0073]

[0074] in is the plastic strain in the loading direction, which is calculated by the following formula:

[0075]

[0076] The modulus in the loading direction is obtained by converting the eccentric experimental plastic strain-stress data in different directions into equivalent plastic strain-equivalent stress data using formulas (24) to (27) to calibrate the plastic potential parameters and determine the parameters of the power function in formula (22).

[0077] The Chinese annotations of the letters in this invention are summarized as follows:

[0078] A: K-order tensor in n-dimensional space; β: coordinate system conversion coefficient; e: coordinate system basis vector; B: 2-order tensor in 3-dimensional space; [B]: matrix composed of the components of tensor B; [β]: matrix composed of coordinate system conversion coefficient β; σ: stress tensor; ε: strain tensor; Stress vector in Voigt reduced representation; Strain vector in Voigt reduced representation; [T] σ : stress vector transformation matrix under Voigt reduction representation; [T] ε : strain vector transformation matrix under Voigt reduction representation; [S]: flexibility matrix; displacement gradient; F: deformation gradient; The angle between fibers; σ PK-I : Piola-Kirchhoff stress tensor of the first kind; σ PK-II : Piola-Kirchhoff stress tensor of the second kind; E G : Green's strain tensor; dε: strain increment; dε el : elastic strain increment; dε pl : plastic strain increment; f: plastic potential; dλ: calculation factor; f dev : plastic potential sphere function; f dil : Plastic potential partial function; a1: Plastic potential parameter; b1: Plastic potential parameter; ε pl-dev : plastic strain spherical deflection; Equivalent stress; Equivalent plastic strain; A: power function parameter; n: power function parameter; σ x : stress in the tensile direction of the eccentric tensile test; Plastic strain in the tensile direction of eccentric tensile test; E x : modulus in the tensile direction of the eccentric tensile test; k: fiber orientation parameter.

[0079] The beneficial effects of the present invention compared with the prior art are:

[0080] Unlike traditional unidirectional composite materials, the present invention's two-dimensional woven composite materials contain fibers in both the warp and weft directions. Compared to existing finite deformation theories based on the fiber direction as the principal axis of orthotropic materials, the present invention offers the following advantages: It establishes a macroscopic mechanical constitutive model for two-dimensional woven composite materials that remains orthotropic under finite deformation. This plasticity model also considers the plastic behavior in the fiber direction.

[0081] The prediction results of the present invention have been verified by experimental data, and the analysis method of the present invention is more consistent with the experimental results and has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 Schematic diagram of the RVE model of the present invention;

[0083] Figure 2 This is a comparison diagram of the RVE of the present invention and the theoretically calculated fiber angle.

[0084] Figure 3 This is the curve of the fiber angle flat direction modulus changing with the fiber angle of the present invention.

[0085] Figure 4 The plastic strain-equivalent stress curve of the eccentric tensile test of the present invention is

[0086] Figure 5 This is the equivalent plastic strain-equivalent stress curve of the eccentric tensile test of the present invention.

[0087] Figure 6 These are the stress-strain curves at various eccentric angles obtained through finite element prediction and experiments of the present invention. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solution and effect of the present invention clearer and more specific, the following examples are given to further illustrate the present invention in detail. It should be noted that the specific implementation described here is only used to explain the present invention and is not intended to limit the present invention.

[0089] Eccentric tensile test analysis

[0090] Step 1: Calculate the initial material constants in the coordinate system with the fiber angle bisector as the material principal axis.

[0091] First, the flexibility matrix before conversion is established according to formula (5) in the above specification:

[0092]

[0093] Since the initial angle of the fiber is 90 degrees, it is only necessary to rotate the coordinate system with the fiber direction as the material principal axis 45 degrees along the three axes to obtain the coordinate system with the fiber angle bisector as the material principal axis. The [β] matrix has the following form:

[0094]

[0095] Substituting formula (29) into formula (2) yields the stress tensor σ and stress tensor ε when the fiber angle bisector is the principal axis of the material. The stress tensor σ and stress tensor ε are then expressed in Voigt reduction notation to obtain the stress vector in Voigt reduction notation: and strain vector The transformation matrix:

[0096]

[0097] Substituting formula (30) into formula (6) yields the converted flexibility matrix:

[0098]

[0099] According to the above process, the material constants in the coordinate system with the fiber direction as the material principal axis in Table 1 are converted through formulas (2) to (6) to obtain the initial material constants in the coordinate system with the fiber angle bisector as the material principal axis as shown in Table 2.

[0100] Table 1. Mechanical properties of two-dimensional glass fiber plain weave composite single-layer plate before conversion

[0101]

[0102] Table 2. Mechanical properties of converted two-dimensional glass fiber plain weave composite single-layer board

[0103]

[0104] Step 2: Establish the RVE model as Figure 1 As shown, the volume V RVE =0.22×1.25×1.25. Use formula (12) to apply uniaxial tension and compression loads in one direction in a coordinate system with the fiber angle bisector as the material principal axis. For uniaxial tension, apply the following load:

[0105]

[0106] For unidirectional compression, apply the following load:

[0107]

[0108] The changes in the cosine value of the fiber angle in the finite element results and the theoretical calculation during the loading process are calculated respectively. The theoretical calculation is performed in the following way. First, the displacement of the reference point in the RVE is established, and the displacement gradient is established. Then the deformation gradient F is calculated by formula (8); finally, because the x-axis and y-axis of the coordinate system in the RVE model are along the fiber direction, we set as well as Substituting into formula (9) we can get the theoretical cosine value of the fiber angle.

[0109] Comparing the fiber angles obtained by finite element results and theoretical calculations, such as Figure 2 As shown in Figure 2, the established RVE is consistent with the theoretical results, proving the effectiveness of RVE. The second-type Piola-Kirchhoff stress σ is calculated using formulas (10) and (11): PK-II Tensor and Green's strain tensor E G Calculate the modulus under different fiber angles, and the fitting curve is as follows Figure 3 As shown. The Young's modulus in three directions in the coordinate system with the fiber angle bisector as the material principal axis is obtained:

[0110]

[0111] Considering this modulus change as a kind of "damage", the change of shear modulus with fiber angle can be obtained according to the theory of continuous damage mechanics:

[0112]

[0113] According to Maxwell's theorem, the Poisson's ratio in each direction changes with the fiber angle:

[0114]

[0115] Therefore, the flexibility matrix of a two-dimensional woven composite material at any fiber angle is given by:

[0116]

[0117] Step 3: Perform eccentric tensile tests at 0, 15, 30, and 45 degrees. To avoid confusion, the degrees here refer to the angle at which the fiber deviates from the loading direction. The plastic strain-stress curve is obtained according to formula (27): Figure 4 Combining formulas (25) and (26), the equivalent plastic strain-stress curve is obtained as follows: Figure 5 As shown in Table 3, the parameters in formula (19) are obtained by calibration.

[0118] Table 3. Plastic potential parameters

[0119]

[0120] The plastic potential f and equivalent stress of this material are for:

[0121]

[0122] The expression for plastic strain increment is given in matrix form:

[0123]

[0124] Step 4: Verify the validity of the model. The orthotropic elastic constitutive model of the two-dimensional woven composite material under the fiber redirection behavior is established by formula (37), and the plastic behavior of the two-dimensional woven composite material is calculated by formula (39). The VUMAT subroutine of ABAQUS is used to establish the above macroscopic mechanical constitutive model, and the experimental results are compared with the simulation results. Figure 6 As shown in Figure 3, the good agreement indicates that the established model can effectively predict the nonlinear stress-strain response of two-dimensional woven composites under finite deformation.

[0125] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A method for constructing a mechanical constitutive model for a two-dimensional woven composite material, characterized in that: The method described is divided into two parts: geometric nonlinearity caused by fiber reorientation and material nonlinearity caused by plastic behavior. Its establishment includes the following process: Step 1: Determine the initial material constants of the orthotropic constitutive model; Step 2: Analyze the transformation of material properties with applied deformation and determine the geometric nonlinear parameters; Step 3: Establish a plastic constitutive model and determine the nonlinear parameters of the material. Step 3 is specifically as follows: Step 3.1: Determine the plastic potential: The strain increment can be decomposed into the following two parts: dε=dε el +dε pl (13) where dε el is the elastic strain increment, and its relationship with the stress increment is determined by steps 1 and 2; dε pl is the plastic strain increment, which is obtained from the following formula: Where f is the plastic potential and dλ is the calculation factor. From formula (13), it can be seen that the plastic strain and the elastic strain are decoupled, so the coordinate transformation can be performed separately. That is, the plastic strain and elastic strain in different coordinate systems can be obtained by combining formula (2). Since plastic deformation can be divided into two parts: spherical deformation and deviatoric deformation, the plastic potential can also be divided into the spherical function f dev And the partial function f dil , the expression is: Since the plastic deformation in the fiber direction is very small, it is assumed that the plastic deformation in the fiber direction is caused by the partial deformation; and the angle between the fiber and the 1 direction after deformation is According to formula (2), the spherical plastic strain is converted to two fiber directions and can be obtained: Formula (16) shows that: Then f dev Corrected to: Step 3.2: Determine the explicit expression for the plastic strain increment: Substitute the equivalent stress Defined as: The expression for the calculation factor display is obtained by calculating the plastic work: Formula (20) shows that: in Represents the equivalent plastic strain, which is related to the equivalent stress There is the following relationship between them: According to formula (14), the explicit expression of plastic strain increment is: Step 3.3: Calibrate the parameters in the plasticity model: Perform an eccentric tension or compression test with the load direction as the x-direction. Use formula (2) to obtain the stress components in the coordinate system with the fiber angle bisector as the material principal axis: According to formula (19), the equivalent stress for: The equivalent plastic strain is calculated by the following formula: in is the plastic strain in the loading direction, which is calculated by the following formula: E x is the modulus in the loading direction; the plastic potential parameters are calibrated and the parameters of the power function in formula (22) are determined by converting the eccentric experimental plastic strain-stress data in different directions into equivalent plastic strain-equivalent stress data through formulas (24) to (27).

2. The method for constructing a mechanical constitutive model for a two-dimensional woven composite material according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1: Determine the principal axes of the orthotropic material: For composite material models, there are three types of symmetry: reflection symmetry, rotational symmetry, and translational symmetry. Translational symmetry is when a structure of infinite size is translated a certain distance in a certain direction and then coincides with the original structure. Reflection symmetry is when a structure of infinite or finite size is mirror-symmetric along a plane in space and then coincides with the original structure. The vertical axis of this plane is called the reflection symmetry axis. Rotational symmetry is when a structure of infinite or finite size is rotated along a certain axis in space by a certain angle and then coincides with the original structure. This axis is called the rotational symmetry axis. Rotational symmetry means that the structure coincides with the original structure after being rotated 180 degrees along a certain axis. The application of translational symmetry is mainly concentrated in the representative volume element analysis method RVE; the plane perpendicular to the reflection symmetry axis or the rotational symmetry axis is the elastic symmetry plane of a material. A material with two orthogonal elastic symmetry planes must have a third elastic symmetry plane, and the three elastic symmetry planes are orthogonal to each other; for two-dimensional woven composite materials, when the fiber angle is 90 degrees, there are 5 rotational symmetry axes, namely: 2 fiber directions, 2 fiber angle bisector directions, and 1 perpendicular to the two-dimensional plane direction; after fiber redirection, there are 3 rotational symmetry axes, namely: 2 fiber angle bisector directions, and 1 perpendicular to the two-dimensional plane direction; therefore, the two fiber angle bisectors and the direction perpendicular to the two-dimensional plane can be used as the main axes of the orthotropic material.

3. The method for constructing a mechanical constitutive model for a two-dimensional woven composite material according to claim 2, characterized in that: Calculate the initial material constants for the material principal axes determined in step 1.1: According to tensor analysis theory, for a K-order tensor A in n-dimensional space, its components in the two coordinate systems have the following transformation relationship: in Indicates the conversion coefficient, e' i and e r Represent the basis vectors of the two coordinate systems respectively; by transforming the elastic tensor or the flexibility tensor, the constitutive relation with the fiber angle bisector as the principal axis of the material can be obtained, but since additional transformations are required to obtain the material constants, it is not intuitive enough; in particular, for a second-order tensor B in a three-dimensional space, formula (1) can be expressed in the following matrix form: Where [B] represents the matrix composed of the components of the tensor B, and the components of the [β] matrix are the coordinate system conversion coefficients; therefore, the components of the stress tensor σ and stress tensor ε under the fiber angle bisector as the material principal axis can be obtained by formula (2); Then use the Voigt reduction representation to get the stress vector and strain vector The expression is: where σ ij and ε ij denote the components of the stress tensor σ and stress tensor ε respectively; from this, the stress vector in Voigt reduction representation can be obtained and strain vector The transformation matrix is ​​expressed as: Since the flexibility matrix [S] has the following form: and Therefore, the initial material constants can be obtained by converting the flexibility matrix [S] into a coordinate system with the fiber angle bisector as the material principal axis. The conversion formula is as follows: The material constants with the fiber angle bisector as the material principal axis can be decoupled from [S']; Since the initial fiber angle is 90 degrees, it is only necessary to rotate the coordinate system with the fiber direction as the material principal axis 45 degrees along the three axes to obtain the coordinate system with the fiber angle bisector as the material principal axis. According to the method in step 1.1, the material constants with the fiber angle bisector as the material principal axis can be obtained.

4. The method for constructing a mechanical constitutive model for a two-dimensional woven composite material according to claim 3, characterized in that: The step 2 is specifically as follows: Step 2.1: Calculate the fiber angle after deformation: Establish an RVE model with the X-axis and Y-axis as the fiber direction; apply periodic boundary conditions: in is the displacement gradient. According to the theory of continuum mechanics, the deformation gradient F can be calculated by the following formula: The angle between the two vectors in the current configuration after deformation The cosine value can be calculated by the following formula: Step 2.2: Select stress tensor and strain tensor to establish constitutive relations: Due to the second-type Piola-Kirchhoff stress σ PK-II Tensor and Green's strain tensor E G is an energy dual, so the orthogonal anisotropic constitution is established between the two; The Green strain tensor E is calculated by the following formula G : HAVE BEEN G =1 / 2×(F T FI)(10) The second type of Piola-Kirchhoff stress σ is calculated by the following formula PK-II : s PK-II =JF -1 ·s·F -T =F -1 ·s PK-I (11) where σ PK-I is the first-kind Piola-Kirchhoff stress tensor, which is directly obtained from the RVE model, and J is the determinant value of the deformation gradient F; Step 2.3: Determine the variation trend and parameters of material constants with fiber reorientation behavior in the coordinate system with the fiber angle plane as the principal axis of the material; by setting the first-class Piola-Kirchhoff stress tensor σ PK-I In the following form: The RVE can be subjected to a unidirectional tensile or compressive load in the 1-direction coordinate system with the fiber angle plane as the principal axis of the material, thereby calculating the modulus, where a positive V indicates tension in the 1-direction and a negative V indicates compression in the 1-direction. Combining formulas (9) to (11), the trend of the modulus in the 1-direction with the fiber redirection behavior can be obtained, and the geometric nonlinear parameters can be calibrated. Since the angle between the fibers in the 2-direction is complementary to the angle between the fibers in the 1-direction, the trend of the modulus in the 2-direction with the fiber redirection behavior can also be established. The change trends of the remaining materials are determined based on continuum damage mechanics.

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