A method for constructing an elastoplastic constitutive model of thermoplastic composite material
By constructing an initial yield criterion and a hybrid hardening model that consider tension-compression anisotropy, the problem of the inability to accurately describe the stress-strain relationship of thermoplastic composites in the existing technology is solved, and high-precision stress-strain relationship prediction under complex loading conditions is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA AIRPLANT STRENGTH RES INST
- Filing Date
- 2026-06-08
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies, when describing the stress-strain relationship of thermoplastic composites, neglect the anisotropic effect of tension and compression and the complex hardening behavior, resulting in an inability to accurately describe their mechanical behavior.
An initial yield criterion and a hybrid hardening model considering tension-compression anisotropy are constructed. The movement of the yield surface center is described by the Armstrong-Frederick nonlinear kinematic hardening model, and the changes in the shape and size of the yield surface are characterized by the exponential hardening model. Plastic flow rules and consistency conditions are established, and the consistency tangent stiffness matrix is derived.
It achieves high-precision prediction of stress-strain relationship of thermoplastic composites under complex loading conditions, breaking through the limitations of existing technology and enabling a more accurate description of tension-compression anisotropy effect and hardening behavior.
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Abstract
Description
Technical Field
[0001] This application relates to the field of mechanical analysis technology of composite materials, and in particular to a method for constructing an elastoplastic constitutive model of thermoplastic composite materials. Background Technology
[0002] Thermoplastic composites have attracted widespread attention in the aerospace field due to their advantages such as high performance, low cost, and ease of maintenance. The study of their mechanical behavior has become a research hotspot in the international fields of solid mechanics and materials science. Currently, the elastoplastic stress analysis of thermoplastic composites mainly utilizes the anisotropic Hill yield criterion and single-parameter plasticity models. However, the Hill yield criterion neglects the influence of tension-compression anisotropy, and most hardening models are isotropic hardening, failing to consider the influence of complex hardening behaviors. Therefore, it is difficult to accurately describe the stress-strain relationship of thermoplastic composites, necessitating the development of a more effective elastoplastic constitutive model. Summary of the Invention
[0003] In view of this, the embodiments of this application provide a method for constructing an elastoplastic constitutive model of thermoplastic composite materials, considering the initial yield criterion of tension-compression anisotropy, proposing a novel hybrid hardening model that considers the movement and change in size of the yield surface center, and establishing an elastoplastic constitutive model of thermoplastic composite materials, providing a technical approach for high-precision calculation of stress in thermoplastic composite materials.
[0004] This application provides a method for constructing an elastoplastic constitutive model of a thermoplastic composite material, including:
[0005] An initial yield criterion is constructed, and an initial yield function is established based on the stress invariant theory of transversely isotropic composite materials. A hybrid hardening model is constructed to describe the movement of the yield surface center, the shape of the yield surface, and the change in the size of the yield surface during the plastic deformation of the material. A subsequent yield criterion is constructed, and the subsequent yield surface function is obtained based on the initial yield function and the hybrid hardening model. A plastic flow law is constructed, and the relationship between the plastic strain increment and the gradient of the subsequent yield surface function is established based on the subsequent yield surface function. Based on the consistency condition, by combining the stress-strain relationship, the plastic flow rule, and the hybrid hardening model, an explicit expression for the consistent tangent stiffness matrix is obtained.
[0006] According to a specific implementation of this application, the stress invariant theory of the transversely isotropic composite material includes four independent stress invariants, the expressions of which are as follows: , Where I1, I2, I3, and I4 are the first stress invariant, the second stress invariant, the third stress invariant, and the fourth stress invariant, respectively, and σ11 σ 22 σ 33 τ 12 τ 13 and τ 23 These are the principal axial stresses of the material. The first stress component, the second stress component, the third stress component, the fourth stress component, the fifth stress component, and the sixth stress component.
[0007] According to a specific implementation of an embodiment of this application, establishing the initial yield function includes: An expression for the plastic strain increment is established using the correlation flow rule; Considering the longitudinal direction as linear elastic, a simplified initial yield function containing undetermined correlation coefficients is obtained; The yield conditions under longitudinal shear loading, transverse shear loading, transverse tensile loading, and transverse compressive loading are applied to the stress state of material yielding, the undetermined correlation coefficients are determined, and the initial yield function is obtained.
[0008] According to a specific implementation of an embodiment of this application, the expression for the plastic strain increment is: , in, This represents the increment of plastic strain. is the plasticity increment coefficient, which is always positive; f is the yield function; a1, a2, a3, a4, b1, b2 and c 12 These are the first undetermined correlation coefficient, the second undetermined correlation coefficient, the third undetermined correlation coefficient, the fourth undetermined correlation coefficient, the fifth undetermined correlation coefficient, the sixth undetermined correlation coefficient, and the seventh undetermined correlation coefficient, respectively. The expression for the longitudinal linear elasticity is: , in, For plastic strain increment The first component; The expression for the initial yield function is: , Where f(σ,R0) is the initial yield function, R0 is the initial yield strength, and R TT0 R is the transverse tensile yield strength. TC0 R is the transverse compressive yield strength. LS0 R is the in-plane shear yield strength. TS0 This represents the transverse shear yield strength.
[0009] According to a specific implementation of this application, the movement of the yield surface center adopts the Armstrong-Frederick nonlinear kinematic hardening model, which is characterized by the back stress increment equation; the change of the yield surface shape and yield surface size adopts the exponential hardening model, which is characterized by the subsequent yield strength evolution equation.
[0010] According to a specific implementation of an embodiment of this application, the back stress increment equation is: , Where α is the back stress, dα is the back stress increment, and C p For linear strengthening terms, material constants, For the material constants of the dynamic recovery term, This represents the equivalent plastic strain increment. The expression for the subsequent yield strength is: , Where R is the subsequent yield strength, R TT R is the yield strength after transverse tensile stress. TC R is the yield strength following transverse compression. LS R is the in-plane shear subsequent yield strength. TS Q is the subsequent yield strength after transverse shear. TT Q is the first material constant related to the yield strength after transverse tensile stress. TC Q is the first material constant related to the yield strength after transverse compression. LS Q is the first material constant related to the in-plane shear yield strength. TS This is the first material constant related to the yield strength after transverse shear. This is the second material constant related to the yield strength after transverse tensile stress. This is the second material constant related to the yield strength after transverse compression. This is the second material constant related to the yield strength after in-plane shear. This is the second material constant related to the yield strength after transverse shear. This is the equivalent plastic strain.
[0011] According to a specific implementation of an embodiment of this application, the expression for the subsequent yield surface function is: , in, This is the subsequent yield surface function.
[0012] According to a specific implementation of this application, the expression for the relationship between the plastic strain increment and the gradient of the subsequent yield surface function is as follows: , Where N is the plastic flow direction function.
[0013] According to a specific implementation of an embodiment of this application, the expression for the consistency condition is:
[0014] , in, Effective stress is expressed as the difference between the principal axial stress and the back stress of the material. The expression for the stress-strain relationship is: , , Among them, C 0 Here is the elastic stiffness matrix. For elastic strain increment, This represents the total strain increment.
[0015] According to a specific implementation of this application, the explicit expression of the uniform tangent stiffness matrix is: , in, This is the uniform tangent stiffness matrix.
[0016] Beneficial effects: The method for constructing the elastoplastic constitutive model of thermoplastic composites in this application determines the undetermined coefficients of the initial yield criterion by utilizing yield data under different loading conditions. This clearly distinguishes between transverse tensile yield strength and transverse compressive yield strength in the yield criterion, thus overcoming the technical limitation of the existing Hill yield criterion that ignores the influence of tensile-compressive anisotropy. It can accurately describe the transverse tensile-compressive anisotropy effect of thermoplastic composites. By employing a hybrid hardening model to simultaneously describe the movement of the yield surface center and the changes in the shape and size of the yield surface, on the one hand, the evolution of back stress is described using the nonlinear kinematic hardening model proposed by Armstrong and Frederick, achieving accurate capture of the movement of the yield surface center; on the other hand, the evolution of subsequent yield strength is described using an exponential hardening model, achieving accurate characterization of yield surface expansion and shape distortion. This hybrid hardening model combines the advantages of both isotropic hardening and kinematic hardening, enabling a more comprehensive description of the hardening behavior of thermoplastic composites under complex loading conditions, especially the description of the differences in hardening laws in different loading directions. This significantly improves the model's prediction accuracy of stress-strain relationships under complex loading conditions. By establishing a complete theoretical system from the initial yield criterion to the subsequent yield criterion, from the hardening evolution law to the flow law, and from the plasticity increment coefficient to the uniform tangential stiffness matrix, the system fully considers the tensile-compressive anisotropy effect and complex hardening behavior of materials, providing a reliable technical approach for high-precision stress calculation of thermoplastic composite structures. Attached Figure Description
[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0018] Figure 1 This is a flowchart of a method for constructing an elastoplastic constitutive model of a thermoplastic composite material according to an embodiment of the present invention. Detailed Implementation
[0019] The embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0020] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0021] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0022] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0023] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0024] This application provides a method for constructing an elastoplastic constitutive model of thermoplastic composite materials. The initial yield function is established in the form of a quadratic polynomial of stress invariants. A hybrid hardening model is used to simultaneously describe the movement of the yield surface center and the changes in the shape and size of the yield surface. A plastic flow rule is established based on relevant flow rules. The uniform tangent stiffness matrix is derived according to the consistency condition, thereby achieving a high-precision description of the elastoplastic mechanical behavior of thermoplastic composite materials.
[0025] In one embodiment, a method for constructing an elastoplastic constitutive model of a thermoplastic composite material is provided, referring to... Figure 1This includes the following steps: An initial yield criterion is constructed, and an initial yield function is established based on the stress invariant theory of transversely isotropic composite materials. A hybrid hardening model is constructed to describe the movement of the yield surface center, the shape of the yield surface, and the change in the size of the yield surface during the plastic deformation of the material. A subsequent yield criterion is constructed, and the subsequent yield surface function is obtained based on the initial yield function and the hybrid hardening model. A plastic flow law is constructed, and the relationship between the plastic strain increment and the gradient of the subsequent yield surface function is established based on the subsequent yield surface function. Based on the consistency condition, by combining the stress-strain relationship, the plastic flow rule, and the hybrid hardening model, an explicit expression for the consistent tangent stiffness matrix is obtained.
[0026] In one embodiment, unidirectional fiber-reinforced composite materials are typically considered transversely isotropic materials. The stress invariant theory of such transversely isotropic composite materials includes four independent stress invariants, expressed as follows: (1), Where I1, I2, I3, and I4 are the first stress invariant, the second stress invariant, the third stress invariant, and the fourth stress invariant, respectively, and σ 11 σ 22 σ 33 τ 12 τ 13 and τ 23 These are the principal axial stresses of the material. The first stress component, the second stress component, the third stress component, the fourth stress component, the fifth stress component, and the sixth stress component.
[0027] Furthermore, the initial yield function can be Taylor-expanded into a power series of stress invariants. The quadratic form typically shows good agreement with experimental data; therefore, the yield function can be cut off to the quadratic term of the stress. This yields the following expression: (2), Where f(σ,R0) is the initial yield function, and a1, a2, a3, a4, b1, b2, and c are... 12 These are the first undetermined correlation coefficient, the second undetermined correlation coefficient, the third undetermined correlation coefficient, the fourth undetermined correlation coefficient, the fifth undetermined correlation coefficient, the sixth undetermined correlation coefficient, and the seventh undetermined correlation coefficient, respectively. R0 is the initial yield strength, which has 6 components, R LT0 R LC0 R TT0 R TC0 R LS0 RTS0 These are respectively represented as longitudinal tensile yield strength, longitudinal compressive yield strength, transverse tensile yield strength, transverse compressive yield strength, in-plane shear yield strength, and transverse shear yield strength.
[0028] Furthermore, establishing the initial yield function includes: An expression for the plastic strain increment is established using the correlation flow rule; Considering the longitudinal direction as linear elastic, a simplified initial yield function containing undetermined correlation coefficients is obtained; The yield conditions under longitudinal shear loading, transverse shear loading, transverse tensile loading, and transverse compressive loading are applied to the stress state of material yielding, the undetermined correlation coefficients are determined, and the initial yield function is obtained.
[0029] Furthermore, using the correlation flow rule, the expression for the plastic strain increment is: (3), in, This represents the increment of plastic strain. is the plasticity increment coefficient, which is always positive; f is the yield function; a1, a2, a3, a4, b1, b2 and c 12 These are the first undetermined correlation coefficient, the second undetermined correlation coefficient, the third undetermined correlation coefficient, the fourth undetermined correlation coefficient, the fifth undetermined correlation coefficient, the sixth undetermined correlation coefficient, and the seventh undetermined correlation coefficient, respectively. Considering the longitudinal direction (fiber direction) to be linearly elastic, we have the following expression: (4), in, For plastic strain increment The first component; Therefore, the solution can be obtained as follows: (5); Therefore, the initial yield function simplifies to: (6), Among them, a2, a3, a4, and b2 are still undetermined correlation coefficients, totaling 4; Initial yield strength, with 4 components.
[0030] Considering longitudinal and transverse shear loading until the material yields: (7), Substituting this into the formula (6) for the initial yield function: (8), Therefore, we can solve for: (9).
[0031] Similarly, consider the transverse tension and compression to the material yield, and substitute them into the formula (6) of the initial yield function: (10) (11), Therefore, we can conclude that: (12) Therefore, the initial yield function is completely determined, and its expression is: (13) Where f(σ,R0) is the initial yield function, R0 is the initial yield strength, and R TT0 R is the transverse tensile yield strength. TC0 R is the transverse compressive yield strength. LS0 R is the in-plane shear yield strength. TS0 This represents the transverse shear yield strength.
[0032] In one embodiment, the movement of the yield surface center is characterized by the Armstrong-Frederick nonlinear kinematic hardening model, which is described by the back stress increment equation; the changes in the yield surface shape and size are characterized by the exponential hardening model, which is described by the subsequent yield strength evolution equation.
[0033] Furthermore, the equation for the incremental back stress is: , Where α is the back stress, dα is the back stress increment, and C p For linear strengthening terms, material constants, For dynamic recovery term material constants; The equivalent plastic strain increment is defined in this embodiment as the plastic strain increment. The 2-norm (modulus) of a second-order symmetric tensor, which can be simplified to a one-dimensional vector. The expression for the subsequent yield strength is: , Where R is the subsequent yield strength, R TT R is the yield strength after transverse tensile stress. TC R is the yield strength following transverse compression. LS R is the in-plane shear subsequent yield strength. TS Q is the subsequent yield strength after transverse shear. TT Q is the first material constant related to the yield strength after transverse tensile stress. TCQ is the first material constant related to the yield strength after transverse compression. LS Q is the first material constant related to the in-plane shear yield strength. TS This is the first material constant related to the yield strength after transverse shear. This is the second material constant related to the yield strength after transverse tensile stress. This is the second material constant related to the yield strength after transverse compression. This is the second material constant related to the yield strength after in-plane shear. This is the second material constant related to the yield strength after transverse shear. This is the equivalent plastic strain.
[0034] Furthermore, the expression for the subsequent yield surface function is: , in, This is the subsequent yield surface function.
[0035] In practice, the hardening model describes the changes in the shape and position of the yield surface during material deformation, which is related to the material's stress state, hardening parameters, and plastic strain. Currently, models describing the hardening behavior of materials during plastic deformation can be categorized into isotropic hardening models, kinematic hardening models, and hybrid hardening models. The isotropic hardening model shows that the shape and center of the yield surface remain unchanged, and the yield surface uniformly enlarges and shrinks; the kinematic hardening model shows that the size and shape of the yield surface remain unchanged, and the center of the yield surface moves with the stress state and loading history; the hybrid hardening model shows that the center, size, and shape of the yield surface all change with the stress state and loading history. This embodiment uses a hybrid hardening model, and the subsequent yield surface function is expressed as: (14) in The back stress represents the movement of the center of the yield surface; The subsequent yield strength represents the change in the shape and size of the yield surface. This is applied when the movement of the yield surface center is not considered (back stress is zero). When each component increases proportionally to the initial yield strength, the yield surface will be uniformly enlarged and reduced (isotropic hardening).
[0036] The shift of the yield surface center is described by the nonlinear kinematic hardening model proposed by Armstrong and Frederick, with the back stress increment taking the following form: (15) in: , Back stress; dα is the back stress increment; For linear strengthening terms, material constants are used. For dynamic recovery term material constants; , This represents the increment of plastic strain. , This represents the equivalent plastic strain increment.
[0037] The subsequent yield strength is selected using an exponential hardening model: (16) in, R is the subsequent yield strength.
[0038] In one embodiment, the relationship between the plastic strain increment and the gradient of the subsequent yield surface function is expressed as follows: , Where N is the plastic flow direction function.
[0039] In specific implementation, the construction of the plastic flow rule, based on the subsequent yield surface function, establishes the relationship between the plastic strain increment and the gradient of the subsequent yield surface function, including: Prager and Drucker, based on elastic potential theory, proposed that a plastic potential function G also exists during the plastic deformation stage, and established a similar plastic potential theory to elasticity. This theory states that for generally stable materials, the direction of the plastic strain increment is consistent with the gradient direction of the plastic potential function G. (17) in: This is the plasticity increment coefficient, which is always positive; N is a function of the direction of plastic flow; This represents the magnitude of the gradient of the plastic potential function.
[0040] Obviously, according to the formula for calculating the equivalent plastic strain increment, we can obtain: (18) Assuming that the plastic deformation of the material satisfies the relevant flow laws, and the plastic potential function G is taken as the yield criterion f, then the plastic strain increment is as follows: (19).
[0041] In one embodiment, the expression for the consistency condition is:
[0042] , in, Effective stress is expressed as the difference between the principal axial stress and the back stress of the material. The expression for the stress-strain relationship is: , , Among them, C 0 Here is the elastic stiffness matrix. For elastic strain increment, This represents the total strain increment.
[0043] Furthermore, the explicit expression for the uniform tangent stiffness matrix is: , in, This is the uniform tangent stiffness matrix.
[0044] In specific implementation, the explicit expression for the uniform tangent stiffness matrix is obtained by simultaneously applying the stress-strain relationship, the plastic flow rule, and the hybrid hardening model based on the consistency condition, including: During the yielding process of a material, the yield function value remains zero, and the rate of change of the yield function also remains zero. This condition is called the uniformity condition. According to the subsequent yield criterion, the uniformity condition is as follows: (20) , Effective stress is expressed as the difference between the principal axial stress and the back stress of the material. in: (twenty one); The total strain increment of a material is equal to the sum of the elastic strain increment and the plastic strain increment, as shown in formula (22): (twenty two), This represents the elastic strain increment. This represents the total strain increment; After a material reaches plastic yield, the stress-strain relationship can be expressed as: (twenty three), in: This is the elastic stiffness matrix.
[0045] Substituting equations (15) and (23) into equation (21): (twenty four), Differentiating equation (16) yields: (25), Substituting equations (24) and (25) into equation (20), we get: (26) Therefore, we can solve for: (27) Substituting equation (27) into equation (23), we get: (28) Therefore, the uniform tangent stiffness matrix is: (29) — Uniform tangent stiffness matrix.
[0046] Compared with existing technologies that use the traditional Hill yield criterion and single-parameter hardening model, the technical solution of this invention can more accurately describe the transverse tensile-compressive anisotropy effect of thermoplastic composites, more accurately capture the movement of the yield surface center under cyclic loading, and more comprehensively characterize the evolution of the yield surface shape and size. This significantly improves the accuracy of stress calculation for thermoplastic composite structures and provides more reliable technical support for the safety assessment of aerospace structures.
[0047] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for constructing an elastoplastic constitutive model of a thermoplastic composite material, characterized in that, include: An initial yield criterion is constructed, and an initial yield function is established based on the stress invariant theory of transversely isotropic composite materials. A hybrid hardening model is constructed to describe the movement of the yield surface center, the shape of the yield surface, and the change in the size of the yield surface during the plastic deformation of the material. A subsequent yield criterion is constructed, and the subsequent yield surface function is obtained based on the initial yield function and the hybrid hardening model. A plastic flow law is constructed, and the relationship between the plastic strain increment and the gradient of the subsequent yield surface function is established based on the subsequent yield surface function. Based on the consistency condition, by combining the stress-strain relationship, the plastic flow rule, and the hybrid hardening model, an explicit expression for the consistent tangent stiffness matrix is obtained.
2. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 1, characterized in that, The stress invariant theory of the transversely isotropic composite material includes four independent stress invariants, expressed as follows: ， Where I1, I2, I3, and I4 are the first stress invariant, the second stress invariant, the third stress invariant, and the fourth stress invariant, respectively, and σ 11 σ 22 σ 33 τ 12 τ 13 and τ 23 These are the principal axial stresses of the material. The first stress component, the second stress component, the third stress component, the fourth stress component, the fifth stress component, and the sixth stress component.
3. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 2, characterized in that, The establishment of the initial yield function includes: An expression for the plastic strain increment is established using the correlation flow rule; Considering the longitudinal direction as linear elastic, a simplified initial yield function containing undetermined correlation coefficients is obtained; The yield conditions under longitudinal shear loading, transverse shear loading, transverse tensile loading, and transverse compressive loading are applied to the stress state of material yielding, the undetermined correlation coefficients are determined, and the initial yield function is obtained.
4. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 3, characterized in that, The expression for the plastic strain increment is: ， in, This represents the increment of plastic strain. is the plasticity increment coefficient, which is always positive; f is the yield function; a1, a2, a3, a4, b1, b2 and c 12 These are the first undetermined correlation coefficient, the second undetermined correlation coefficient, the third undetermined correlation coefficient, the fourth undetermined correlation coefficient, the fifth undetermined correlation coefficient, the sixth undetermined correlation coefficient, and the seventh undetermined correlation coefficient, respectively. The expression for the longitudinal linear elasticity is: ， in, For plastic strain increment The first component; The expression for the initial yield function is: ， Where f(σ,R0) is the initial yield function, R0 is the initial yield strength, and R TT0 R is the transverse tensile yield strength. TC0 R is the transverse compressive yield strength. LS0 R is the in-plane shear yield strength. TS0 This represents the transverse shear yield strength.
5. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 4, characterized in that, The movement of the center of the yield surface is characterized by the Armstrong-Frederick nonlinear kinematic hardening model, which is described by the back stress increment equation; the changes in the shape and size of the yield surface are characterized by the exponential hardening model, which is described by the subsequent yield strength evolution equation.
6. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 5, characterized in that, The equation for the back stress increment is: ， Where α is the back stress, dα is the back stress increment, and C p For linear strengthening terms, material constants, For the material constants of the dynamic recovery term, This represents the equivalent plastic strain increment. The expression for the subsequent yield strength is: ， Where R is the subsequent yield strength, R TT R is the yield strength after transverse tensile stress. TC R is the yield strength after transverse compression. LS R is the in-plane shear successor yield strength. TS Q is the subsequent yield strength after transverse shear. TT Q is the first material constant related to the yield strength after transverse tensile stress. TC Q is the first material constant related to the yield strength after transverse compression. LS Q is the first material constant related to the in-plane shear yield strength. TS This is the first material constant related to the yield strength after transverse shear. This is the second material constant related to the yield strength after transverse tensile stress. This is the second material constant related to the yield strength after transverse compression. This is the second material constant related to the yield strength after in-plane shear. This is the second material constant related to the yield strength after transverse shear. This is the equivalent plastic strain.
7. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 6, characterized in that, The expression for the subsequent yield surface function is: ， in, This is the subsequent yield surface function.
8. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 4, characterized in that, The expression for the relationship between the plastic strain increment and the subsequent yield surface function gradient is as follows: ， Where N is the plastic flow direction function.
9. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 7, characterized in that, The expression for the consistency condition is: ， in, Effective stress is expressed as the difference between the principal axial stress and the back stress of the material. The expression for the stress-strain relationship is: ， ， Among them, C 0 Here is the elastic stiffness matrix. For elastic strain increment, This represents the total strain increment.
10. The method for constructing an elastoplastic constitutive model of thermoplastic composite materials according to claim 9, characterized in that, The explicit expression for the uniform tangent stiffness matrix is: ， in, This is the uniform tangent stiffness matrix.