Composite material nonlinear mechanical constitutive model construction and finite element analysis method
By establishing orthogonal anisotropic elastoplastic and damage models, the difficulties in describing the nonlinear mechanical response and damage failure process of 2D C/SiC composite materials were solved, achieving high-precision finite element simulation and strength prediction, and improving the analytical capabilities of materials under complex loads.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-27
- Publication Date
- 2026-04-10
AI Technical Summary
Existing nonlinear constitutive models for 2D C/SiC composite materials are difficult to describe their nonlinear mechanical response and damage failure process, especially under complex loads such as multiaxial and random loads, where their adaptability and accuracy are poor. Furthermore, numerical implementation can easily lead to poor convergence and accuracy of finite element solutions.
An orthotropic elastoplastic model was established. By defining the orthotropic linear elastic constitutive equation, stiffness matrix, yield equation, and plastic potential function of the composite material, the target strain and stress were calculated using the back-mapping algorithm. Combined with the damage model, the consistent tangent stiffness matrix of the orthotropic elastoplastic damage coupling was derived to realize finite element analysis.
It achieves high-precision nonlinear mechanical response and damage simulation of 2D C/SiC composite materials, improves the convergence performance of the finite element solver under complex loads, and accurately predicts material strength and failure process.
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Figure CN121835236A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of finite element analysis, in particular to a composite nonlinear mechanics constitutive model construction and finite element analysis method. BACKGROUND
[0002] 2D C / SiC composite material has significant anisotropy and complex structure, and the existing nonlinear constitutive model is difficult to describe the nonlinear mechanical response and damage failure process at the same time. At present, most of the models are macroscopic phenomenological models, which do not fully consider the anisotropic elastic-plastic behavior of the material under different loading conditions, especially under complex loads such as multi-axial and random loads. The adaptability and accuracy of the existing model are poor. In addition, the existing constitutive model usually ignores the damage evolution process of the material, cannot associate the material inelastic deformation with the damage process, and cannot effectively predict the strength degradation and failure mechanism of the material.
[0003] In addition, in the numerical implementation process, many elastic-plastic models rely on elastic-plastic stiffness matrix for calculation, which is easy to cause numerical instability in the nonlinear iteration process, resulting in poor convergence and precision of finite element solution, and inaccurate calculation results.
[0004] Therefore, it is urgent to provide a new nonlinear mechanics constitutive model construction and finite element analysis method for 2D C / SiC composite material. SUMMARY
[0005] In order to solve the problems that the traditional nonlinear constitutive model cannot consider the anisotropic elastic-plastic behavior under different loading conditions, cannot associate the material inelastic deformation with the damage process, leads to poor accuracy and prediction effect of the model, and the traditional numerical implementation method also leads to poor convergence and precision of finite element solution, the present application provides a composite nonlinear mechanics constitutive model construction and finite element analysis method.
[0006] In one aspect, a composite nonlinear mechanics constitutive model construction and finite element analysis method is provided, which comprises: defining an orthotropic linear elastic constitutive equation, a stiffness matrix, a yield equation and a plastic potential function of the composite material to define an orthotropic elastic-plastic constitutive model; using a return mapping algorithm to calculate the numerical value of the orthotropic elastic-plastic constitutive model, and calculating the final converged target elastic strain, target plastic strain and target effective stress; determining a consistent tangent stiffness matrix without considering damage based on the plastic mechanics calculation method; The target elastic strain, target plastic strain, target effective stress, and uniform tangent stiffness matrix without considering damage are embedded into the damage model to determine the uniform tangent stiffness matrix of orthotropic elastoplastic damage coupling, thereby obtaining the numerical values of the orthotropic elastoplastic damage constitutive model for finite element calculation and analysis.
[0007] On the other hand, a device for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials is provided, used to implement the steps described in any method embodiment of the specification, the device comprising: Define the unit, which is used to define the orthogonal anisotropic linear elastic constitutive equation, stiffness matrix, yield equation and plastic potential function of composite materials, so as to define the orthogonal anisotropic elastoplastic constitutive model; The calculation unit is used to calculate the numerical values of the orthogonal anisotropic elastoplastic constitutive model using the return mapping algorithm, and to calculate the target elastic strain, target plastic strain and target effective stress that finally converge. The element is defined to determine the uniform tangent stiffness matrix without considering damage, based on plasticity calculations. An embedded unit is used to embed the target elastic strain, the target plastic strain, the target effective stress, and the uniform tangent stiffness matrix without considering damage into the damage model, so as to determine the uniform tangent stiffness matrix of the orthogonal anisotropic elastoplastic damage coupling, obtain the numerical value of the orthogonal anisotropic elastoplastic damage constitutive model, and perform finite element calculation analysis.
[0008] On the other hand, a computer device is provided, the computer device including a memory and a processor, the memory for storing a computer program, and the processor for executing the computer program stored in the memory to implement the steps of the method described above.
[0009] On the other hand, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when the computer program is executed by a processor, it implements the steps of the method described above.
[0010] On the other hand, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the method described above.
[0011] The technical solution provided by this invention can bring at least the following beneficial effects: To address the difficulties in describing the nonlinear mechanical response of composite materials and the inaccuracy of numerical results, this invention first establishes an orthotropic elastoplastic model. Then, considering the damage and failure process of the material, an orthotropic elastoplastic damage constitutive model is established, along with a numerical solution method for this model. Based on this, a consistent tangent stiffness matrix for the three-term coupling of orthotropic elastoplastic damage is derived, which enhances the convergence performance of the finite element solver under complex loads. This invention achieves high-precision elastoplastic damage simulation of orthotropic materials and structures, enabling high-precision prediction of the nonlinear mechanical response of 2D C / SiC composite materials. Simultaneously, by coupling the elastoplastic constitutive model and the damage constitutive model, accurate prediction of material strength and failure processes is achieved. Attached Figure Description
[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0013] Figure 1 This is a flowchart of a method for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials according to an embodiment of the present invention; Figure 2 This is a flowchart of the numerical calculation of an orthogonal anisotropic elastoplastic constitutive model provided in an embodiment of the present invention; Figure 3 This is a simulation result diagram of equivalent plastic strain and damage evolution curve provided by an embodiment of the present invention; Figure 4 This is a simulation result diagram of a load-displacement curve provided by an embodiment of the present invention; Figure 5 This is a cloud map of equivalent plastic strain simulation results provided in an embodiment of the present invention; Figure 6 This is a cloud map of axial damage simulation results provided in an embodiment of the present invention; Figure 7 This is a structural diagram of a device for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials, provided in an embodiment of the present invention. Figure 8 This is a hardware architecture diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation
[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0015] The following describes the specific implementation of the above concept.
[0016] Please refer to Figure 1 This invention provides a method for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials. The method includes: Step 100: Define the orthogonal anisotropic linear elastic constitutive equation, stiffness matrix, yield equation, and plastic potential function of the composite material to define the orthogonal anisotropic elastoplastic constitutive model. Step 102: Use the return mapping algorithm to calculate the numerical values of the orthogonal anisotropic elastoplastic constitutive model, and calculate the target elastic strain, target plastic strain and target effective stress that finally converge. Step 104: Based on the plasticity calculation method, determine the uniform tangent stiffness matrix without considering damage; Step 106: Embed the target elastic strain, target plastic strain, target effective stress, and uniform tangent stiffness matrix without considering damage into the damage model to determine the uniform tangent stiffness matrix of orthogonal anisotropic elastoplastic damage coupling, and obtain the numerical values of the orthogonal anisotropic elastoplastic damage constitutive model for finite element calculation and analysis.
[0017] This invention addresses the difficulties in describing the nonlinear mechanical response of composite materials and the inaccuracies in numerical results. First, an orthotropic elastoplastic model is established. Then, considering the material's damage and failure process, an orthotropic elastoplastic damage constitutive model is established, along with a numerical solution method. Based on this, a consistent tangent stiffness matrix for the three-term coupling of orthotropic elastoplastic damage is derived, enhancing the convergence performance of the finite element solver under complex loads. This invention achieves high-precision elastoplastic damage simulation of orthotropic materials and structures, enabling high-precision prediction of the nonlinear mechanical response of 2D C / SiC composite materials. Simultaneously, by coupling the elastoplastic constitutive model and the damage constitutive model, accurate prediction of material strength and failure processes is achieved.
[0018] The following description Figure 1 The execution method for each step is shown.
[0019] For step 100: In some implementations, step 100 may include B1-B6: B1 defines the orthotropic linear elastic constitutive equation based on the anisotropic normal strain and shear strain, the effective stress components, and the elastic modulus and shear modulus; wherein the anisotropic components of the elastic modulus are all different, which is used to characterize the orthotropic anisotropy.
[0020] In this step, the orthotropic linear elastic constitutive equation is defined as: (1) (2) in, For total strain, For elastic strain, For plastic strain, S For the material's compliance matrix and C Let be the stiffness matrix of the material. Expanding equation (2) yields: (3) in, , These are the components of normal strain and shear strain in elastic strain, respectively. For effective stress components, , These are the elastic modulus and the shear modulus, respectively. , Poisson's ratio, i and j These are the row number and column number, indicating the direction.
[0021] In this embodiment, the traditional constitutive equation is orthogonal and isotropic, that is... It is difficult to accurately simulate the significant anisotropy and complex structure of 2D C / SiC composite materials.
[0022] B2 defines the stiffness matrix, yield function, and plastic potential function, and defines the yield equation based on the yield function.
[0023] Material compliance matrix S and stiffness matrix C Represented as: (4) The Hill yield function is defined as follows: (5) in, Let be the yield function. For effective stress, For the subsequent yield strength, the coefficient matrix P It can be defined as: (6) Among them, coefficient C i Defined as: (7) in, This represents the initial yield strength in each direction.
[0024] The yield equation is defined as follows: (8) in, f The yield equation is... For effective stress, P Let be the coefficient matrix. Define the square root value of the yield equation. .
[0025] definition The first derivative is ,definition The second derivative is : (9) (10) Define the plastic potential function as: (11) in, g Let be the plastic potential function. For effective stress, P It is a coefficient matrix.
[0026] definition The first derivative is ,definition The second derivative is : (12) (13) B3 makes the yield equation equal to the plastic potential function, so that the direction of plastic flow can be determined by the correlation flow rule, and the rate of change of plastic strain can be defined.
[0027] The yield equation is the same as the plastic potential function, that is, the direction of plastic flow is determined by the correlation flow rule, and the rate of change of plastic strain is defined as follows: (14) in, The rate of change of plastic strain, The rate of change of the plastic multiplier. g Let be the plastic potential function. For effective stress, P It is a coefficient matrix.
[0028] B4 uses an exponential isotropic hardening criterion to define the subsequent yield strength, and then differentiates the subsequent yield strength with respect to the equivalent plastic strain to obtain the hardening slope.
[0029] The subsequent yield strength is defined using an exponential isotropic hardening criterion: (15) in, For subsequent yield strength, The initial yield strength, For equivalent plastic strain, Q , b These are hardening parameters, which can be calibrated experimentally.
[0030] Differentiating the subsequent yield strength with respect to the equivalent plastic strain yields the hardening slope: (16) in, H The hardening slope, For subsequent yield strength, This is the equivalent plastic strain.
[0031] B5. Based on the principle of energy equivalence, the plastic potential rate of change is defined by using the product of effective stress and plastic strain rate of change as equal to the product of subsequent yield strength and equivalent plastic strain rate of change.
[0032] In this step, under uniaxial stress, the axial stress exactly matches the equivalent stress of that stress state. Therefore, the material hardening behavior under uniaxial stress is usually used to describe the isotropic hardening of materials. For this purpose, it is necessary to find the equivalent plastic strain increment corresponding to the rate of change of plastic strain.
[0033] Based on energy equivalence, the rate of change of plastic potential can be defined as: (17) in, The rate of change of plastic potential, For effective stress, The rate of change of plastic strain, For subsequent yield strength, It represents the equivalent rate of change of plastic strain.
[0034] B6. Substitute the expression defining the rate of change of plastic strain into the expression defining the rate of change of plastic potential to define the equivalent rate of change of plastic strain.
[0035] Substituting formula (14) into formula (17), we obtain the equivalent plastic strain change rate as follows: (18) in, The equivalent rate of change of plastic strain, The rate of change of the plastic multiplier. For effective stress, g Let be the plastic potential function. f This is the yield equation.
[0036] It should be noted that the orthotropic elastoplastic constitutive model is a complex constitutive model that cannot be represented by a single equation. All formulas in step 100 can be regarded as orthotropic elastoplastic constitutive models.
[0037] Regarding step 102: In some implementations, step 102 may include: For each iteration, execute: S1: Obtain the current plastic multiplier increment. Based on the current plastic multiplier increment, the effective stress update formula, the elastic strain update formula, and the equivalent plastic strain update formula, update the effective stress, elastic strain, and equivalent plastic strain respectively.
[0038] In this embodiment, the computational plasticity method is used to implement this process. Therefore, the return mapping algorithm steps for orthotropic anisotropic elastoplastic constitutive models are derived. That is, if the stress state at a given time tn is known, the stress tensor at time tn+1 is completely determined according to the definition of strain increment. In other words, the stress at the end of the strain increment is calculated based on the stress, strain, and hardening variables at the beginning of the increment, which can be referenced... Figure 2 The flowchart.
[0039] First, calculate the trial strain. , obtain the plastic multiplier increment after the previous iteration update.
[0040] The formula for updating elastic strain is: (19) in, For the first t n+1 The elastic strain of the step, To test the waters and prepare for a response, For the plastic multiplier increment, For effective stress, g Let be the plastic potential function. It is the first t n+1 The step of strain increment.
[0041] Multiplying both sides of equation (19) by the stiffness matrix C, we get (20) in, The effective stress at step tn+1, For the trial stress at step tn+1, C Here is the stiffness matrix. For the increment of plastic strain, This is the plasticity correction section.
[0042] The plastic strain increment is calculated based on the plastic strain change rate defined in equation (14), and the plastic strain increment is substituted into equation (20) to obtain the effective stress update formula as follows: (twenty one) in, The effective stress at step tn+1, For the plastic multiplier increment, C Here is the stiffness matrix. P The coefficient matrix, For the trial stress at step tn+1, I It is an identity matrix.
[0043] The equivalent plastic strain update formula can be written as: (twenty two) in, The equivalent plastic strain at step tn+1 is... For the plastic multiplier increment, The effective stress at step tn+1, P It is a coefficient matrix.
[0044] The yield function of this model can be written as: (twenty three) in, Let be the yield function. For the plastic multiplier increment, P The coefficient matrix, For subsequent yield strength, This is the equivalent plastic strain at step tn+1.
[0045] Thus, the final system of equations consisting of equations (19), (21), (22), and (23) is simplified to a system concerning the plastic multiplier increment. The function is used to update the effective stress, elastic strain, and equivalent plastic strain by substituting the current plastic multiplier increment into the above equations.
[0046] S2 determines whether the difference between the yield equation under the current effective stress and the square of the subsequent yield strength under the current equivalent plastic strain is less than the set error, in order to check whether the consistency condition is met.
[0047] In this embodiment, the consistency condition is: (twenty four) In the formula, The yield equation under the current effective stress is as follows: The value is the square of the subsequent yield strength under the current equivalent plastic strain. To set the error.
[0048] S3, if so, then directly use the current equivalent plastic strain to calculate the target plastic strain, and use the current effective stress and current elastic strain as the target effective stress and target elastic strain, and end the iteration.
[0049] S3. If not, use the return mapping algorithm to update the plastic multiplier increment and jump to step S1.
[0050] In this step, the plastic multiplier increment is updated as follows: (25) in, The plastic multiplier increment is obtained in the k-th iteration. The plastic multiplier increment is obtained in the (k-1)th iteration. The increment of the plastic multiplier increment obtained in the k-th iteration is... Let be the yield function. The yield function at the (k-1)th iteration Regarding the increment of plastic multipliers The differential.
[0051] Wherein, the yield function is related to the plastic multiplier increment The differential is: (26) in, For yield function Regarding the increment of plastic multipliers The differential, For effective stress Regarding the increment of plastic multipliers The differential, For subsequent yield strength Regarding equivalent plastic strain The differential, For equivalent plastic strain Regarding the increment of plastic multipliers The differential, P It is a coefficient matrix.
[0052] Regarding step 104: In some implementations, step 104 may include: Differentiating the elastic strain update formula yields the first differential expression; Differentiating the updated formula for equivalent plastic strain yields the second differential expression. The yield function is transformed into a function of the plastic multiplier increment, and the third differential is obtained by differentiating this function. By combining the first, second, and third differential equations, we obtain the uniform tangent stiffness matrix without considering damage.
[0053] In this embodiment, the first differential expression is obtained by differentiating the elastic strain update formula, i.e., formula (20): (27) in, For the trial strain in step tn+1, C Here is the stiffness matrix. The effective stress at step tn+1, For the plastic multiplier increment, For the (tn+1)th step , For the (tn+1)th step , , The definition is consistent with the previous one.
[0054] Differentiating the equivalent plastic strain update formula, i.e., formula (22), yields the second differential: (28) in, The equivalent plastic strain at step tn+1 is... The effective stress at step tn+1, For the plastic multiplier increment, For the (tn+1)th step , For the (tn+1)th step , For the (tn+1)th step , For the (tn+1)th step , , , , The definition is consistent with the previous one.
[0055] Transforming the yield function into a function of the plastic multiplier increment, i.e., differentiating formula (23), yields the third differential: (29) in, The equivalent plastic strain at step tn+1 is... For the (tn+1)th step , For subsequent yield strength, H The hardening slope, The effective stress at step tn+1, The definition is consistent with the previous one.
[0056] Combined equations (27), (28), and (29), let The uniform tangent stiffness matrix, neglecting damage, is: (30) in, For effective stress, In response, To test the waters and prepare for a response, C Here is the stiffness matrix. For the current plastic multiplier increment, Where H is the subsequent yield strength and H is the hardening slope. For the (tn+1)th step , For the (tn+1)th step , For the (tn+1)th step , For the (tn+1)th step , , , , The definition is consistent with the previous one.
[0057] Regarding step 106: In some implementations, step 106 may include H1-H6: H1, based on the target effective stress and damage initiation criterion, calculates the damage threshold factor.
[0058] In this embodiment, considering the requirements of material failure behavior under actual working conditions, the proposed plasticity algorithm is embedded into the damage model to realize the simulation of the mechanical response of materials and structures in the elastoplastic damage process, which is applicable to engineering problems such as fracture strength analysis.
[0059] The criteria for damage initiation are: (31) in, The damage function, Xij The breaking strength of the material in all directions, t , c They represent stretching and compression, respectively. The effective stress component is the target.
[0060] Damage threshold factor of materials r I It can be represented as: (32) H2 determines whether the damage threshold factor is greater than 1; if not, there is no damage evolution and the damage tensor remains unchanged; if so, it indicates that damage evolution exists, and the new damage tensor is determined using the exponential damage evolution criterion.
[0061] The exponential damage evolution criterion is: (33) in, d I For the damage tensor, A I It is a softening factor.
[0062] H3 calculates the nominal stress of the material using the current damage tensor and the target effective stress.
[0063] In the event of damage, the nominal stress of the material It can be represented as: (34) in, S ( d ) represents the compliance matrix containing damage. This represents the stiffness matrix including damage. In response, d Let be the damage tensor. The compliance matrix containing damage can be represented as: (35) in, E ij , G ij These are the elastic modulus and the shear modulus, respectively. Poisson's ratio, d i For damage tensor d The amount.
[0064] H4. Using the target elastic strain, target plastic strain, target effective stress, and the uniform tangent stiffness matrix without considering damage, combined with the nominal stress and the current damage tensor, the uniform tangent stiffness matrix of orthogonal anisotropic elastoplastic damage coupling is determined. H5 uses the target elastic strain, target plastic strain, target effective stress, nominal stress, and current damage tensor, as well as the consistent tangent stiffness matrix of orthotropic elastoplastic damage coupling, as numerical inputs into the finite element analysis software to perform composite material analysis.
[0065] The uniform tangent stiffness matrix for orthotropic elastoplastic damage coupling is: (36) in, The nominal stress at step tn+1 is For the strain at step tn+1, For the elastic strain at step tn+1, The effective stress at step tn+1, This represents the stiffness matrix including damage. For the damage tensor after regularization, For the unregularized damage tensor, The viscosity coefficient, Let I be the time increment, and let I be the identity matrix.
[0066] It is understandable that the target elastic strain, target plastic strain, target effective stress, nominal stress, and current damage tensor, as well as the consistent tangent stiffness matrix of the orthotropic elastoplastic damage coupling, are used as the numerical calculation results of the orthotropic elastoplastic damage constitutive model.
[0067] An orthogonal anisotropic elastoplastic damage constitutive model was implemented using the finite element method software ABAQUS by writing a user material subroutine (UMAT). A standard dog bone-shaped specimen was selected as the simulation example model, and the relevant calculation results are shown below. Figure 3 , Figure 4 , Figure 5 , Figure 6 .from Figure 3 , 4 As can be seen from points 5 and 6, the method of the present invention can accurately simulate the plastic evolution behavior of 2D C / SiC composite materials, obtain the inelastic deformation evolution process of the material, and exhibit good nonlinear stress-strain response characteristics. At the same time, the method of the present invention can accurately simulate the damage evolution behavior of 2D C / SiC composite materials, obtain the failure strength of the material, and can be applied to the strength analysis of orthogonal anisotropic materials and structures.
[0068] In summary, this invention addresses the difficulties in describing the nonlinear mechanical response of composite materials and the inaccuracies in numerical implementation results by establishing an orthogonal anisotropic elastoplastic constitutive model. Furthermore, considering the damage and failure process of materials, an orthogonal anisotropic elastoplastic damage constitutive model is established. Based on this, a consistent tangent stiffness matrix is derived, and a numerical solution method for this model is established. This invention achieves high-precision elastoplastic damage simulation of orthogonal anisotropic materials and structures, providing reliable support for strength assessment and life prediction of 2D C / SiC composite materials and similar materials in engineering. Moreover, the method established in this invention has good versatility and engineering applicability, applicable not only to material models with nonlinear yield behavior such as 2D C / SiC composite materials, but also to anisotropic materials, such as 3D printed metal matrix materials with anisotropic mechanical behavior.
[0069] This method can provide reliable theoretical support and efficient numerical tools for material constitutive modeling, nonlinear response analysis, structural strength assessment, and high-precision finite element simulation, and has broad prospects for scientific research and engineering applications.
[0070] Please refer to Figure 7 This invention provides a device for constructing a nonlinear mechanical constitutive model and performing finite element analysis on a 2D C / SiC composite material, used to implement the steps of any method embodiment in the specification. The device includes: Define unit 701 to define the orthogonal anisotropic linear elastic constitutive equation, stiffness matrix, yield equation and plastic potential function of composite materials, so as to define the orthogonal anisotropic elastoplastic constitutive model. The calculation unit 702 is used to calculate the numerical values of the orthogonal anisotropic elastoplastic constitutive model using the return mapping algorithm, and to calculate the target elastic strain, target plastic strain and target effective stress that finally converge. Element 703 is defined to determine the uniform tangent stiffness matrix without considering damage, based on plasticity calculations. Embedded element 704 is used to embed the target elastic strain, target plastic strain, target effective stress, and uniform tangent stiffness matrix without considering damage into the damage model to determine the uniform tangent stiffness matrix of orthogonal anisotropic elastoplastic damage coupling, and obtain the numerical value of the orthogonal anisotropic elastoplastic damage constitutive model for finite element calculation and analysis.
[0071] It should be noted that the 2D C / SiC composite material nonlinear mechanical constitutive model construction and finite element analysis device provided in the above embodiments is only an example of the division of the above functional units. In practical applications, the above functions can be assigned to different functional units as needed, that is, the internal structure of the device can be divided into different functional units to complete all or part of the functions described above. In addition, the above device embodiments and method embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.
[0072] Embodiments of this application also provide a computer device, please refer to... Figure 8 The computer device includes a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, at least one program, code set or instruction set being loaded and executed by the processor to implement the 2D C / SiC composite material nonlinear mechanical constitutive model construction and finite element analysis method provided in the above method embodiments.
[0073] The embodiments of this application also provide a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, at least one program, code set, or instruction set is loaded and executed by a processor to implement the 2D C / SiC composite material nonlinear mechanical constitutive model construction and finite element analysis method provided in the above method embodiments.
[0074] Embodiments of this application also provide a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium and executes the computer program, causing the computer device to perform any of the 2D C / SiC composite material nonlinear mechanical constitutive model construction and finite element analysis methods described in the above embodiments.
[0075] For ease of description, the above systems or devices are described separately as various modules or units based on their functions. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware components.
[0076] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of the embodiments of this application.
[0077] Finally, it should be noted that in this document, relational terms such as first, second, third, and fourth are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.
[0078] The above are merely preferred embodiments of this application. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this application, and these improvements and modifications should also be considered within the scope of protection of this application.
Claims
1. A method for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials, characterized in that, The method includes: Define the orthogonal anisotropic linear elastic constitutive equation, stiffness matrix, yield equation, and plastic potential function for composite materials to define the orthogonal anisotropic elastoplastic constitutive model; The numerical values of the orthogonal anisotropic elastoplastic constitutive model are calculated using the return mapping algorithm, and the target elastic strain, target plastic strain, and target effective stress are calculated at the final convergence. Based on plasticity calculations, the uniform tangent stiffness matrix is determined without considering damage. The target elastic strain, target plastic strain, target effective stress, and uniform tangent stiffness matrix without considering damage are embedded into the damage model to determine the uniform tangent stiffness matrix of orthotropic elastoplastic damage coupling, thereby obtaining the numerical values of the orthotropic elastoplastic damage constitutive model for finite element calculation and analysis.
2. The method as described in claim 1, characterized in that, The definition of the orthotropic linear elastic constitutive equation, stiffness matrix, yield equation, and plastic potential function of the composite material is used to define an orthotropic elastoplastic constitutive model, including: Based on the anisotropic normal strain and shear strain, effective stress components, and elastic modulus and shear modulus, an orthotropic linear elastic constitutive equation is defined; wherein, the anisotropic components of the elastic modulus are all different, which is used to characterize orthotropic anisotropy. Define the stiffness matrix, yield function, and plastic potential function, and define the yield equation based on the yield function; This makes the yield equation equal to the plastic potential function, so as to determine the direction of plastic flow using the correlation flow rule and define the rate of change of plastic strain; An exponential isotropic hardening criterion is adopted to define the subsequent yield strength, and the hardening slope is obtained by differentiating the subsequent yield strength with respect to the equivalent plastic strain. Based on the principle of energy equivalence, the product of effective stress and the rate of change of plastic strain is equal to the product of the subsequent yield strength and the equivalent rate of change of plastic strain, and the rate of change of plastic potential is defined. Substitute the expression defining the rate of change of plastic strain into the expression defining the rate of change of plastic potential to define the equivalent rate of change of plastic strain.
3. The method as described in claim 1, characterized in that, The numerical calculation of the orthogonal anisotropic elastoplastic constitutive model using the return mapping algorithm, and the calculation of the finally converged target elastic strain, target plastic strain, and target effective stress, include: For each iteration, execute: S1, obtain the current plastic multiplier increment, and update the effective stress, elastic strain and equivalent plastic strain respectively based on the current plastic multiplier increment, effective stress update formula, elastic strain update formula and equivalent plastic strain update formula; S2, determine whether the difference between the yield equation under the current effective stress and the square of the subsequent yield strength under the current equivalent plastic strain is less than the set error, in order to check whether the consistency condition is met. S3, if so, then directly use the current equivalent plastic strain to calculate the target plastic strain, and use the current effective stress and current elastic strain as the target effective stress and target elastic strain, and end the iteration; S3. If not, use the return mapping algorithm to update the plastic multiplier increment and jump to step S1.
4. The method according to claim 3, characterized in that, The plastic multiplier increment is updated in the following manner: in, The plastic multiplier increment is obtained in the k-th iteration. The plastic multiplier increment is obtained in the (k-1)th iteration. This is the increment of the plastic multiplier increment obtained in the k-th iteration. Let be the yield function. The yield function at the (k-1)th iteration Regarding the increment of plastic multipliers The differential.
5. The method according to claim 3, characterized in that, The determination of the uniform tangent stiffness matrix without considering damage, based on the plasticity calculation method, includes: Differentiating the elastic strain update formula yields the first differential expression; Differentiating the equivalent plastic strain update formula yields the second differential expression; The yield function is transformed into a function of the plastic multiplier increment, and the differential of this function is obtained to obtain the third differential expression; By combining the first differential equation, the second differential equation, and the third differential equation, we obtain the uniform tangent stiffness matrix without considering damage.
6. The method according to claim 1, characterized in that, The process involves embedding the target elastic strain, target plastic strain, target effective stress, and the uniform tangent stiffness matrix (without considering damage) into the damage model to determine the uniform tangent stiffness matrix of the orthotropic elastoplastic damage coupling, thereby obtaining the numerical values of the orthotropic elastoplastic damage constitutive model for finite element analysis. This includes: Based on the target effective stress and damage initiation criterion, calculate the damage threshold factor; Determine whether the damage threshold factor is greater than 1; if not, there is no damage evolution and the damage tensor remains unchanged; if yes, it indicates that damage evolution exists, and a new damage tensor is determined using the exponential damage evolution criterion. Calculate the nominal stress of the material using the current damage tensor and the target effective stress; Using the target elastic strain, the target plastic strain, the target effective stress, and the uniform tangent stiffness matrix without considering damage, combined with the nominal stress and the current damage tensor, the uniform tangent stiffness matrix of orthogonal anisotropic elastoplastic damage coupling is determined. The target elastic strain, target plastic strain, target effective stress, nominal stress, current damage tensor, and the consistent tangent stiffness matrix of orthotropic elastoplastic damage coupling are used as numerical inputs into the finite element analysis software for composite material analysis as the orthotropic elastoplastic damage constitutive model.
7. A device for constructing a nonlinear mechanical constitutive model and performing finite element analysis on composite materials, used to implement the steps of the method described in any one of claims 1-6, characterized in that, The device includes: Define the unit, which is used to define the orthogonal anisotropic linear elastic constitutive equation, stiffness matrix, yield equation and plastic potential function of composite materials, so as to define the orthogonal anisotropic elastoplastic constitutive model; The calculation unit is used to calculate the numerical values of the orthogonal anisotropic elastoplastic constitutive model using the return mapping algorithm, and to calculate the target elastic strain, target plastic strain and target effective stress that finally converge. The element is defined to determine the uniform tangent stiffness matrix without considering damage, based on plasticity calculations. An embedded unit is used to embed the target elastic strain, the target plastic strain, the target effective stress, and the uniform tangent stiffness matrix without considering damage into the damage model, so as to determine the uniform tangent stiffness matrix of the orthogonal anisotropic elastoplastic damage coupling, obtain the numerical value of the orthogonal anisotropic elastoplastic damage constitutive model, and perform finite element calculation analysis.
8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the method according to any one of claims 1-6.
9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method described in any one of claims 1-6.
10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the steps of the method according to any one of claims 1-6.