Loading history-related data-driven multi-scale concurrent simulation method and system

Abstract

The present invention provides a data-driven multi-scale concurrent simulation method and system related to loading history, including: updating a cluster material data set according to a cluster material state variable; taking the minimum energy deviation between the cluster and the data point as the optimization target, taking the Lippmann-Schwinger equation and the homogenization strain constraint as the constraint condition, establishing an objective function; solving the objective function minimization problem under the constraint condition by the Lagrange multiplier method, and establishing a linear equation system; solving the linear equation system, updating the mapping relationship between the cluster material data point and the cluster equilibrium constraint point; through repeated mapping of the cluster material data point and the cluster equilibrium constraint point, the mapping relationship converges; updating the cluster material state variable according to the cluster material data point, and calculating the homogenization stress according to the cluster equilibrium constraint point. The present invention can realize multi-scale concurrent simulation of materials without constitutive model conditions, and can accurately predict the mechanical behavior related to the material loading history at different scales.

Description

Technical Field

[0001] The present invention relates to the technical field of material mechanical behavior analysis, and in particular to a loading history-related data-driven multi-scale concurrent simulation method and system. Background Art

[0002] With the development of materials science, the microstructure of materials is becoming more and more refined, and the microstructure also determines the strengthening mechanism and macroscopic properties of materials. For example, for fiber-reinforced composite materials, there are resin cross-linked network structures, unidirectional fiber reinforcement structures, fiber braided structures, and component geometric structures at different scales; for aluminum alloy materials, there are multiple strengthening mechanisms such as solid solution strengthening, particle strengthening, deformation strengthening, and fine grain strengthening at different scales. The multi-scale simulation method of materials can establish the intrinsic connection between the organization and performance of materials at different scales, and has become a research hotspot in recent years. The representative volume element method (RVE) is a commonly used method in multi-scale analysis. By establishing a periodic finite element model representing the local microscopic characteristics of the material, the mechanical response evolution process of the material at the microscopic scale is predicted. However, in multi-scale concurrent calculations, the homogenized constitutive model of the RVE model needs to be called at each integral point of each incremental step at the macroscopic scale to participate in the calculation. The traditional high-fidelity RVE model has too much computational complexity and too high solution cost to meet the needs of multi-scale concurrent calculations. It is urgent to reduce the order of RVE to improve its solution speed.

[0003] The self-consistent clustering analysis (SCA) method is a high-precision and efficient multi-scale concurrent simulation method for materials. It can significantly improve the computational efficiency of RVE, effectively reduce the solution cost, and has good solution accuracy. In this method, the RVE is first divided into clusters by a machine learning clustering algorithm. The same cluster is considered to have uniform stress and strain, thereby reducing the number of degrees of freedom of the model; then, combined with the homogenized strain constraint at the macroscopic integration point, the stress and strain distribution of each microscopic cluster is obtained by solving the Lippmann-Schwinger equation; finally, according to the cluster stress and strain distribution, the homogenized stress of RVE is obtained and returned to the macroscopic integration point to realize the macro-micro multi-scale concurrent simulation of the material. The self-consistent clustering analysis method can deeply analyze the complex elastic-plastic, damage and other nonlinear mechanical behaviors of each component phase in the material from multiple scales. However, in the process of adaptive clustering analysis, it is still necessary to provide the phenomenological constitutive model of each component phase of RVE. As the mechanical behavior of materials becomes more and more complex, the existing phenomenological constitutive models are often difficult to accurately describe the actual mechanical behavior of materials. In addition, phenomenological constitutive models generally have multiple model parameters that need to be calibrated through experiments. The parameter calibration process will bring new deviations, which will be further amplified in the multi-scale concurrent simulation process, affecting the accuracy and reliability of the analysis results.

[0004] Data-driven computational mechanics is an emerging numerical solution paradigm that does not rely on material constitutive models. It has been rapidly developed and improved in recent years. Starting directly from the material data set obtained from the experiment, combined with constraints such as compatibility conditions and equilibrium equations, this method obtains the optimal solution of the system equilibrium state by minimizing the system free energy. This method does not need to establish a phenomenological constitutive model of the material, and can directly solve the mechanical response of the structure through the discrete stress-strain data points of the material, which can fundamentally avoid the system deviation caused by the phenomenological constitutive model and material parameter calibration. However, as a new computational paradigm, the data-driven computational mechanics method system is not as mature as the finite element method. When dealing with mechanical behaviors related to loading history such as material plasticity, this method still has certain limitations; on the other hand, the current theoretical system of data-driven computational mechanics methods is only limited to structural simulation analysis at a single scale, and cannot be applied to multi-scale concurrent simulation of materials. Therefore, it is of great significance to establish a data-driven multi-scale concurrent simulation method related to loading history. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for multi-scale concurrent simulation driven by data related to loading history.

[0006] According to a method and system for loading history-related data-driven multi-scale concurrent simulation provided by the present invention, the scheme is as follows:

[0007] In a first aspect, a method for loading history-related data-driven multi-scale concurrent simulation is provided, the method comprising: an offline phase and an online phase;

[0008] The offline stage includes:

[0009] Step S1.1: Establish an RVE model representing the microscopic characteristics of the material structure and calculate its elastic mechanical response;

[0010] Step S1.2: Calculate the strain concentration tensor at the integration point according to the elastic strain distribution of the RVE;

[0011] Step S1.3: Based on the strain concentration tensor, the integration points are divided into clusters using the K-means clustering algorithm;

[0012] Step S1.4: Calculate the cluster interaction tensor components by Green’s function and Fourier transform method;

[0013] The online phase includes:

[0014] Step S2.1: Input the initial reference material Lame constants and the interaction tensor components generated in the offline stage;

[0015] Step S2.2: Calculate the interaction tensor between each cluster based on the reference material Lame constant and the interaction tensor components generated in the offline stage;

[0016] Step S2.3: solving the Lippmann-Schwinger equation by a data-driven method;

[0017] Step S2.4: Calculate the RVE homogenization Lame constant based on the cluster equilibrium constraint point at time t+1;

[0018] Step S2.5: Update the reference material Lame constant according to the RVE homogenization Lame constant, repeat steps S2.2 to S2.4 until the RVE homogenization Lame constant is consistent with the reference material Lame constant, and obtain the final cluster equilibrium constraint point and RVE homogenization stress at time t+1;

[0019] Step S2.6: Return the homogenized stress of RVE to the macroscopic integration point to obtain the macroscopic and microscopic mechanical responses of the material.

[0020] Preferably, step S1.2 comprises: according to the strain distribution ε under six orthogonal loading conditions m(x), calculate the strain concentration tensor A(x) at the integration point; the strain concentration tensor A(x) is related to the macroscopic homogenized strain ε M and microscopic strain distribution ε m The fourth-order tensor of (x) is calculated by the following expression:

[0021] ε m (x) = A(x):ε M .

[0022] Preferably, the step S1.3 comprises:

[0023] Based on the strain concentration tensor A(x) of the integration point, the integration points in RVE are clustered by the K-means clustering algorithm, that is, the following least squares optimization process of the strain concentration tensor is completed:

[0024]

[0025] Among them, S represents the final cluster division result, S J represents the Jth cluster, A n represents the strain concentration tensor at the nth integration point, represents the average strain concentration tensor of all integration points in the Jth cluster, N is the total number of clusters, and ||A|| represents the 2-norm of any second-order tensor A, that is, the 1 / 2 power of the sum of the squares of each element of A.

[0026] Preferably, the step S1.4 comprises:

[0027] Combined Green's function and Fourier transform methods to calculate the interaction tensor components between individual clusters and The expressions are:

[0028]

[0029]

[0030] Where, Ω is the volume of RVE, c I is the volume fraction of the Ith cluster, χ I (x) is the characteristic function of the Ith cluster, Φ 1 and Φ 2 is the part of the Green function that is independent of the reference material constitutive structure and has the following form in Fourier space:

[0031]

[0032]

[0033] Among them, ξ is the coordinate vector in Fourier space,i is the coordinate of the i-th direction in Fourier space, |ξ| is the distance of the Fourier space coordinate from the origin, δ ij is the Kronecker delta symbol, satisfying

[0034]

[0035] Preferably, the step S2.3 comprises:

[0036] Step S2.3.1: Input the homogenized strain increment of the micro-scale RVE according to the strain constraint of the macro-integration point;

[0037] Step S2.3.2: updating the cluster material data set at time t according to the initial material data set, the initial material state variables and the cluster material state variables at time t;

[0038] Step S2.3.3: assigning initial material data points to each cluster based on the cluster material data set at time t;

[0039] Step S2.3.4: Taking the minimum energy deviation between the cluster stress-strain state and the data point stress-strain state as the optimization goal, taking the Lippmann-Schwinger equation and the homogenization strain constraint as constraints, and establishing the objective function under the constraints;

[0040] Step S2.3.5: Using the Lagrange multiplier method to solve the objective function minimization problem under the above constraints, a linear equation system about the stress-strain state of the cluster is established by finding the minimum point of the objective function;

[0041] Step S2.3.6: Solve the above linear equations to obtain the cluster stress-strain distribution state that satisfies the constraint conditions, and use it as the new cluster equilibrium constraint point;

[0042] Step S2.3.7: According to the cluster equilibrium constraint point, find the data point with the closest energy deviation in the cluster material data set at time t, and use it as the new cluster material data point;

[0043] Step S2.3.8: Repeat steps S2.3.6 to S2.3.7 until the material data points of the cluster converge, and obtain the cluster material data points and cluster equilibrium constraint points at time t+1;

[0044] Step S2.3.9: Update the cluster material state variables according to the cluster material data points at time t+1;

[0045] Step S2.3.10: Update the RVE homogenized stress according to the cluster equilibrium constraint point at time t+1.

[0046] In a second aspect, a data-driven multi-scale concurrent simulation system related to loading history is provided, the system comprising: an offline phase and an online phase;

[0047] The offline stage includes:

[0048] Module M1.1: Establish an RVE model that represents the microscopic characteristics of the material structure and calculate its elastic mechanical response;

[0049] Module M1.2: Calculate the strain concentration tensor at the integration point based on the elastic strain distribution of the RVE;

[0050] Module M1.3: Based on the strain concentration tensor, the integration points are clustered using the K-means clustering algorithm;

[0051] Module M1.4: Calculate the cluster interaction tensor components by Green's function and Fourier transform methods;

[0052] The online phase includes:

[0053] Module M2.1: Input the initial reference material Lame constants and the interaction tensor components generated in the offline stage;

[0054] Module M2.2: Calculate the interaction tensor between clusters based on the reference material Lame constant and the interaction tensor components generated in the offline stage;

[0055] Module M2.3: Solving the Lippmann-Schwinger equation via a data-driven approach;

[0056] Module M2.4: Calculate the RVE homogenization Lame constant based on the cluster equilibrium constraint point at time t+1;

[0057] Module M2.5: Update the reference material Lame constant according to the RVE homogenization Lame constant, repeat modules M2.2 to M2.4 until the RVE homogenization Lame constant is consistent with the reference material Lame constant, and obtain the final cluster equilibrium constraint point and RVE homogenization stress at time t+1;

[0058] Module M2.6: Return the homogenized stress of RVE to the macroscopic integration point to obtain the macroscopic and microscopic mechanical responses of the material.

[0059] Preferably, the module M1.2 comprises: according to the strain distribution ε under six orthogonal loading conditions m (x), calculate the strain concentration tensor A(x) at the integration point; the strain concentration tensor A(x) is related to the macroscopic homogenized strain ε M and microscopic strain distribution ε m The fourth-order tensor of (x) is calculated by the following expression:

[0060] ε m (x) = A(x):ε M .

[0061] Preferably, the module M1.3 comprises:

[0062] Based on the strain concentration tensor A(x) of the integration point, the integration points in RVE are clustered by the K-means clustering algorithm, that is, the following least squares optimization process of the strain concentration tensor is completed:

[0063]

[0064] Among them, S represents the final cluster division result, S J represents the Jth cluster, A n represents the strain concentration tensor at the nth integration point, represents the average strain concentration tensor of all integration points in the Jth cluster, N is the total number of clusters, and ||A|| represents the 2-norm of any second-order tensor A, that is, the 1 / 2 power of the sum of the squares of each element of A.

[0065] Preferably, the module M1.4 comprises:

[0066] Combined Green's function and Fourier transform methods to calculate the interaction tensor components between individual clusters and The expressions are:

[0067]

[0068]

[0069] Where, Ω is the volume of RVE, c I is the volume fraction of the Ith cluster, χ I (x) is the characteristic function of the I-th cluster, Φ 1 and Φ 2 is the part of the Green function that is independent of the reference material constitutive structure and has the following form in Fourier space:

[0070]

[0071]

[0072] Among them, ξ is the coordinate vector in Fourier space, i is the coordinate of the i-th direction in Fourier space, |ξ| is the distance of the Fourier space coordinate from the origin, δ ij is the Kronecker delta symbol, satisfying

[0073]

[0074] Preferably, the module M2.3 comprises:

[0075] Module M2.3.1: Input the homogenized strain increment of the microscale RVE according to the strain constraints at the macroscopic integration points;

[0076] Module M2.3.2: Update the cluster material data set at time t based on the initial material data set, the initial material state variables and the cluster material state variables at time t;

[0077] Module M2.3.3: Assign initial material data points to each cluster based on the cluster material data set at time t;

[0078] Module M2.3.4: Taking the minimum energy deviation between the cluster stress-strain state and the data point stress-strain state as the optimization goal, and taking the Lippmann-Schwinger equation and the homogenization strain constraint as the constraint conditions, establish the objective function under the constraint conditions;

[0079] Module M2.3.5: Use the Lagrange multiplier method to solve the objective function minimization problem under the above constraints. By finding the minimum point of the objective function, a linear equation system about the stress-strain state of the cluster is established;

[0080] Module M2.3.6: Solve the above linear equations to obtain the cluster stress-strain distribution state that satisfies the constraint conditions and use it as the new cluster equilibrium constraint point;

[0081] Module M2.3.7: Based on the cluster equilibrium constraint point, find the data point with the closest energy deviation in the cluster material data set at time t and use it as the new cluster material data point;

[0082] Module M2.3.8: Repeat Module M2.3.6 to Module M2.3.7 until the material data points of the cluster converge, and obtain the cluster material data points and cluster equilibrium constraint points at time t+1;

[0083] Module M2.3.9: Update the cluster material state variables according to the cluster material data points at time t+1;

[0084] Module M2.3.10: Update the RVE homogenized stresses based on the cluster equilibrium constraint points at time t+1.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] 1. The present invention can significantly improve the solution efficiency of RVE, effectively reduce the solution cost, and realize macro-micro multi-scale concurrent simulation of materials on the existing finite element platform;

[0087] 2. The present invention can directly predict the macro-micro mechanical response of the material through a series of discrete data points without any phenomenological constitutive model, and can completely avoid the systematic deviation caused by the material constitutive model and parameter calibration process in multi-scale analysis;

[0088] 3. The present invention can predict complex mechanical behaviors related to loading history, such as plastic deformation and hardening of materials during loading, further expanding the application scope and field of data-driven methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0090] Figure 1 A flow chart of the offline phase of the multi-scale concurrent simulation method driven by loading history-related data;

[0091] Figure 2 Flowchart of the online phases of the multi-scale concurrent simulation method driven by loading history-related data;

[0092] Figure 3 A flowchart of the steps for solving the Lippmann-Schwinger equation using a data-driven approach in the online phase;

[0093] Figure 4 It is a macroscopic finite element model in multi-scale concurrent simulation process;

[0094] Figure 5 It is a microscopic RVE model in the multi-scale concurrent simulation process;

[0095] Figure 6 is the displacement-time curve of the loading point during cyclic loading;

[0096] Figure 7 Macroscopic finite element model for the final moment of cyclic loading;

[0097] Figure 8 is the stress distribution along the X direction in the micro RVE model at the final moment of cyclic loading;

[0098] Fig. 9 is the stress-strain curve of the matrix during cyclic loading;

[0099] Fig.10 is the stress-strain curve of the fiber during cyclic loading. DETAILED DESCRIPTION

[0100] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0101] An embodiment of the present invention provides a data-driven multi-scale concurrent simulation method related to loading history, the method comprising: an offline phase and an online phase, specifically as follows:

[0102] Reference Figure 1 As shown, the offline stage includes:

[0103] Step S1.1: Establish an RVE model representing the microscopic characteristics of the material structure. The linear elastic constitutive model is used for each component phase material to calculate its strain distribution ε under six orthogonal loading conditions. m (x);

[0104] Step S1.2: According to the strain distribution ε under six orthogonal loading conditions m (x), calculate the strain concentration tensor A(x) at the integration point; the strain concentration tensor A(x) is related to the macroscopic homogenized strain ε M and microscopic strain distribution ε m The fourth-order tensor of (x) is calculated by the following expression:

[0105] ε m (x) = A(x):ε M .

[0106] Step S1.3: Based on the strain concentration tensor A(x) of the integration point, the integration points in the RVE are clustered by the K-means clustering algorithm, that is, the following least squares optimization process of the strain concentration tensor is completed:

[0107]

[0108] Among them, S represents the final cluster division result, S J represents the Jth cluster, A n represents the strain concentration tensor at the nth integration point, represents the average strain concentration tensor of all integration points in the Jth cluster, N is the total number of clusters, and ||A|| represents the 2-norm of any second-order tensor A, that is, the 1 / 2 power of the sum of the squares of each element of A.

[0109] Step S1.4: Combine Green's function and Fourier transform methods to calculate the interaction tensor components between clusters and The expressions are:

[0110]

[0111]

[0112] Where, Ω is the volume of RVE, c I is the volume fraction of the Ith cluster, χ I (x) is the characteristic function of the I-th cluster, Φ 1 and Φ 2 is the part of the Green function that is independent of the reference material constitutive structure and has the following form in Fourier space:

[0113]

[0114]

[0115] Among them, ξ is the coordinate vector in Fourier space, i is the coordinate of the i-th direction in Fourier space, |ξ| is the distance of the Fourier space coordinate from the origin, δ ij is the Kronecker delta symbol, satisfying

[0116]

[0117] Reference Figure 2 As shown, the online phase includes:

[0118] Step S2.1: Input the initial reference material Lame constant λ 0 and μ 0 , and the interaction tensor components generated in the offline phase;

[0119] Step S2.2: According to the reference material Lame constant λ 0 and μ 0 and the interaction tensor components generated in the offline phase and The interaction tensor D between clusters is calculated by the following expression IJ

[0120]

[0121] Step S2.3: Input the initial material data set consisting of discrete stress-strain data points and the initial material state variables, and define the relationship between the material data set and the state variables, and solve the Lippmann-Schwinger equation using a data-driven method. Figure 3 As shown, the process specifically includes the following steps:

[0122] Step S2.3.1: Input the homogenized strain increment of the microscale RVE according to the constraints at the macroscopic integration point of the current increment step

[0123] Step S2.3.2: Based on the initial material data set E0, the initial material state variable V0, and the material state variable V of the Ith cluster at time t t I , update the material data set of cluster I at time t

[0124] Step S2.3.3: From the material dataset Assign initial material data points to cluster I in

[0125] Step S2.3.4: Read the stress-strain state of cluster I at time t The optimization goal is to minimize the energy deviation between the cluster stress-strain state and the data point stress-strain state, and the objective function is defined as:

[0126]

[0127] Among them, Δε I and Δσ I is the cluster strain increment and cluster stress increment of the current incremental step; N is the total number of clusters, ω I is the volume fraction of the Ith cluster, C I is the custom stiffness matrix of the I-th cluster.

[0128] The corresponding constraint is the Lippmann-Schwinger equation

[0129]

[0130] and homogenization strain conditions

[0131]

[0132] Among them, Δε 0 The reference material strain increment for the current increment; Δε I and Δσ I is the cluster strain increment and cluster stress increment of the current increment; C 0 Represents the stiffness matrix of the reference material.

[0133] Step S2.3.5: Use the Lagrange multiplier method to solve the objective function minimization problem under the above constraints. The Lagrangian function containing the constraints is expressed as:

[0134]

[0135] Among them, η I and η N+1 is the Lagrange multiplier. In the Lagrangian function L, the optimization variables include Δε I , Δσ I , Δε 0 , η I and η N+1 Five parts. Let the partial derivatives of the Lagrangian function L with respect to each optimization variable be zero, and we can get the linear equations for each optimization variable:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] Among them, δ IJ represents the Kronecker delta symbol; ω J represents the volume fraction of the Jth cluster; C J represents the custom stiffness matrix of the Jth cluster; U4 represents the fourth-order unit tensor; η J represents the Lagrange multiplier of the Jth cluster.

[0142] Step S2.3.6: Solve the above linear equations to obtain the cluster strain increment Δε that satisfies the constraints I and cluster stress increment Δσ I ; Then the equilibrium constraint point of the cluster at time t+1 is It can be expressed as:

[0143]

[0144]

[0145] Implementing data points from clustered materials To the cluster balance constraint point 's mapping.

[0146] Step S2.3.7: Balance the constraint points according to the cluster Find the data point with the closest energy deviation in the cluster material data set at time t, the material data point of the cluster It can be expressed as:

[0147]

[0148] Achieve cluster balance constraint points To cluster material data points 's mapping.

[0149] Step S2.3.8: Repeat steps S2.3.6 to S2.3.7 until the cluster material data points are Reach convergence and obtain the cluster equilibrium constraint point at time t+1 and cluster material data points at time t+1

[0150] Step S2.3.9: Cluster material data points according to time t+1 Update the cluster material state variable V at time t+1 t+1 ;

[0151] Step S2.3.10: According to the cluster balance constraint point at time t+1 Update the RVE homogenized stress at time t+1

[0152] Step S2.4: Cluster balance constraint points based on the cluster at time t+1 Calculate the RVE homogenization Lame constant λ RVE and μ RVE .

[0153] Step S2.5: Homogenize the Lame constant (λ) according to RVE RVE ,μ RVE ), update the reference material Lame constant (λ 0 ,μ 0 ); Repeat steps S2.2 to S2.4 until (λ RVE ,μ RVE ) and (λ 0 ,μ 0 ) to keep consistent, and obtain the final cluster stress-strain distribution at time t+1 and RVE homogenization stress

[0154] Step S2.6: Homogenize the RVE stress Return the macroscopic integration point to obtain the macroscopic and microscopic mechanical responses of the material, and realize data-driven multi-scale concurrent simulation related to the loading history.

[0155] Taking unidirectional fiber-reinforced composite materials as an example, this method is verified through multi-scale concurrent simulation of axial tension-compression-tension cyclic loading process.

[0156] Unidirectional fiber reinforced composite materials are composed of matrix phase and fiber phase. Based on the MATLAB platform, relevant programs are written to generate a large number of stress and strain data points through the phenomenological constitutive models of matrix materials and fiber materials. Among them, the data set of matrix material is generated by elastic-plastic constitutive model, the isotropic linear elastic model is used in the elastic stage, and the Mises yield criterion and isotropic linear hardening model are used in the plastic stage. The strain data range in the X direction is set to (-0.2, 0.2), and the strain data range in other directions is set to (-0.01, 0.01). The data set of fiber material is generated by orthotropic linear elastic constitutive model, the strain data range in the X direction is set to (-0.1, 0.1), and the strain data range in other directions is set to (-0.01, 0.01). For matrix phase and fiber phase, 100,000 data points are generated in their respective strain data ranges.

[0157] Based on this method, a subroutine was written to realize data-driven multi-scale concurrent simulation of composite material cyclic loading process through Abaqus finite element platform. The macroscopic finite element model and micro RVE model in the multi-scale concurrent simulation process are shown in Figure 2. Figure 4 and Figure 5 For the convenience of testing, the macro model contains only one unit with a unit size of 1 mm. The loading condition is a tension-compression-tension cycle along the X direction. The displacement-time curve of the loading reference point is shown in Figure 6 As shown, the displacement amplitude is 0.05 mm. The microscopic model is an RVE model representing the fiber distribution characteristics of the composite material. The fiber diameter is 7 μm, the fiber volume fraction is 50%, and the size of the RVE is 50 μm. In order to improve the calculation efficiency, the RVE is divided into two clusters in total, in which the matrix material and the fiber material are each divided into one cluster.

[0158] The stress distribution along the X direction in the macroscopic finite element model and the microscopic RVE model at the final moment of cyclic loading is shown in Figure 7 and Figure 8 As shown. It can be seen that in the micro RVE model, due to the higher elastic modulus of the fiber, the tensile stress is mainly borne by the fiber, and the stress level of the matrix is ​​very small, which is consistent with the general stress distribution characteristics of the composite material under axial tension. In the macro finite element model, the homogenized tensile stress is approximately half of the fiber tensile stress, which is consistent with the prediction results of the homogenization theory under axial tension. This result verifies the accuracy of this method.

[0159] The stress-strain curves of the matrix and fiber during cyclic loading are shown in Fig. 9 and Fig.10As shown. It can be seen that for fiber materials, their deformation process is always elastic deformation, and their stress-strain relationship remains linear, which is independent of the loading history. For matrix materials, the deformation process includes plastic deformation and hardening processes, and their stress-strain relationship obviously depends on their loading history. During the first stretching process, the matrix material first undergoes elastic deformation along a linear path, and then enters the positive yield and plastic hardening stage. During the first compression process, the matrix material first unloads along the elastic path, and then enters the reverse loading process. The reverse loading process also goes through the elastic deformation stage and the plastic hardening stage. Affected by the first stretching process, the initial yield stress of the reverse loading is also increased. During the second stretching process, due to the two hardening processes, its initial yield stress is significantly higher than that of the first stretching process. This result proves that the method of the present invention can accurately predict the mechanical behavior related to the loading history of materials at different scales.

[0160] The embodiments of the present invention provide a method and system for multi-scale concurrent simulation based on data driven by loading history, which can realize multi-scale concurrent simulation of materials without a constitutive model, fundamentally avoid the system deviation caused by the constitutive model of materials in multi-scale analysis, and accurately predict the mechanical behavior related to the loading history of materials at different scales.

[0161] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0162] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A data-driven multi-scale concurrent simulation method related to loading history, characterized in that: include: Offline stage and online stage; The offline stage includes: Step S1.1: Establish an RVE model representing the microscopic characteristics of the material structure and calculate its elastic mechanical response; Step S1.2: Calculate the strain concentration tensor at the integration point according to the elastic strain distribution of the RVE; Step S1.3: Based on the strain concentration tensor, the integration points are divided into clusters using the K-means clustering algorithm; Step S1.4: Calculate the cluster interaction tensor components by Green’s function and Fourier transform method; The online phase includes: Step S2.1: Input the initial reference material Lame constants and the interaction tensor components generated in the offline stage; Step S2.2: Calculate the interaction tensor between each cluster based on the reference material Lame constant and the interaction tensor components generated in the offline stage; Step S2.3: solving the Lippmann-Schwinger equation by a data-driven method; Step S2.4: Calculate the RVE homogenization Lame constant based on the cluster equilibrium constraint point at time t+1; Step S2.5: Update the reference material Lame constant according to the RVE homogenization Lame constant, repeat steps S2.2 to S2.4 until the RVE homogenization Lame constant is consistent with the reference material Lame constant, and obtain the final cluster equilibrium constraint point and RVE homogenization stress at time t+1; Step S2.6: Return the homogenized stress of RVE to the macroscopic integration point to obtain the macroscopic and microscopic mechanical response of the material; The step S2.3 comprises: Step S2.3.1: Input the homogenized strain increment of the micro-scale RVE according to the strain constraint of the macro-integration point; Step S2.3.2: updating the cluster material data set at time t according to the initial material data set, the initial material state variables and the cluster material state variables at time t; Step S2.3.3: assigning initial material data points to each cluster based on the cluster material data set at time t; Step S2.3.4: Taking the minimum energy deviation between the cluster stress-strain state and the data point stress-strain state as the optimization goal, taking the Lippmann-Schwinger equation and the homogenization strain constraint as constraints, and establishing the objective function under the constraints; Step S2.3.5: Using the Lagrange multiplier method to solve the objective function minimization problem under the above constraints, a linear equation system about the stress-strain state of the cluster is established by finding the minimum point of the objective function; Step S2.3.6: Solve the above linear equations to obtain the cluster stress-strain distribution state that satisfies the constraint conditions, and use it as the new cluster equilibrium constraint point; Step S2.3.7: According to the cluster equilibrium constraint point, find the data point with the closest energy deviation in the cluster material data set at time t, and use it as the new cluster material data point; Step S2.3.8: Repeat steps S2.3.6 to S2.3.7 until the material data points of the cluster converge, and obtain the cluster material data points and cluster equilibrium constraint points at time t+1; Step S2.3.9: Update the cluster material state variables according to the cluster material data points at time t+1; Step S2.3.10: Update the RVE homogenized stress according to the cluster equilibrium constraint point at time t+1.

2. The data-driven multi-scale concurrent simulation method for loading history according to claim 1, characterized in that: The step S1.2 comprises: according to the strain distribution ε under six orthogonal loading conditions m (x), calculate the strain concentration tensor A(x) at the integration point; the strain concentration tensor A(x) is related to the macroscopic homogenized strain ε M and microscopic strain distribution ε m The fourth-order tensor of (x) is calculated by the following expression: e m (x)=A(x):e M 。 3. The method for multi-scale concurrent simulation based on data driven by loading history according to claim 1, characterized in that: The step S1.3 comprises: Based on the strain concentration tensor A(x) of the integration point, the integration points in RVE are clustered by the K-means clustering algorithm, that is, the following least squares optimization process of the strain concentration tensor is completed: Among them, S represents the final cluster division result, S J represents the Jth cluster, A n represents the strain concentration tensor at the nth integration point, represents the average strain concentration tensor of all integration points in the Jth cluster, N is the total number of clusters, and ||A|| represents the 2-norm of any second-order tensor A, that is, the 1 / 2 power of the sum of the squares of each element of A.

4. The method for multi-scale concurrent simulation based on data driven by loading history according to claim 1, characterized in that: The step S1.4 comprises: Combined Green's function and Fourier transform methods to calculate the interaction tensor components between individual clusters and The expressions are: Where, Ω is the volume of RVE, c I is the volume fraction of the Ith cluster, χ I (x) is the characteristic function of the I-th cluster, Φ 1 and Φ 2 is the part of the Green function that is independent of the reference material constitutive structure and has the following form in Fourier space: Among them, ξ is the coordinate vector in Fourier space, i is the coordinate of the i-th direction in Fourier space, |ξ| is the distance from the origin to the Fourier space coordinate, δ ij is the Kronecker delta symbol, satisfying 5. A data-driven multi-scale concurrent simulation system with loading history, characterized in that: include: Offline stage and online stage; The offline stage includes: Module M1.1: Establish an RVE model that represents the microscopic characteristics of the material structure and calculate its elastic mechanical response; Module M1.2: Calculate the strain concentration tensor at the integration point based on the elastic strain distribution of the RVE; Module M1.3: Based on the strain concentration tensor, the integration points are clustered using the K-means clustering algorithm; Module M1.4: Calculate the cluster interaction tensor components by Green's function and Fourier transform methods; The online phase includes: Module M2.1: Input the initial reference material Lame constants and the interaction tensor components generated in the offline stage; Module M2.2: Calculate the interaction tensor between clusters based on the reference material Lame constant and the interaction tensor components generated in the offline stage; Module M2.3: Solving the Lippmann-Schwinger equation via a data-driven approach; Module M2.4: Calculate the RVE homogenization Lame constant based on the cluster equilibrium constraint point at time t+1; Module M2.5: Update the reference material Lame constant according to the RVE homogenization Lame constant, repeat modules M2.2 to M2.4 until the RVE homogenization Lame constant is consistent with the reference material Lame constant, and obtain the final cluster equilibrium constraint point and RVE homogenization stress at time t+1; Module M2.6: Return the homogenized stress of RVE to the macroscopic integration point to obtain the macroscopic and microscopic mechanical response of the material; The module M2.3 includes: Module M2.3.1: Input the homogenized strain increment of the microscale RVE according to the strain constraints at the macroscopic integration points; Module M2.3.2: Update the cluster material data set at time t based on the initial material data set, the initial material state variables and the cluster material state variables at time t; Module M2.3.3: Assign initial material data points to each cluster based on the cluster material data set at time t; Module M2.3.4: Taking the minimum energy deviation between the cluster stress-strain state and the data point stress-strain state as the optimization goal, and taking the Lippmann-Schwinger equation and the homogenization strain constraint as the constraint conditions, establish the objective function under the constraint conditions; Module M2.3.5: Use the Lagrange multiplier method to solve the objective function minimization problem under the above constraints. By finding the minimum point of the objective function, a linear equation system about the stress-strain state of the cluster is established; Module M2.3.6: Solve the above linear equations to obtain the cluster stress-strain distribution state that satisfies the constraint conditions and use it as the new cluster equilibrium constraint point; Module M2.3.7: Based on the cluster equilibrium constraint point, find the data point with the closest energy deviation in the cluster material data set at time t and use it as the new cluster material data point; Module M2.3.8: Repeat Module M2.3.6 to Module M2.3.7 until the material data points of the cluster converge, and obtain the cluster material data points and cluster equilibrium constraint points at time t+1; Module M2.3.9: Update the cluster material state variables according to the cluster material data points at time t+1; Module M2.3.10: Update the RVE homogenized stresses based on the cluster equilibrium constraint points at time t+1.

6. The data-driven multi-scale concurrent simulation system for loading history according to claim 5, characterized in that: The module M1.2 includes: strain distribution ε according to six orthogonal loading conditions m (x), calculate the strain concentration tensor A(x) at the integration point; the strain concentration tensor A(x) is related to the macroscopic homogenized strain ε M and microscopic strain distribution ε m The fourth-order tensor of (x) is calculated by the following expression: e m (x)=A(x):e M 。 7. The data-driven multi-scale concurrent simulation system for loading history according to claim 5, characterized in that: The module M1.3 includes: Based on the strain concentration tensor A(x) of the integration point, the integration points in RVE are clustered by the K-means clustering algorithm, that is, the following least squares optimization process of the strain concentration tensor is completed: Among them, S represents the final cluster division result, S J represents the Jth cluster, A n represents the strain concentration tensor at the nth integration point, represents the average strain concentration tensor of all integration points in the Jth cluster, N is the total number of clusters, and ||A|| represents the 2-norm of any second-order tensor A, that is, the 1 / 2 power of the sum of the squares of each element of A.

8. The data-driven multi-scale concurrent simulation system for loading history according to claim 5, characterized in that: The module M1.4 includes: Combined Green's function and Fourier transform methods to calculate the interaction tensor components between individual clusters and The expressions are: Where, Ω is the volume of RVE, c I is the volume fraction of the Ith cluster, χ I (x) is the characteristic function of the I-th cluster, Φ 1 and Φ 2 is the part of the Green function that is independent of the reference material constitutive structure and has the following form in Fourier space: Among them, ξ is the coordinate vector in Fourier space, i is the coordinate of the i-th direction in Fourier space, |ξ| is the distance from the origin to the Fourier space coordinate, δ ij is the Kronecker delta symbol, satisfying

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