A method and system for predicting the Poisson's ratio performance of microstructures based on the representative volume element method

Abstract

The present invention belongs to the field of predicting the equivalent performance of microstructures, and specifically discloses a method and system for predicting the Poisson's ratio performance of microstructures based on the representative volume element method, which includes the steps of: extracting the geometric features of the target microstructure, constructing a set of feature lines, and obtaining the original local level set value; adding a feature coefficient to the original local level set value to obtain a local level set function, establishing a geometric model of the microstructure, and obtaining the volume fraction of the microstructure; based on the representative volume element method, constructing an equivalent model according to the geometric model of the microstructure; further constructing an equivalent Poisson's ratio performance calculation model for the microstructure; sampling the volume fraction of the microstructure, and obtaining the corresponding equivalent Poisson's ratio according to the equivalent Poisson's ratio performance calculation model, to obtain multiple groups of volume fraction and equivalent Poisson's ratio sample data; training a surrogate model according to the sample data to obtain a performance prediction model, and realizing the prediction of the Poisson's ratio performance of the microstructure. The present invention can achieve fast and high-precision prediction of the Poisson's ratio performance of microstructures.

Description

Technical Field

[0001] The present invention belongs to the field of prediction of equivalent properties of microstructures, and more specifically, relates to a method and system for predicting the Poisson's ratio performance of microstructures based on the representative volume element method. Background Art

[0002] Poisson's ratio refers to the ratio of the transverse normal strain to the axial normal strain when a material is uniaxially tensioned or compressed. It is also called the transverse deformation coefficient and is an elastic constant reflecting the transverse deformation of the material. The elastic modulus and shear modulus of a material are closely related to Poisson's ratio. When Poisson's ratio changes from a positive number to a negative number, the shear resistance of the material is significantly improved. Negative Poisson's ratio metamaterials and structures have excellent mechanical properties such as shear resistance, impact resistance, fracture resistance, energy absorption and vibration isolation, variable permeability, and surface isotropy. In aerospace, negative Poisson's ratio materials have good impact resistance and are important applications in aircraft wings and fuselages. In navigation, due to their excellent vibration isolation and noise reduction performance, they can be applied to the vibration reduction of ship equipment. In biomedicine, negative Poisson's ratio metamaterials can be used as raw materials for manufacturing equipment such as artificial skin, vascular stents, and medical bandages.

[0003] Therefore, how to accurately solve the Poisson's ratio performance of structural materials has important practical and engineering significance. However, at present, based on finite element simulation or experimental calculation for Poisson's ratio prediction, it is impossible to achieve or the implementation cost is too high and the calculation efficiency is too low, and it is difficult to find the optimal design scheme. Summary of the Invention

[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a method and system for predicting the Poisson's ratio performance of microstructures based on the representative volume element method. The purpose is to improve the calculation accuracy of the equivalent Poisson's ratio based on the representative volume element method, improve the prediction efficiency based on the surrogate model, and combine with the Poisson's ratio performance calculation model to achieve fast and accurate prediction of the equivalent Poisson's ratio performance of microstructures.

[0005] To achieve the above object, according to one aspect of the present invention, a method for predicting the Poisson's ratio performance of microstructures based on the representative volume element method is proposed, including the following steps:

[0006] S1. Extract the geometric features of the target microstructure, construct a set of feature lines, and then obtain the original local level set value; add a feature coefficient to the original local level set value to obtain a local level set function, thereby establishing a geometric model of the microstructure and obtaining the volume fraction of the microstructure;

[0007] S2. Based on the representative volume element method, construct an equivalent model according to the geometric model of the microstructure; and then construct an equivalent Poisson's ratio performance calculation model of the microstructure according to the equivalent model;

[0008] S3. Sample the volume fraction of the microstructure, and obtain the corresponding equivalent Poisson's ratio according to the equivalent Poisson's ratio performance calculation model, so as to obtain multiple groups of volume fraction and equivalent Poisson's ratio sample data; train the surrogate model based on the sample data to obtain a performance prediction model, thereby realizing the prediction of the Poisson's ratio performance of the microstructure.

[0009] As a further preference, in step S1, the method for constructing the local level set function is specifically as follows:

[0010] Construct a set of feature lines η = {L1, L2,..., L J}; L j represents the j-th feature line of the microstructure, j ∈ 1, 2,..., J;

[0011] Discretize the rectangular parameter space using a finite element grid, and calculate the original local level set value of the microstructure based on the set of feature lines η represents the extended signed distance value of the j-th feature line;

[0012] Furthermore, invert the original local level set value and add a feature coefficient h to obtain the local level set function Φ(η, x) to characterize microstructures with different volume fractions, that is, Φ(η, x) = -φ(η, x) + h.

[0013] As a further preference, in step S1, the calculation formula for the volume fraction v of the microstructure is as follows:

[0014]

[0015]

[0016] where Ω is the set of all possible shapes, D is the design domain of the microstructure, s is the area of the design domain, x is the coordinate of the node in the high-dimensional space, and H represents the Heaviside function.

[0017] As a further preference, during the process of establishing the geometric model of the microstructure, the dynamic structure interface is implicitly embedded as the zero level set surface of the high-dimensional local level set function Φ(η, x), which is defined as follows:

[0018]

[0019] where Γ represents the structure boundary and corresponds to the zero level set surface, and Φ can be freely expressed as any shape.

[0020] As a further preference, in step S2, an equivalent model is constructed based on the representative volume element method, that is, the original heterogeneous material is equivalently replaced by a homogeneous material; then, based on the equivalent model, axial loading is applied to the homogeneous material, and for a specified axial displacement, the corresponding lateral displacement generated is obtained, thereby obtaining the equivalent Poisson's ratio.

[0021] As a further preference, in step S3, Latin hypercube sampling is used to sample the microstructure volume fraction.

[0022] As a further preference, in step S3, the surrogate model is specifically a Kriging surrogate model.

[0023] According to another aspect of the present invention, a microstructure Poisson's ratio performance prediction system based on the representative volume element method is provided, which includes a processor for executing the above-mentioned microstructure Poisson's ratio performance prediction method based on the representative volume element method.

[0024] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the following technical advantages are mainly possessed:

[0025] 1. The present invention constructs a local level set function of the microstructure based on the gradient microstructure geometric features, constructs a microstructure geometric model from the local level set function, and realizes the generation of gradient substructures of any microstructure configuration; and constructs a homogenized equivalent model based on the representative volume element method, and then calculates the equivalent Poisson's ratio performance of the microstructure; finally, in combination with the surrogate model, fast and high-precision prediction of the microstructure Poisson's ratio performance is realized.

[0026] 2. The present invention uses a local level set function to construct a gradient-filled microstructure geometric model. Based on the microstructure geometric features, gradient substructures of any microstructure configuration can be obtained, and a clearer and smoother boundary can be obtained by generating the microstructure using the level set function.

[0027] 3. The present invention constructs an equivalent homogeneous model based on the representative volume element method for calculation, which is closer to the actual performance of the material, fully considers the structural form and size effect, has high model calculation accuracy, and obtains material properties more in line with engineering practical applications.

[0028] 4. The present invention uses a Kriging surrogate model to construct a fast prediction model for Poisson's ratio performance, which can realize fast performance prediction with high precision and high efficiency, and greatly reduces the calculation cost of the equivalent performance of the microstructure. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flowchart of the microstructure Poisson's ratio performance prediction method based on the representative volume element method according to an embodiment of the present invention;

[0030] Figure 2 It is a schematic diagram of the initial microstructure configuration according to an embodiment of the present invention;

[0031] Figure 3 In (a) and (b) are schematic diagrams of the characteristic line set and the local level set function of the embodiment of the present invention;

[0032] Figure 4 is a schematic diagram of the boundary conditions and external loads of the equivalent model of the embodiment of the present invention;

[0033] Figure 5 In (a) and (b) are the stress nephogram and displacement nephogram of the microstructure of the embodiment of the present invention;

[0034] Figure 6 is a curve graph of the relationship between the volume fraction of the microstructure and the equivalent Poisson's ratio performance of the embodiment of the present invention;

[0035] Figure 7 is the model accuracy curve of the embodiment of the present invention. Detailed implementation manners

[0036] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0037] A method for predicting the Poisson's ratio performance of a microstructure based on the representative volume element method provided by an embodiment of the present invention, as Figure 1 shown, includes the following steps:

[0038] S1. Construct a geometric model of a gradient-filled microstructure based on the local level set. Specifically, construct a set of characteristic lines according to the geometric characteristics of the target filled microstructure; discretize the rectangular parameter space using finite element meshes, and calculate the extended signed distance value for each microstructure based on the set of characteristic lines, thereby obtaining the original local level set value; invert the original local level set value, and add a characteristic coefficient h to characterize the microstructures with different volume fractions, and calculate the volume fraction of the microstructures under different characteristic coefficients based on the local level set function;

[0039] S2. Based on the theory of the representative volume element method and the geometric model of the gradient-filled microstructure obtained in step S1, construct a parametric model of the gradient microstructure; calculate the performance manifestations of the microstructure under different parameter spaces, and explore the mechanical properties of the gradient microstructure under external loads based on COMSOL finite element simulation; construct a homogeneous equivalent model of the microstructure based on the representative volume element method, and construct an equivalent Poisson's ratio performance calculation model of the gradient microstructure based on the combined simulation programming of MATLAB and COMSOL;

[0040] S3. Construct a surrogate model based on the equivalent Poisson's ratio performance calculation model obtained in step S2 to achieve high-precision prediction of the microstructure performance. Specifically, determine the value range of the design variables, that is, the value range of the characteristic parameters of the gradient microstructure; use the Latin hypercube experimental design method to select an appropriate number of samples in the parameter space for training, and construct a Kriging surrogate model based on the training samples; select an appropriate number of test samples to calculate the absolute error and root mean square error between the Kriging surrogate model solution and the finite element solution to verify the accuracy of the model.

[0041] As a further preference, in step S1, the method for constructing the local level set function of the microstructure based on the extended signed distance function based on the geometric characteristics of the gradient microstructure can be used for generating similar sub-configurations of the microstructure with complex configurations. Extract the geometric characteristics of the target microstructure, and based on the microstructure characteristics, use geometric elements to extract the corresponding characteristic lines to construct a set of characteristic lines:

[0042] η = {L1, L2,..., L J}

[0043] where L j (j ∈ 1, 2,..., J) represents the j-th characteristic line of the microstructure. Discretize the rectangular parameter space using a finite element mesh, and calculate the local level set value of the microstructure based on the set of characteristic lines η:

[0044]

[0045] where represents the extended signed distance value from the j-th characteristic line, x is the coordinate of the node in the high-dimensional space, and the extended signed distance value is obtained from the extended signed distance function of each characteristic line:

[0046]

[0047] where α is the coefficient of the extended signed distance function, which can control the change rate of the local level set value, and η represents the position of the characteristic line. The extended signed distance function satisfies

[0048] For the corresponding microstructural substructures with arbitrary volume fractions, invert the local level set and add the characteristic coefficient h to obtain the local level set function to characterize the microstructures with different volume fractions:

[0049] Φ(η, x) = -φ(η, x) + h

[0050] where φ(η, x) is the constructed original local level set value, h represents the characteristic coefficient, and the microstructures with specific volume fractions can be embedded into the local level set function. The dynamic structural interface is implicitly embedded as the zero level set surface of the high-dimensional level set function Φ(η, x), which is defined as follows:

[0051]

[0052] Among them, Ω is the set of all possible shapes, Γ represents the structural boundary and corresponds to the zero level set surface, Φ can be freely expressed as any shape, and D is the design domain of the microstructure. Moreover, the microstructure constructed based on the level set-based boundary description technology has the advantages of smooth, clear boundary shape and no need for re-meshing, etc.

[0053] By exploring the mapping relationship between the characteristic coefficient and the volume fraction, using the characteristic coefficient of the interpolated level set function as the matrix design variable, the geometric model construction of the gradient-filled microstructure is completed, and the volume fraction of the microstructure is obtained from the level set value function:

[0054]

[0055] Among them, s represents the area of the design domain, and H represents the Heaviside function:

[0056]

[0057] v is a piecewise quadratic function, monotonically increasing between [0,1], and its piecewise condition depends on the basic shape of the predefined characteristic line. Similarly, the range of the volume fraction v can be controlled by restricting the range of h.

[0058] As a further preference, in step S2, a homogenized material equivalent substitution method based on the representative volume element theory can model any metamaterial microstructure as a homogeneous orthotropic medium with a certain effective modulus, and this effective modulus describes the "average" material properties of the composite material. To describe this macroscopically homogeneous medium, the macroscopic stress and the macroscopic strain are obtained by dividing the stress tensor σ ij and the strain tensor ε ij by the mean value of the representative volume element (Representative Volume Element, abbreviated as RVE):

[0059]

[0060] Placing the RVE under the appropriate boundary traction t, or the boundary displacement u i results in the average stress and the strain in the homogeneous medium. The total strain energy U (strain energy of the homogeneous material) stored in the effective medium volume V is:

[0061]

[0062] The strain energy U' (strain energy of inhomogeneous material) stored in the heterogeneous RVE with volume V is:

[0063]

[0064] From U' - U, we get:

[0065]

[0066] Based on the equilibrium equation, we can obtain Therefore, the above U' - U can be modified to:

[0067]

[0068] Based on Gauss's theorem, the volume integral is converted into a surface integral, where n is the unit normal vector, and on the surface S, u' = u, obtaining U' = U. This ensures the equivalence of the strain energy between the equivalent homogeneous material and the original inhomogeneous material. Therefore, the equivalent properties of the original inhomogeneous material can be determined by considering the RVE as an equivalent homogeneous material. Based on the representative volume element method, the equivalent substitution of the homogeneous material can be realized to solve the equivalent properties of the microstructure. In this invention, the structural Poisson's ratio property is taken as an example, but it is not limited to the Poisson's ratio property.

[0069] As a further preference, in step S2, a method for constructing a calculation model of the equivalent Poisson's ratio property of a gradient microstructure. The regular cuboid equivalent homogeneous material obtained by the equivalent substitution of the RVE has lengths a and b in the x and y directions respectively, and a thickness h along the xy plane. The xy - direction plane is intercepted, and the lower boundary and the left boundary are respectively set with displacements of 0 in the y - direction and x - direction. A specified displacement δ1 is applied on the y = b plane, generating a displacement δ2 in the x - direction. For the axial loading of the homogeneous material, the average strain can be simplified as the ratio of the structural displacement:

[0070]

[0071] Where, is the average strain in the x - direction, and a is the equivalent length of the RVE equivalent material in the x - direction. Therefore, the equivalent Poisson's ratio of the RVE is obtained as:

[0072]

[0073] As a further preference, in step S3, a fast prediction method based on the Kriging surrogate model. The Kriging method starts from the variable correlation and variability, and is a method for unbiased and minimum - variance estimation of variable values within a finite region based on a stochastic process. For the input x within the sample space, its response form is as follows:

[0074] y(x) = f(x, β)+z(x)

[0075] Where β is the regression coefficient, f(x,β) is the regression model, representing the mathematical expectation of y(x), which is a global approximation. z(x) is a random process, representing the deviation from the global approximation, and it has the following statistical properties:

[0076] The mean is 0:

[0077] E[z(x)] = 0

[0078] The variance is σ 2 :

[0079] Var[z(x)] = σ 2

[0080] For any two points x i , x j in the sample space, the covariance is

[0081] Cov[z(x i ), z(x j )] = σ 2 R(θ, x i , x j )

[0082] Where R is the correlation matrix, and R(θ, x i , x j ) is the correlation function with parameter θ between any two sample points x i , x j , which plays a key role in the accuracy of the simulation. R has many forms, and the widely used one is the Gaussian correlation function:

[0083]

[0084] The Kriging model has good continuity and local estimation, and has good prediction effect when simulating nonlinear problems. The present invention adopts the Kriging surrogate model technology to study the rapid prediction of the equivalent Poisson's ratio performance of the lattice microstructure.

[0085] As a further optimization, in step S3, a test design strategy based on Latin hypercube design. Latin hypercube design is also called Latin hypercube sampling (abbreviated as LHS), which is an efficient and popular full-space test design method. The essence of the Latin hypercube sampling method is a stratified sampling method that is relatively uniform on each level, avoiding local aggregation of sampling samples, and enabling rapid convergence even with a small number of samples. The Latin hypercube sampling method can avoid repeated sampling of samples, reduce the number of samplings, and make the sampled samples cover a wider range.

[0086] Its basic principle: If n samplings are carried out, assuming that the sample space created by the design variables is [0, 1], first divide the sample space into n equal parts, and conduct random sampling within each small interval Randomly draw the random numbers within these n intervals in a shuffled order. The n numbers obtained satisfy the following two conditions: (1) Each sample point is obtained by random sampling within a small interval; (2) There is exactly one sample point within each small interval. The sample point can be obtained by the following formula:

[0087]

[0088] where i represents the i-th sample point, and z represents a random number between [0, 1]. Then, x i represents the value x of the i-th sample point. k i is a random sampling from {0, 1, …, n - 1}. When i takes values from 1 to n, k i takes one of the values, and each time sampling is carried out, k i does not take repeated values. This ensures that there is exactly one sample point within each small interval and the sample point is randomly sampled within the small interval.

[0089] When generating random samples in sampling acquisition, simply using random sampling will lead to local data aggregation. Latin hypercube design well solves this problem. Therefore, the present invention adopts Latin hypercube design for model experiment design, specifically adopts Latin hypercube sampling to sample the microstructural volume fraction, inversely deduce the characteristic coefficient according to the microstructural volume fraction, and then calculate the corresponding equivalent Poisson's ratio according to the equivalent Poisson's ratio performance of the model, so as to obtain multiple groups of volume fraction and equivalent Poisson's ratio sample data.

[0090] As a further preference, in step S3, a surrogate model accuracy evaluation strategy based on an error index is to predict the test samples in an additional n sample spaces by using the constructed Kriging surrogate model, and use the following 2 error indices to evaluate the prediction accuracy of the Kriging model in the design space:

[0091] (1) Maximal Errors (ME for short). The maximal absolute error ME is the maximum error generated when the constructed Kriging model predicts all test samples, which can reflect the accuracy of the model in a local range of the design space. The maximal absolute error ME is:

[0092]

[0093] where f i is the true value of the i-th sample point, is the approximate value of the corresponding sample point, and n is the number of sample points.

[0094] (2) The Root Mean Square Errors (RMSE for short). The root mean square error is the square root of the ratio of the sum of the squares of the deviations between the predicted values and the true values to the number of samples n. It is often used to measure the deviation between the predicted values and the true values and is sensitive to outliers in the data. It is defined as:

[0095]

[0096] where f i is the true value of the i-th sample point, is the approximate value of the corresponding sample point, and n is the number of sample points.

[0097] The following are specific examples:

[0098] The prototype microstructure is as Figure 2 shown. The overall size of the structure is 40mm x 40mm, the finite element mesh is 100 x 100, and the properties of the matrix material are defined as the elastic modulus E0 = 1 and the Poisson's ratio μ = 0.3. Feature lines are extracted from the prototype microstructure to construct a set of feature lines. Based on the set of feature lines, the extended signed distance function of each microstructure in the design domain is calculated, and finally, a set of feature lines and a local level set function are constructed as Figure 3 shown. Different volume fraction microstructure models are constructed based on the feature coefficient h, and a gradient microstructure geometric model is successfully constructed.

[0099] A performance calculation model for the equivalent Poisson's ratio of the microstructure is constructed based on Matlab and COMSOL. Different volume fraction microstructures are obtained based on Matlab and the parametric microstructure model, and the microstructures are imported into COMSOL for analysis. Boundary conditions are applied to the equivalent model as Figure 4 shown. A specified displacement constraint x = 0 is applied to the left boundary of the microstructure, a specified displacement constraint y = 0 is applied to the lower boundary of the microstructure, and a specified displacement of y = -1mm is applied to the upper boundary of the microstructure. The stress and displacement deformation diagrams of the microstructure are as Figure 5 shown. When the volume fraction v = 0.5, the displacement in the x direction of the microstructure is measured to be 0.841mm. The strain of the structure can be calculated from the displacement as ε x = 0.021, ε y = -0.025, and the Poisson's ratio of the structure can be calculated from the formula to be 0.84.

[0100] Taking the constructed equivalent Poisson's ratio calculation model as the basic method, sample data is collected. The initial sampling points are designed to be 20, and the total number of samplings is designed to be 600. The experimental design strategy is Latin hypercube design. The volume fraction v sample space is between [0.1, 0.95]. A Kriging surrogate model is constructed, and predictions are made based on the surrogate model. The performance relationship curve between the structural gradient microstructure volume fraction and the equivalent Poisson's ratio is obtained as Figure 6 shown. The equivalent Poisson's ratio of the microstructure gradually decreases as the material volume fraction increases. And the time required to predict the Poisson's ratio performance according to the model is within 1 s. The prediction accuracy of the constructed Kriging surrogate model is evaluated within the global and local ranges of the design space, and the prediction accuracy curve of the model is obtained as Figure 7 shown, and the accuracy rate is above 98%. The maximum absolute error of the constructed model is 7.26e -3 , and the root mean square error is 4.02e -3 . The results show that the method proposed by the invention has high accuracy and calculation efficiency.

[0101] The present invention provides a high-precision equivalent performance prediction scheme, which improves the calculation accuracy of the equivalent Poisson's ratio based on the representative volume element method, and improves the prediction efficiency based on the surrogate model to obtain accurate predictions of material properties. Specifically, based on the representative volume element theory, the heterogeneous material is homogenized and simulated to obtain a homogeneous material with the same properties and easy-to-analyze performance. Combining the surrogate model technology, instead of executing the simulation program or experiment, the objective function and constraints are approximately represented by a mathematical model, searched in the design space to obtain the optimal solution of the approximate problem, and then the approximate model is corrected by the actual simulation analysis at the optimal solution, and then searched until convergence. The surrogate model has the same input and output parameters as the actual simulation program. Combined with the Poisson's ratio calculation model, it can quickly and accurately predict the equivalent Poisson's ratio performance of the corresponding microstructure.

[0102] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the Poisson's ratio performance of microstructures based on the representative volume element method, characterized in that It includes the following steps: S1. Extract the geometric features of the target microstructure, construct a set of feature lines, and then obtain the original local level set values; add a feature coefficient to the original local level set values to obtain a local level set function, thereby establishing a microstructure geometric model and obtaining the volume fraction of the microstructure; S2. Based on the representative volume element method, construct an equivalent model according to the microstructure geometric model; and then, according to the equivalent model, construct an equivalent Poisson's ratio performance calculation model for the microstructure; S3. Sample the volume fraction of the microstructure, and obtain the corresponding equivalent Poisson's ratio according to the equivalent Poisson's ratio performance calculation model, so as to obtain multiple groups of volume fraction and equivalent Poisson's ratio sample data; train the surrogate model according to the sample data to obtain a performance prediction model, thereby realizing the prediction of the Poisson's ratio performance of the microstructure.

2. The method for predicting the Poisson's ratio performance of the microstructure based on the representative volume element method according to claim 1, wherein, In step S1, the specific method for constructing the local level set function is as follows: Construct the characteristic line set η={L1,L2,...,L J };L j Represents the jth characteristic line of the microstructure, j∈1,2,...,J; Discretize the rectangular parameter space using a finite element mesh and calculate the original local level set values of the microstructure based on the set of characteristic lines η The extended signed distance value representing the j-th characteristic line; Furthermore, invert the original local level set values and add a feature coefficient h to obtain the local level set function Φ(η, x) to represent microstructures with different volume fractions, that is, Φ(η, x) = -φ(η, x) + h.

3. The method for predicting the Poisson's ratio performance of the microstructure based on the representative volume element method according to claim 2, wherein In step S1, the calculation formula for the volume fraction v of the microstructure is as follows: where Ω is the set of all possible shapes, D is the design domain of the microstructure, s is the area of the design domain, x is the coordinate of the node in the high-dimensional space, and H represents the Heaviside function.

4. The method for predicting the Poisson's ratio performance of the microstructure based on the representative volume element method according to claim 3, wherein During the process of establishing the microstructure geometric model, the dynamic structure interface is implicitly embedded as the zero level set surface of the high-dimensional local level set function Φ(η, x), which is defined as follows: where Γ represents the structure boundary and corresponds to the zero level set surface, and Φ can be freely expressed as any shape.

5. The method for predicting the Poisson's ratio performance of a microstructure based on the representative volume element method according to claim 1, wherein In step S2, based on the representative volume element method, construct an equivalent model, that is, equivalently replace the original heterogeneous material with a homogeneous material; and then, based on the equivalent model, apply an axial load to the homogeneous material, then for a specified axial displacement, obtain the corresponding lateral displacement generated, thereby obtaining the equivalent Poisson's ratio.

6. The method for predicting the Poisson's ratio performance of a microstructure based on the representative volume element method according to claim 1, wherein In step S3, Latin hypercube sampling is used to sample the volume fraction of the microstructure.

7. The method for predicting the Poisson's ratio performance of a microstructure based on the representative volume element method according to any one of claims 1-6, characterized in that, In step S3, the surrogate model is specifically a Kriging surrogate model.

8. A microstructural Poisson's ratio performance prediction system based on the representative volume element method, characterized in that, It includes a processor, and the processor is used to execute the method for predicting the Poisson's ratio performance of the microstructure based on the representative volume element method according to any one of claims 1-7.

Images