General constitutive modeling method for complex yield evolution of data-physical driven metals

Abstract

This invention discloses a data-physics driven general constitutive modeling method for the complex yield evolution of metals, including: establishing a multi-directional radial yield label set; selecting a reference loading direction; constructing a reference hardening benchmark; normalizing and feature-encoding the cumulative plastic strain in the multi-directional radial yield label set; inputting the feature-encoded cumulative plastic strain into a first sub-network and a second sub-network respectively; obtaining a metric operator; obtaining the positive and negative support weights corresponding to the support vectors in each direction; constructing metric components; constructing directional support components; obtaining the convex gauge yield function; obtaining a smart model of the yield surface; predicting the radial yield stress; and obtaining the complete yield surface. This invention addresses the problem of limited adaptability of fixed analytical functions to complex yield surface morphologies in existing technologies, achieving the goal of separating and characterizing overall hardening, global anisotropic distortion, and local directional asymmetry.

Description

Technical Field

[0001] This invention relates to the field of constitutive modeling of metallic materials, and more specifically to a data-physics driven general constitutive modeling method for complex yield evolution of metals. Background Technology

[0002] After a metallic material undergoes plastic deformation, its yield state typically evolves throughout the deformation history. This evolution manifests not only as an overall increase, decrease, or saturation of the yield stress, but also as changes in the yield strength relationship between different material directions, variations in the overall shape and principal direction of the yield surface, changes in local curvature, and changes in the degree of asymmetry between opposite loading directions such as tension and compression. For metallic materials with pronounced texture characteristics, such as titanium alloys and magnesium alloys, their macroscopic yield behavior is also influenced by factors such as crystal structure, slip and twinning mechanisms, and loading paths, thus potentially exhibiting complex anisotropy and asymmetry under different stress states, including axial, transverse, shear, and biaxial. Traditional analytical yield models typically predefine the form of the yield function and then describe the directionality and asymmetry of the yield surface through material parameters. These models are clearly expressive, computationally efficient, and can obtain numerically continuous evolution results by setting strain-related parameter functions or calibrating parameters at several cumulative plastic strain levels and performing interpolation.

[0003] However, the geometric shape of the yield surface that can be represented by analytical models is limited by the predefined function form. When a material simultaneously exhibits overall distortion, local convexity, shear differential, biaxial differential, and tensile-compression asymmetry, multiple analytical terms and undetermined parameters are usually required, which can easily lead to problems such as parameter coupling, complex calibration, and difficulty in distinguishing the effects of different parameters. For methods that use independent calibration of individual strain levels followed by parameter interpolation, the convexity, directional compatibility, and rationality of asymmetric evolution of the yield surface in intermediate states usually require additional checks.

[0004] With the development of machine learning technology, existing methods have directly regressed radial yield stress by accumulating plastic strain and loading direction. These methods have strong data fitting capabilities, but the outputs of each loading direction are essentially still independent scalar predictions and cannot necessarily form a yield surface that satisfies the requirements of plasticity theory in the complete stress space. When the training data coverage is insufficient or the loading directions are sparse, problems such as local concavity, unclosed yield surface, non-first-order positive homogeneity, or non-unique radial intersection points may occur. Furthermore, ordinary neural networks typically mix global hardening, global anisotropic changes, and local asymmetric responses in the same set of network parameters, and their continuous evolution is mainly encoded in the network weights.

[0005] Therefore, there is an urgent need for an intelligent modeling method that can separate and characterize overall hardening, global anisotropic distortion, and local directional asymmetry, while maintaining convexity, first-order homogeneity, and radial uniqueness in a unified model structure. Summary of the Invention

[0006] This invention provides a data-physics driven general constitutive modeling method for complex yield evolution in metals, which solves the problems in existing technologies such as the limited adaptability of fixed analytical functions to complex yield surface morphology, the reliance on post-interpolation of discrete parameter sets for strain level modeling, the difficulty of ordinary neural networks in maintaining the geometric acceptability of the yield surface, and the difficulty in interpreting the evolution law of intelligent constitutive models. It achieves the goal of separating and characterizing overall hardening, global anisotropic distortion, and local directional asymmetry, while maintaining convexity, first-order homogeneity, and radial uniqueness in a unified model structure.

[0007] This invention is achieved through the following technical solution:

[0008] A data-physics-driven general constitutive modeling method for complex yield evolution in metals includes the following steps:

[0009] S1. Obtain the response data of the metallic material to be modeled under several different loading directions and several different cumulative plastic strain states, and establish a multi-directional radial yield tag set; the multi-directional radial yield tag set includes cumulative plastic strain, loading direction and radial yield stress;

[0010] S2. Based on the multi-directional radial yield tag set, select at least one loading direction as a reference loading direction; construct a reference hardening benchmark based on the radial yield stress of the reference loading direction under different cumulative plastic strain states.

[0011] S3. Based on the reference hardening benchmark, normalize and feature-encode the cumulative plastic strain in the multi-directional radial yield tag set;

[0012] S4. Input the cumulative plastic strain after feature encoding into the first sub-network and the second sub-network respectively;

[0013] The first sub-network is used to output metric evolution parameters and obtain metric operators;

[0014] The second sub-network is used to set multiple directional support vectors in the deviatoric stress space and output the positive support weight and negative support weight corresponding to each directional support vector;

[0015] S5. Construct metric components using the metric operator;

[0016] Using the positive and negative support weights, a directional support component is constructed;

[0017] The metric component and the directional support component are convexly aggregated and normalized based on the reference hardening datum to obtain the convex gauge yield function.

[0018] S6. Based on the multi-directional radial yield label set, train the convex gauge yield function to obtain the yield surface intelligent model;

[0019] S7. Input the given cumulative plastic strain of the metal material to be modeled into the yield surface intelligent model to predict the radial yield stress and obtain the complete yield surface.

[0020] To address the limitations of existing technologies, such as the limited adaptability of fixed analytical functions to complex yield surface morphologies, reliance on post-hoc interpolation of discrete parameter sets for strain level modeling, the difficulty of maintaining the geometric acceptability of the yield surface in ordinary neural networks, and the difficulty in explaining the evolutionary laws of intelligent constitutive models, this application first proposes a data-physics-driven general constitutive modeling method for complex yield evolution in metals. This method first acquires response data of the metal material to be modeled under several different loading directions and several different cumulative plastic strain states, establishing a multi-directional radial yield label set. Then, a reference loading direction is selected, and a reference hardening benchmark is constructed based on the radial yield stress under different cumulative plastic strain states along the reference loading direction. This benchmark is used to characterize the overall dimensional evolution of the yield surface. That is, under any cumulative plastic strain state, the radial yield stress in other directions is normalized using the radial yield stress in the reference loading direction as the benchmark, and then feature-encoded for subsequent computational model training. The reference hardening benchmark can be obtained through interpolation of the radial yield response curve in the reference loading direction, fitting of an explicit hardening function, identification of a parameter generation model with positive constraints, or a combination thereof. Feature encoding can be implemented using existing encoding methods such as multinomial features, radial basis function features, and low-frequency periodic features, enabling the model to identify features that change rapidly at the beginning, tend to stabilize later, and evolve in multiple stages.

[0021] Subsequently, the cumulative plastic strain after feature encoding is input into the pre-established first and second sub-networks, respectively. The first sub-network outputs the metric evolution parameters and obtains the metric operator, while the second sub-network outputs the positive and negative support weights corresponding to the support vectors in each direction. Then, the metric components and directional support components are constructed and convex aggregation is performed to obtain the convex gauge yield function. The metric components are used to describe the global smooth anisotropic distortion, principal direction variation, and overall curvature variation of the yield surface; the directional support components are used to characterize the local directional strength correction that the metric components cannot fully describe, as well as the yield asymmetry between opposite loading directions. The convex gauge yield function, as the core prediction model of this application, refers to the yield function obtained under a given cumulative plastic strain. Under stress state The convex gauge yield function is a function that satisfies nonnegativity, convexity, and positive homogeneity of the first order. The convex gauge yield function takes a value of zero at the stress origin. Its value is not greater than the sub-level set of the reference hardening datum, which is used to define the elastic domain of the material. Its value is equal to the isosurface of the reference hardening datum, which is used to define the yield surface of the material. The convex gauge yield function does not require equal values ​​in the positive and reactive force directions, thus enabling it to characterize tensile-compression asymmetry. This application trains the convex gauge yield function based on a multi-directional radial yield label set to obtain a smart model of the yield surface, which is used to predict radial yield stress. Finally, by inputting the given cumulative plastic strain of the metallic material to be modeled into the smart model of the yield surface, the radial yield stress can be predicted, thereby obtaining the complete yield surface.

[0022] Furthermore, in step S1, the response data is obtained through physical and mechanical experiments and / or micromechanical virtual experiments;

[0023] The physical and mechanical tests include any one or more of the following: uniaxial tensile test, uniaxial compression test, shear test, biaxial loading test, reverse loading test, and non-proportional loading test;

[0024] The micromechanical virtual experiments include any one or more of the following: viscoplastic self-consistent virtual experiments, crystal plasticity finite element virtual experiments, representative volume element virtual experiments, and multi-scale homogenization virtual experiments.

[0025] The aforementioned different loading directions include at least two sets of loading states in opposite directions, and at least one of the following: non-axial loading state, shear loading state, and biaxial loading state.

[0026] Furthermore, step S2 specifically includes:

[0027] S201. From the set of multi-directional radial yield labels, select the unit loading direction with complete hardening response as the reference loading direction;

[0028] S202. Extract the radial yield stress under different cumulative plastic strains in the reference loading direction, arrange them in ascending order of cumulative plastic strain, and form a reference hardening data sequence.

[0029] S203. Merge the repeated points or data points within the preset strain tolerance range in the reference hardening data sequence, and use a continuous interpolation function or explicit hardening function for fitting to obtain a reference hardening benchmark that is continuous and positive within the modeling interval.

[0030] Furthermore, both the first sub-network and the second sub-network are multilayer perceptron models with continuous activation functions;

[0031] The input parameters of the first sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the metric operators;

[0032] The input parameters of the second sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the positive support weight and the negative support weight.

[0033] Furthermore, in step S5, the method for constructing metric components using the metric operator includes:

[0034] S501, Constructing a positive semidefinite metric matrix : In the formula: The metric operator is the cumulative plastic strain p; T is the transpose operator.

[0035] S502. Construct metric components based on the positive semidefinite metric matrix:

[0036] ;

[0037] In the formula: For measuring components; The stress that requires yield testing The deviatoric stress vector in the material coordinate system.

[0038] The positive semi-definite metric matrix is ​​used to define the direction-related metrics in the deviatoric stress space and to characterize the changes in the global principal direction of the yield surface, the degree of stretching in different directions, and the overall curvature as a function of cumulative plastic strain; the metric components are used to characterize the global smooth anisotropic distortion of the yield surface.

[0039] Furthermore, in step S5, the constructed directional support component is:

[0040] ;

[0041] In the formula: Representative stress The cumulative plastic strain p corresponds to the first Each direction supports the component; For the first Support vectors in each direction; , The first The positive support weight and negative support weight corresponding to each directional support vector; This represents taking the maximum internal value.

[0042] Furthermore, in step S5, the yield function of the convex gauge is obtained as follows:

[0043] ;

[0044] In the formula: Represents cumulative plastic strain State used to determine stress state The yield function that determines whether yielding occurs; This represents the reference hardening benchmark, i.e., the reference loading direction in the cumulative plastic strain. The radial yield stress under the condition is used to characterize the overall dimensional evolution of the yield surface; This represents the yield function value of the convex gauge after normalization to the reference loading direction, used to represent the stress state. Converted to the equivalent yield relative to the reference loading direction; The representation consists of the metric component and the support components in each direction, according to The yield function value of the original convex gauge formed by convex polymerization; q represents the value of the yield function of the original convex gauge in the unit loading direction; q is the convex convergence index; K is the number of directional support vectors; Loading direction in units.

[0045] Furthermore, the intelligent model of the yield surface predicts the radial yield stress using the following formula:

[0046] ;

[0047] In the formula: Represents cumulative plastic strain The radial yield stress amplitude predicted along the unit loading direction under the stress state is, in other words, the stress state. A positive scalar that satisfies the condition that the yield function is zero; The value of the normalized convex gauge yield function in the unit loading direction is used to characterize the difference in yield strength between this loading direction and the reference loading direction. In this formula... The loading direction of the representative unit.

[0048] Those skilled in the art will understand that "unit loading direction" in this application means any loading direction in stress space.

[0049] Furthermore, in step S7, the predicted radial yield stress is substituted into the yield function. Based on the zero-level set of the yield function, a complete yield surface under a given cumulative plastic strain is generated as the evolved yield surface, which is used for yield determination of metallic materials and elastoplastic constitutive calculations.

[0050] Furthermore, step S8 involves performing dimensionality reduction analysis and explicit function fitting on the convex gauge yield function after training to obtain an explicit evolutionary yield surface model.

[0051] The metric operator, along with the positive and negative support weights, trained under multiple cumulative plastic strain levels, forms the metric parameter trajectory and the directional support parameter trajectory, respectively. These metric parameter trajectories and directional support parameter trajectories are then centered and decomposed to extract the dominant adaptive modes that meet the preset cumulative explained variance requirements. The modal coefficients of the dominant adaptive modes are fitted using a single-stage saturation function, a two-stage saturation function, a saturation function with a linear correction term, or a combination thereof. Based on the fitted modal coefficients, the explicit metric operator, explicit positive and negative support weights are reconstructed and substituted into the convex gauge yield function to obtain an explicit evolutionary yield surface model that does not require calling the original metric parameter generation branch and directional support parameter generation branch.

[0052] Compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0053] 1. This invention does not perform independent direct regression of the radial yield stress in each loading direction, but establishes a unified convex yield gauge in the complete deviatoric stress space, which can form a continuous, closed and convex yield surface.

[0054] 2. This invention characterizes the overall size evolution of the yield surface, global anisotropic distortion, and local directional asymmetry by referring to the hardening benchmark, metric branch, and directional support branch, respectively, thereby reducing parameter coupling between different evolutionary effects and improving the physical interpretability of the model.

[0055] 3. The present invention adopts a positive semi-definite metric structure, a non-negative bounded direction support structure and a convex polymerization method, so that the yield surface under the fixed cumulative plastic strain state maintains its external convexity, first positive homogeneity and radial uniqueness, which is beneficial to improving the stability of elastoplastic constitutive calculation.

[0056] 4. This invention improves the ability to identify tensile-compression asymmetry, shear direction difference, biaxial direction difference and local convex features by using opposite-direction paired response constraints and key direction contrast constraints, and determines the expression capacity of metric branches and directional support branches by calibrating outer layer parameters.

[0057] 5. This invention can transform the continuous evolution relationship parameterized by the neural network into a low-dimensional explicit evolution law, improve the interpretability of the model while maintaining the main geometric features of the yield surface, and facilitate its application in finite element material subroutines and numerical calculations of metal forming. Attached Figure Description

[0058] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0059] Figure 1This is a flowchart illustrating a specific embodiment 1 of the present invention;

[0060] Figure 2 The results of the viscoplastic self-consistent model calibration and tensile and compression tests in Example 2 of this invention are shown.

[0061] Figure 3 For Embodiment 2 of the present invention, in the cumulative plastic strain Comparison of radial yield labels of the proposed model, the traditional reference model, and experimental and viscoplastic self-consistent virtual tests at different stress sections at 0.30; among them, Figure 3 (a) is section, Figure 3 (b) is section, Figure 3 (c) is section, Figure 3 (d) is Three-dimensional yield surface in stress space;

[0062] Figure 4 For Embodiment 3 of the present invention, in the cumulative plastic strain At 0.30, a comparison of the yield surfaces of the original prediction model and the explicit white-box model under different stress sections is shown; among them, Figure 4 (a) is section, Figure 4 (b) is section, Figure 4 (c) is section. Detailed Implementation

[0063] 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 embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0064] Example 1:

[0065] like Figure 1 The data shown represents a general constitutive modeling method for the complex yield evolution of metals driven by physics, comprising the following steps:

[0066] Step S1: Obtain response data of the metal material to be modeled under several different loading directions and several different cumulative plastic strain states, and establish a multi-directional radial yield tag set; the multi-directional radial yield tag set includes cumulative plastic strain, loading direction and radial yield stress.

[0067] In this embodiment, the response data is obtained through physical and mechanical experiments and / or micromechanical virtual experiments;

[0068] The physical and mechanical tests include any one or more of the following: uniaxial tensile test, uniaxial compression test, shear test, biaxial loading test, reverse loading test, and non-proportional loading test;

[0069] The micromechanical virtual experiments include any one or more of the following: viscoplastic self-consistent virtual experiments, crystal plasticity finite element virtual experiments, representative volume element virtual experiments, and multi-scale homogenization virtual experiments.

[0070] The aforementioned different loading directions include at least two sets of loading states in opposite directions, and at least one of the following: non-axial loading state, shear loading state, and biaxial loading state.

[0071] Preferably, the various loading directions include at least: tensile state in the principal direction of the material, compressive state in the principal direction of the material, non-axial loading state, shear-related loading state, and biaxial loading state.

[0072] For the unit loading direction in stress space The radial stress path is represented as:

[0073]

[0074] in, Under stress, For the unit loading direction The radial stress amplitude.

[0075] For proportional loading, when the material reaches a preset yield state or is under sustained plastic loading, the radial amplitude of the corresponding stress state is taken as the radial yield stress under the cumulative plastic strain state. When the preset cumulative plastic strain level coincides with the output point of the original physical mechanical test or micromechanical virtual test, the corresponding radial yield stress is directly extracted. When the preset cumulative plastic strain level is located between two adjacent original output points, interpolation is performed on the stress-cumulative plastic strain response curve along the corresponding loading direction. The interpolation can employ linear interpolation, piecewise cubic interpolation, monotonic spline interpolation, or other interpolation methods that maintain the continuity of the response curve.

[0076] When comparing two loading responses in opposite directions, the common cumulative plastic strain range of the two loading response curves is determined, and the two loading response curves are aligned to the common cumulative plastic strain level. A multi-directional radial yield tag set is formed by direct extraction or response curve interpolation, consisting of cumulative plastic strain, loading direction, and radial yield stress.

[0077] Response curve interpolation is used to obtain radial yield labels at a uniform cumulative plastic strain level from the output of discrete physical mechanics experiments or micromechanical virtual experiments, or to align response curves in opposite directions at the same strain level. The intermediate cumulative plastic strain state yield surface after training is directly generated by the same cumulative plastic strain parameterized model, rather than by post-hoc surface interpolation between two independently calibrated yield surfaces.

[0078] Step S2: Based on the multi-directional radial yield tag set, select at least one loading direction as a reference loading direction; based on the radial yield stress of the reference loading direction under different cumulative plastic strain states, construct a reference hardening benchmark.

[0079] Specifically, it includes:

[0080] S201. From the set of multi-directional radial yield labels, select the unit loading direction with complete hardening response as the reference loading direction;

[0081] S202. Extract the radial yield stress under different cumulative plastic strains in the reference loading direction, arrange them in ascending order of cumulative plastic strain, and form a reference hardening data sequence.

[0082] S203. Merge the repeated points or data points within the preset strain tolerance range in the reference hardening data sequence, and use a continuous interpolation function or explicit hardening function for fitting to obtain a reference hardening benchmark that is continuous and positive within the modeling interval.

[0083] The reference hardening datum characterizes the overall dimensional change of the yield surface, and the geometric differences between loading directions are characterized by a normalized convex yield gauge. The reference hardening datum can be obtained through interpolation of the radial yield response curve along the reference loading direction, fitting of an explicit hardening function, identification of a parameter generation model with positive constraints, or a combination thereof. When the material to be modeled exhibits monotonically hardening within the modeling interval, a monotonically non-decreasing constraint is applied to the reference hardening datum. When the material to be modeled exhibits a yield plateau, softening, or non-monotonic evolution, the monotonically non-decreasing constraint is removed, while the positive constraints of the reference hardening datum are retained.

[0084] Step S3: Based on the reference hardening benchmark, normalize and feature-encode the cumulative plastic strain in the multi-directional radial yield tag set.

[0085] This step normalizes the cumulative plastic strain to a preset range and encodes it using at least one of polynomial features, radial basis function features, and low-frequency periodic features, enabling the model to identify initial rapid changes, later stabilization, and multi-stage evolution characteristics.

[0086] Step S4: Input the cumulative plastic strain after feature encoding into the first sub-network and the second sub-network respectively;

[0087] The first sub-network is used to output metric evolution parameters and obtain metric operators;

[0088] The second sub-network is used to set multiple directional support vectors in the deviatoric stress space and output the positive support weight and negative support weight corresponding to each directional support vector.

[0089] In this embodiment, both the first sub-network and the second sub-network are multilayer perceptron models with continuous activation functions.

[0090] The input parameters of the first sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the metric operators; the metric operators are used to construct a positive semi-definite metric matrix to control the overall tensile, compressive, tilting, rotation and curvature changes of the yield surface.

[0091] The input parameters of the second sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the positive support weight and the negative support weight. The common change of the positive support weight and the negative support weight corresponding to the support vector in the same direction is used to control the local symmetry strength correction in that direction, and the difference between them is used to control the yield asymmetry between that direction and its opposite direction. The positive support weight and the negative support weight are generated through a non-negative and upper-bounded mapping method, thereby limiting the magnitude of local directional correction and avoiding unbounded growth of directional support branches.

[0092] Step S5: Construct metric components using the metric operator;

[0093] Using the positive and negative support weights, a directional support component is constructed;

[0094] The metric component and the directional support component are convexly aggregated and normalized based on the reference hardening datum to obtain the convex gauge yield function.

[0095] In this embodiment, the method for constructing metric components using the metric operator includes:

[0096] S501, Constructing a positive semidefinite metric matrix : In the formula: The metric operator is the cumulative plastic strain p; T is the transpose operator.

[0097] S502. Construct metric components based on the positive semidefinite metric matrix:

[0098] ;

[0099] In the formula: For measuring components; The stress that requires yield testing The deviatoric stress vector in the material coordinate system is obtained by transforming the stress state to be evaluated into the deviatoric stress space in the material coordinate system.

[0100] The directional support vectors can be set according to the material principal direction, the physical and mechanical test loading direction, the micromechanical virtual test loading direction, the shear direction, and the biaxial loading direction, or they can be used as training parameters under unit vector constraints. The directional support vectors can be grouped according to the material principal direction support group, the shear-related support group, and the biaxial-related support group, with different directional support groups having their respective support weight upper limits and activation scales set. The loading direction is not directly input into the first and second sub-networks, but rather interacts with the already generated metric operator and directional support weights during the subsequent evaluation of the convex yield strength model. Therefore, the yield strength model in this application learns the continuous relationship between the geometric variables inside the yield surface and the cumulative plastic strain, rather than learning independent radial yield stress curves for each loading direction.

[0101] The metric components are used to describe the globally smooth anisotropic distortion, principal direction variation, and overall curvature variation of the yield surface. Preferably, a non-directional bias operator consistent with the Mises deviatoric stress metric is used as a reference metric, and the first sub-network learns the residual variation relative to the reference metric. The reference metric serves only as a neutral geometric starting point and does not indicate that the metal material to be modeled is isotropic. The anisotropy of the metal material to be modeled is obtained by learning the metric residuals based on multi-directional radial yield labels.

[0102] In this embodiment, the constructed directional support component is:

[0103] ;

[0104] In the formula: Representative stress The cumulative plastic strain p corresponds to the first Each direction supports the component; For the first Support vectors in each direction; , The first The positive support weight and negative support weight corresponding to each directional support vector; This represents taking the maximum internal value.

[0105] The directional support component is used to supplement the local directional convexity, local directional contraction, and positive and negative directional asymmetry that are difficult to fully describe by the metric component.

[0106] In step S5, the yield function of the convex gauge is obtained as follows:

[0107] ;

[0108] In the formula: Represents cumulative plastic strain State used to determine stress state The yield function that determines whether yielding occurs; Represents the hardening reference standard; This represents the yield function value of the convex gauge after normalization to the reference loading direction. The representation consists of the metric component and the support components in each direction, according to The yield function value of the original convex gauge formed by convex polymerization; q represents the value of the yield function of the original convex gauge in the unit loading direction; q is the convex convergence index; K is the number of directional support vectors; Loading direction in units.

[0109] In this embodiment, the metric component and the support components in each direction are first convexly aggregated to form the original convex yield mass model:

[0110] .

[0111] Then, normalize according to the reference loading direction and construct the yield function to obtain the above convex gauge yield function.

[0112] The elastic domain defined by the yield function is the set of stress states where the yield function value is not greater than zero. Since the metric component is a linearly transformed norm and the directional support component is a one-sided linear convex function with non-negative weights and a convexity convergence exponent not less than 1, the yield gauge under a fixed cumulative plastic strain state is convex. Both the metric component and the directional support component satisfy first-order positive homogeneity with respect to stress, and normalization along the reference loading direction does not change this property, thus ensuring a unique positive radial yield stress in any given loading direction.

[0113] Step S6: Based on the multi-directional radial yield label set, train the convex gauge yield function to obtain the yield surface intelligent model.

[0114] The intelligent model of the yield surface predicts the radial yield stress using the following formula:

[0115] ;

[0116] In the formula: Represents cumulative plastic strain The radial yield stress amplitude predicted along the unit loading direction under the condition; This represents the value of the normalized convex gauge yield function in the unit loading direction.

[0117] The above formula allows direct acquisition of the radial yield stress under a given cumulative plastic strain and loading direction, without the need for iterative root finding along the loading direction. Radial data consistency constraints are constructed using the difference between the predicted radial yield stress and the corresponding radial yield label. For two loading states in opposite directions, the average yield response and yield difference are calculated for both loading states at the same cumulative plastic strain level. Based on the differences between the predicted average yield response and the labeled average yield response, and the differences between the predicted yield difference and the labeled yield difference, paired response constraints for opposite directions are constructed. The average yield response characterizes the common yield scale for opposite loading directions, and the yield difference characterizes the asymmetry between opposite loading directions.

[0118] For biaxial loading states and corresponding uniaxial loading states, shear-related loading states and material main direction loading states, or other preset key loading states, key direction comparison constraints are constructed to maintain the relative yield strength between the key loading states.

[0119] The model training objective in this embodiment consists of radial data consistency constraints, opposite-direction paired response constraints, and key-direction contrast constraints. Radial data consistency constraints are the basic constraints; opposite-direction paired response constraints are used to directly supervise the average and differential responses between stretching-compression or other opposite loading directions; and key-direction contrast constraints are used to correct the relative relationships between biaxial-single-axial or other key directions.

[0120] In a more preferred embodiment, the expression capacity of the first and second subnetworks can be determined using an outer layer parameter calibration method. The outer layer parameter calibration method is preferably Bayesian optimization, but grid search, random search, or evolutionary optimization can also be used. The parameters to be calibrated include at least two of the following: the number of residual bases, the magnitude of the residuals, the upper limit of the support weights for different directional support groups, the activation scale of different directional support groups, and the convex aggregation index.

[0121] For each combination of candidate parameters, candidate models are trained using the same dataset partitioning, number of training epochs, optimizer, and training objective. Candidate models are evaluated based on at least three of the following: mean radial error, tail radial error, maximum radial error, opposite-direction paired response error, key-direction contrast error, and contribution states of the metric component and the directional support component from the validation data.

[0122] In this embodiment, a fixed linear mixing ratio between the first and second sub-networks is not pre-set. The relative contribution of the two sub-networks is formed by their actual output amplitude in the convex yield scale model, and is determined by outer layer parameter calibration based on the response characteristics of the metallic material to be modeled.

[0123] Step S7: Input the given cumulative plastic strain of the metallic material to be modeled into the yield surface intelligent model to predict the radial yield stress and obtain the complete yield surface. That is, substitute the predicted radial yield stress into the yield function. Based on the zero-level set of the yield function, a complete yield surface under a given cumulative plastic strain is generated as the evolved yield surface.

[0124] This embodiment takes any given cumulative plastic strain as input to the trained intelligent model of the yield surface, and generates a unified reference hardening amount, metric operator, positive support weight, and negative support weight corresponding to the cumulative plastic strain. Substituting these parameters into the convex gauge yield function, the radial yield stress under any loading direction can be calculated, and the yield surface in the complete stress space can be generated. Under any intermediate cumulative plastic strain state within the model calibration interval, the yield surface is generated by the same cumulative plastic strain parameterized model. Therefore, it can be seen that the continuous evolution of this application originates from the continuous change relationship between the reference hardening benchmark, metric operator, and directional support weight with the cumulative plastic strain, rather than from the post-processing of surface splicing between different independent yield surfaces.

[0125] Step S8: Perform dimensionality reduction analysis and explicit function fitting on the convex gauge yield function after training to obtain the explicit evolution yield surface model.

[0126] This step is optional. The trained metric operator and directional support weights are sampled at multiple cumulative plastic strain levels to form metric parameter trajectories and directional support parameter trajectories. To maintain positive directional support weights, the directional support parameter trajectories can be processed in logarithmic space. The metric parameter trajectories and directional support parameter trajectories are then centered and decomposed in dimensionality reduction to extract several dominant modes that can explain the main evolutionary features. The dimensionality reduction decomposition can employ singular value decomposition, principal component analysis, nonnegative matrix factorization, or other low-rank decomposition methods.

[0127] The relationship between the dominant mode and cumulative plastic strain is fitted using a single-stage saturation function, a two-stage saturation function, a saturation function with a linear correction term, or other continuous functions. Based on the fitted modal coefficients, the explicit metric operator and explicit directional support weights are reconstructed, and then substituted into the original convex gauge yield function to form a directly calculable explicit evolutionary yield surface model.

[0128] The explicitization process does not transform the original model from discontinuous to continuous. Instead, it transforms the evolutionary relationships in the original yield surface intelligent model, which are already continuous but encoded in the network weights and nonlinear activation functions, into a low-dimensional, interpretable, and directly computable explicit expression.

[0129] Example 2:

[0130] This embodiment uses TA18 titanium alloy tubing in a stress-relieved annealed state as the object, and establishes a generalized evolutionary yield surface constitutive model that continuously varies with cumulative plastic strain by combining physical and mechanical tests and viscoplastic self-consistent virtual tests (VPSC). The nominal composition of the TA18 titanium alloy is Ti-3Al-2.5V, and due to the influence of its hexagonal close-packed crystal structure and the texture of the tubing processing, it exhibits obvious plastic anisotropy and tensile-compression asymmetry.

[0131] First, axial uniaxial tensile and uniaxial compression tests were conducted on the TA18 titanium alloy tube to obtain the material's true stress-strain response, initial yield strength, and plastic hardening characteristics, while also acquiring the tube's initial texture information. The viscoplastic self-consistent model was calibrated using the tensile and compression test results and texture information, and the calibrated calculation results were compared with the physical test results. Figure 2 As shown in the figure, the mean absolute percentage error of the axial tensile response is 0.399%, and the mean absolute percentage error of the axial compressive response is 0.441%. This confirms that the calibrated viscoplastic self-consistent model can reasonably characterize the basic plastic response of the TA18 titanium alloy pipe and can be used to generate multi-directional virtual test data.

[0132] Then, multi-directional virtual experiments were conducted using the calibrated viscoplastic self-consistent model. The loading states used included tensile and compressive states in different principal directions of the material, non-axial loading, shear-dependent loading, and biaxial loading, totaling 18 loading states. The cumulative plastic strain and stress state were read from the output of each loading state, and the corresponding stress state was converted into radial yield stress along the corresponding loading direction. For cases where the original output point coincided with the target cumulative plastic strain level, the corresponding radial yield stress was directly extracted; for cases where the target cumulative plastic strain level was located between adjacent output points, the stress-cumulative plastic strain response curve along the corresponding loading direction was interpolated; when it was necessary to calculate paired responses in opposite directions, the two response curves were aligned to a common cumulative plastic strain level. After the above processing, 4537 valid radial yield labels were obtained, with cumulative plastic strain ranging from 0 to 0.30. These were then divided into training, validation, and test sets at approximately 70%, 15%, and 15% ratios, respectively, with corresponding sample sizes of 3179, 679, and 679.

[0133] Subsequently, the axial tensile direction is selected as the reference loading direction, and a reference hardening benchmark is established based on the radial yield response in this direction to describe the overall dimensional evolution of the yield surface. The cumulative plastic strain is normalized to the interval 0 to 1 and encoded using polynomial features of order 3 or lower, radial basis function features, and low-frequency Fourier features. The encoded cumulative plastic strain is input into the metric parameter generation branch (first sub-network) and the directional support parameter generation branch (second sub-network), respectively. Both branches employ a multilayer perceptron with two hidden layers, each containing 64 neurons, and using the SiLU function as the continuous activation function. The metric parameter generation branch (first sub-network) outputs a metric operator that varies with the cumulative plastic strain, describing the overall directionality, principal axis proportion, and global curvature variation of the yield surface. The directional support parameter generation branch (second sub-network) outputs the positive and negative support weights corresponding to the support vectors in each direction, describing the asymmetry between local directional strength and opposite loading directions. Both sub-networks use only the cumulative plastic strain as input to the parameter generation branch; the loading direction only participates in the radial yield stress calculation during the subsequent convex gauge evaluation stage.

[0134] Next, directional support vectors are set according to the material principal direction, shear-related direction, and biaxial-related direction, and divided into core directional support groups and biaxial directional support groups. The metric components and each directional support component are convexly aggregated using a norm with an aggregation index of 2, and normalized according to the reference loading direction to form a convex gauge yield function that continuously varies with cumulative plastic strain, thus obtaining the yield surface intelligent model. Model training employs radial data consistency constraints, opposite-direction paired response constraints, and key-direction contrast constraints. Radial data consistency constraints are used to reduce the overall radial yield error, opposite-direction paired response constraints are used to control the tensile-compression average response and yield difference, and key-direction contrast constraints are used to control the relative yield relationship between the biaxial loading state and the corresponding uniaxial loading state. The final training objective adopts a combination of radial data consistency constraints, paired response constraints, and directional contrast constraints, with the weights of paired response and directional contrast constraints both set to 0.005.

[0135] Furthermore, Bayesian optimization was used to calibrate the expression capacity of the first and second sub-networks. A total of 30 candidate parameters were evaluated in the Bayesian optimization, including the number of residual bases, the magnitude of the residuals, the upper limit of the core direction support weights, the upper limit of the biaxial direction support weights, the core direction support activation scale, and the biaxial direction support activation scale. The search ranges were set to 12–21, 0.04–0.15, 1.50–4.00, 2.00–6.00, 0.08–0.35, and 0.15–0.70, respectively. Based on the mean radial error, tail radial error, maximum error, opposite direction response error, and key direction contrast error of the validation set, the 19th group of candidate parameters was selected as the calibration result. Its metric residual basis number is 15, metric residual amplitude is 0.0690, core direction support weight upper limit is 2.7034, dual-axis direction support weight upper limit is 2.1210, core direction support activation scale is 0.2637, and dual-axis direction support activation scale is 0.6937. The contribution ratio of the metric component to the selected model is 0.4144, and the contribution ratio of the direction support component is 0.5856, indicating that the model utilizes both global metric distortion and local direction support correction.

[0136] After parameter calibration, the convex gauge yield function is retrained using the selected parameters until the training and verification errors stabilize. Inputting any cumulative plastic strain within the range of 0 to 0.30 into the trained model yields the corresponding reference hardening amount, metric operator, positive support weight, and negative support weight. Furthermore, the radial yield stress and complete yield surface under any loading direction can be calculated.

[0137] like Figure 3 As shown, in the cumulative plastic strain At 0.30, the model of this invention is , and In all three stress sections, the radial yield marks passed well in experiments and viscoplastic self-consistent virtual experiments, forming a smooth, closed, and convex yield surface in three-dimensional stress space. Compared with the Mises model, the Hill48 model, and the Yoon2014 model which determines parameters according to discrete strain levels, the model of this invention achieves an average radial error of 0.16% and a tensile-compression asymmetric response error of 0.10%, while maintaining a low maximum error and continuous strain parameterization.

[0138] Therefore, this application can establish a generalized evolutionary yield surface constitutive model that continuously varies with cumulative plastic strain using limited physical experimental data and multi-directional virtual experimental data. The model can simultaneously describe global hardening, global anisotropic distortion, local directional correction, and tension-compression asymmetry, and avoids post-yield surface splicing between multiple independent cumulative plastic strain states.

[0139] Example 3:

[0140] This embodiment uses the intelligent model of the yield surface of TA18 titanium alloy trained in Example 2 as an example to illustrate the specific process of transforming the continuous evolution relationship parameterized by the neural network into an explicit white-box evolution law.

[0141] First, 161 sampling levels were uniformly set within the cumulative plastic strain range of 0 to 0.30, and each sampling level was sequentially input into the yield surface intelligent model trained in Example 2 to obtain the corresponding metric operator, positive support weight, and negative support weight. The residuals of the metric operator at each sampling level relative to the metric operator corresponding to the reference hardening datum were expanded into parameter vectors to form a metric parameter trajectory matrix. Simultaneously, the positive support weight and negative support weight were expanded into parameter vectors after taking the natural logarithm to form a directional support logarithmic weight trajectory matrix, to ensure that the directional support weight obtained subsequently through inverse exponential transformation always remains positive.

[0142] Then, singular value decomposition was performed on the centered metric parameter trajectory matrix and the directional support parameter trajectory matrix, respectively, and the dominant customized mode was selected based on the cumulative explained variance. In this embodiment, both the metric parameter trajectory and the directional support parameter trajectory retained 5 modes. Among them, the first mode of the metric parameter trajectory can explain 99.90% of the trajectory variance, and the first two modes can recover almost all the metric trajectory changes; the cumulative explained variances of the first mode, the first two modes, and the first five modes of the directional support parameter trajectory are 98.15%, 99.94%, and 99.99%, respectively. The above results show that although the original yield surface intelligent model contains a lot of network parameters, the trajectory of its metric operator and directional support weights changing with cumulative plastic strain has obvious low-dimensional characteristics.

[0143] Subsequently, a two-stage saturation function is used to fit the retained metric mode coefficients and directional support mode coefficients. For modes with simpler changes, the two-stage saturation function is degenerated into a single-stage saturation function. For modes that still have a slow linear trend, a linear correction term is added to the saturation function. The explicit metric operator is reconstructed based on the fitted mode coefficients and mode basis, and the fitted directional support logarithmic weights are converted into explicit positive support weights and explicit negative support weights through exponential mapping. The above explicit variables are then substituted back into the convex gauge yield function used in Example 2, and the same reference loading direction normalization method and radial yield stress calculation method are continued to be used, thereby forming an explicit white-box constitutive model that does not require calling the original metric parameter generation branch and directional support parameter generation branch.

[0144] Furthermore, the forward error of the explicit white-box model was evaluated. When only singular value mode reconstruction was used, the average radial error of the obtained model relative to the original intelligent model was 0.03%, indicating that the error introduced by the low-rank dimensionality reduction process was small. After replacing the modal coefficients with explicit saturation functions, the average radial error of the white-box model relative to the original intelligent model was 0.42%, the average radial error relative to the experimental and viscoplastic self-consistent virtual experimental labels was 0.46%, the 95th percentile error was 1.21%, and the maximum error was 4.63%. All directional support weights after reconstruction remained positive within the cumulative plastic strain range of 0 to 0.30, with a minimum value of [missing value]. .

[0145] like Figure 4 As shown, in the cumulative plastic strain At 0.30, the original intelligent model and the explicit white-box model are... , and The yield curves in the three representative stress sections basically coincide, and all of them can pass the radial yield label well in experiments and viscoplastic self-consistent virtual experiments. After explicitization, the global anisotropic distortion, local direction correction and tension-compression asymmetry of the original yield surface intelligent model are still retained, while continuing to satisfy the convexity, first-order homogeneity and radial uniqueness of the yield surface.

[0146] Therefore, the continuous evolution relationship encoded in the neural network weights and nonlinear activation functions in Example 2 is transformed into a white-box evolution law composed of a finite number of dominant evolutionary modes and explicit continuous functions. It can directly calculate the metric operator and directional support weights based on the cumulative plastic strain. It can be further embedded into a finite element material subroutine for calculating the bending, unloading springback, and residual stress of TA18 titanium alloy pipes. It can also be used for the stamping, deep drawing, extrusion, and forging processes of other metal materials.

[0147] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0148] It should be noted that, in this document, relational terms such as "first" and "second" are used only 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 process, method, article, or apparatus.

Claims

1. A data-physics-driven general constitutive modeling method for complex yield evolution of metals, characterized in that, Includes the following steps: S1. Obtain the response data of the metallic material to be modeled under several different loading directions and several different cumulative plastic strain states, and establish a multi-directional radial yield label set; the multi-directional radial yield label set includes cumulative plastic strain, loading direction and radial yield stress; S2. Based on the multi-directional radial yield tag set, select at least one loading direction as a reference loading direction; construct a reference hardening benchmark based on the radial yield stress of the reference loading direction under different cumulative plastic strain states. S3. Based on the reference hardening benchmark, normalize and feature-encode the cumulative plastic strain in the multi-directional radial yield tag set; S4. Input the cumulative plastic strain after feature encoding into the first sub-network and the second sub-network respectively; The first sub-network is used to output metric evolution parameters and obtain metric operators; The second sub-network is used to set multiple directional support vectors in the deviatoric stress space and output the positive support weight and negative support weight corresponding to each directional support vector; S5. Construct metric components using the metric operator; Using the positive and negative support weights, a directional support component is constructed; The metric component and the directional support component are convexly aggregated and normalized based on the reference hardening datum to obtain the convex gauge yield function. S6. Based on the multi-directional radial yield label set, train the convex gauge yield function to obtain the yield surface intelligent model; S7. Input the given cumulative plastic strain of the metal material to be modeled into the yield surface intelligent model to predict the radial yield stress and obtain the complete yield surface.

2. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 1, characterized in that, In step S1, the response data is obtained through physical and mechanical experiments and / or micromechanical virtual experiments; The physical and mechanical tests include any one or more of the following: uniaxial tensile test, uniaxial compression test, shear test, biaxial loading test, reverse loading test, and non-proportional loading test; The micromechanical virtual experiments include any one or more of the following: viscoplastic self-consistent virtual experiments, crystal plasticity finite element virtual experiments, representative volume element virtual experiments, and multi-scale homogenization virtual experiments. The aforementioned different loading directions include at least two sets of loading states in opposite directions, and at least one of the following: non-axial loading state, shear loading state, and biaxial loading state.

3. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 1, characterized in that, Step S2 specifically includes: S201. From the set of multi-directional radial yield labels, select the unit loading direction with complete hardening response as the reference loading direction; S202. Extract the radial yield stress under different cumulative plastic strains in the reference loading direction, arrange them in ascending order of cumulative plastic strain, and form a reference hardening data sequence. S203. Merge the repeated points or data points within the preset strain tolerance range in the reference hardening data sequence, and use a continuous interpolation function or explicit hardening function for fitting to obtain a reference hardening benchmark that is continuous and positive within the modeling interval.

4. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 1, characterized in that, Both the first subnetwork and the second subnetwork are multilayer perceptron models with continuous activation functions; The input parameters of the first sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the metric operators; The input parameters of the second sub-network are the cumulative plastic strain after feature encoding, and the output parameters are the positive support weight and the negative support weight.

5. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 1, characterized in that, In step S5, the method for constructing metric components using the metric operator includes: S501, Constructing a positive semidefinite metric matrix : In the formula: The metric operator is the cumulative plastic strain p; T is the transpose operator. S502. Construct metric components based on the positive semidefinite metric matrix: ； In the formula: For measuring components; The stress that requires yield testing The deviatoric stress vector in the material coordinate system.

6. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 5, characterized in that, In step S5, the constructed directional support components are: ； In the formula: Representative stress The cumulative plastic strain p corresponds to the first Each direction supports the component; For the first Support vectors in each direction; , The first The positive support weight and negative support weight corresponding to each directional support vector; This represents taking the maximum internal value.

7. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 6, characterized in that, In step S5, the yield function of the convex gauge is obtained as follows: ； In the formula: Represents cumulative plastic strain State used to determine stress state The yield function that determines whether yielding occurs; Represents the hardening reference standard; This represents the yield function value of the convex gauge after normalization to the reference loading direction. The representation consists of the metric component and the support components in each direction, according to The yield function value of the original convex gauge formed by convex polymerization; q represents the value of the yield function of the original convex gauge in the unit loading direction; q is the convex convergence index; K is the number of directional support vectors; Loading direction in units.

8. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 7, characterized in that, The intelligent model of the yield surface predicts the radial yield stress using the following formula: ； In the formula: Represents cumulative plastic strain The radial yield stress amplitude predicted along the unit loading direction under the condition; This represents the value of the normalized convex gauge yield function in the unit loading direction.

9. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 7, characterized in that, In step S7, the predicted radial yield stress is substituted into the yield function. Based on the zero-level set of the yield function, a complete yield surface under a given cumulative plastic strain is generated as the evolved yield surface.

10. The data-physics driven general constitutive modeling method for complex yield evolution of metals according to claim 1, characterized in that, Also includes: S8. Perform dimensionality reduction analysis and explicit function fitting on the convex gauge yield function after training to obtain an explicit evolutionary yield surface model.

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