Optimization algorithm for simulating and measuring response of metal constitutive model based on convex optimization

Abstract

An optimization algorithm for simulating and measuring response of a metal constitutive model based on convex optimization constructs an objective function and constraint conditions of a convex optimization problem by collecting and processing stress-strain data of a material. And then, solving by utilizing a convex optimization algorithm to obtain corresponding parameters of the material. The parameters can reflect important information such as mechanical properties and deformation behaviors of the material, and powerful support is provided for research, development and application of the material. In addition, the algorithm monitors the material by defining a loss interval. When the stress-strain data of the material exceeds a preset loss interval, the algorithm gives an alarm in time to remind related personnel to check and maintain the material. The monitoring mode can effectively prevent problems possibly occurring in the using process of the material, and the safety and reliability of the material are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of model algorithms, and relates to an optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization. Background Art

[0002] The metal constitutive model, also known as the stress-strain model of the material, is a model that describes the law of stress-strain variation of metal materials under certain conditions. It actually describes the relationship between stress and strain, strain rate, temperature and other factors during the deformation process of metal materials. The deformation of metal materials is often accompanied by phenomena such as work hardening, recovery and recrystallization, and these characteristic phenomena are affected by factors such as strain, strain rate and temperature.

[0003] In the fields of materials science, mechanics and engineering, metal constitutive models are widely used to predict the behavior of materials or structures under different conditions. Not only can they predict the mechanical properties of materials such as strength, stiffness, and wear resistance, but they can also predict the thermal properties and electrical properties of materials under different environmental conditions such as high temperature, low temperature, and humidity.

[0004] The core of the algorithm is to use the theory and method of convex optimization to transform the material stress-strain data simulation problem and material deformation problem into a convex optimization problem, so as to quickly and accurately calculate the corresponding parameters of the material. Convex optimization theory has significant advantages in optimization problems, especially when the objective function and constraint function are both convex functions. Convex optimization problems can ensure the global optimal solution and avoid the problem of local optimal solution that may exist in non-convex optimization problems; therefore, applying convex optimization theory to the simulation of material stress-strain data can greatly improve the accuracy and reliability of the simulation. However, the algorithm uses fuzzy algorithms and traditional iterations, and its error is large. The traditional method takes a long time to calculate and the numerical value is not accurate enough. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization, and to effectively observe the accuracy of the model simulation according to the proposed loss area parameter, while monitoring the material properties according to previous data.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: an optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization, comprising the following steps: S1, establish the constitutive model, establish a general constitutive model based on monotonic response, accurately model the algorithm, and conduct detailed and comprehensive modeling of the strain process; the core of the modeling process is to build an accurate and effective internal model to fully reflect the complex process of stress and strain changes with load; the entire strain process is divided into two main stages, each of which presents unique mechanical properties; S2, establish a cyclic response model, simulate the cyclic response, and perform secondary modeling on the cyclic response function; when studying the differences in the constitutive relations of materials under cyclic loading and monotonic loading, the cyclic skeleton curve is a key tool that intuitively and effectively reveals the similarities and differences in the mechanical responses of materials under these two loading conditions; the cyclic skeleton curve provides an overview of the performance of the material during cyclic loading by depicting the corresponding points of the maximum stress and strain reached by the material under each load level; S3, establish the optimization objective function; S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm revolves around machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the value of the loss function, the higher the accuracy of the model; to improve the accuracy of the machine learning model, it is necessary to reduce the value of the loss function; to reduce the value of the loss function, use the gradient descent method; there are two parameters in the loss function, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the weight and deviation are continuously adjusted by the gradient descent method to make the value of the loss function smaller and smaller; S5, golden search; assuming that the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search; S6, validation using the model; the step of simulating the response is to use the data to obtain the best Ck solution and incorporate it into the iterative model algorithm to output the stress-strain diagram; the entire optimization process is initiated by importing the experimental data into the optimization algorithm and inputting the known model parameters or estimated model parameters; the algorithm generates a loss in the objective function value when performing the optimization and outputs the optimized extreme values, i.e., the vector set X; the parameters required to create the artificial data and the model are created separately from the material parameters found and input.

[0007] In S1, at the initial stage of loading, before reaching the yield point, there is a linear relationship between stress and strain, and this stage is described by a simplified linear model.

[0008] In S1, the objective function is established through the metal stress-strain relationship: For elastic deformation: ; (1) For the amount of plastic deformation: ; (2) From this we can get: (3) According to the tangent modulus: ; (4) From the yield function we can get: (5) in They represent tangent modulus, elastic modulus and plastic modulus respectively; For application cases, the material accumulation effect can be simplified, and for the yield surface, there are; ; (6) in is the yield onset stress intensity; At the same time, according to the material properties, the yield stress k will change with plasticity; because the yield surface formula should be equal to 0, the yield surface formula will maintain f=0 until the stress reaches the limit point after the yield point, so: (7) (8) (9) is called the rate of change of yield stress; at the same time, the change of stress and the change of yield stress occur simultaneously, so they are approximately the same formula, and we get: (10) Then, according to isotropic hardening, a relationship is introduced: ; (11) is the maximum yield stress, is a material parameter and a constant, representing the hardening ability of the material.

[0009] In S2, the Ramberg-Osgood model is used to fully reflect the true behavior of materials under cyclic loading and simulate the nonlinear stress-strain relationship of metal materials under cyclic loading: (12) Formula (12) is introduced as the plastic deformation detection part to effectively simulate the stress-strain relationship of the constitutive model.

[0010] In S3, an iterative algorithm is used. According to the existing formulas, the formulas related to stress change are all related to the strain change rate, which can be obtained: ; (13) (14) (15) Then build the model from the initial state: ; At the same time, according to the linear and hyperbolic responses of the line segment, the initial state of k is obtained as the initial yield stress: Constant; (16) Yield strength is a conventional material parameter, and its value is determined according to the actual material; the piecewise formula used for modeling is obtained: ; when : (17) when : (18) According to the established relationships (4), (10) and (11) within the model: (19) Substitute into equation (3) and equation (9): (20) It can be seen from formula (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters; Therefore, choose To optimize the operation, first find the objective function; to achieve the expected goal of modeling, introduce artificial experimental data into the objective function: (twenty one) Add parameter space constraints: (twenty two) Among them is The scaling factor uses the least squares method to reduce the error between the model and the artificial data to achieve the optimization purpose.

[0011] In S4, assume that the value of the model loss in the loss function is related to the weight, and the current position of the weight is at point A; if the gradient is found at point A, the loss function moves to the right, and the value of the loss function may become smaller; at the same time, the search for the minimum fixed point is again regarded as an iterative process of generating points, and the direction is regarded as the search direction from the previous point to the new point; the direction determines the direction of the next search, and the step size determines its distance in a specific direction; then write this update formula as follows: ;(twenty three).

[0012] In S5, the function is assumed to be convex in the domain, the minimum interval is determined in the iteration, and is found using the golden search; the algorithm assumes three points whose spacing has the properties of the golden mean; the new interval will be in and The spacing is a+c, or and The golden section search requires these intervals to be equal; if they are not equal, wider intervals are used multiple times, which reduces the convergence rate; to ensure that b = a + c, the algorithm should follow = - + , and must satisfy the following functions: ;(twenty four) ; (25) From this we can get: (26) The method stops if and only if x resides; According to equations (16) and (19), the constraint set X has a relatively simple structure, which leads to a relatively simple projection operation: (27) That is, the projection of the components of vector x is determined by the following equation: (28).

[0013] In S6, as the number of times the iterative optimization algorithm is generated increases, the value of the objective function decreases continuously until it converges. As the number of generations increases, since the final result should gradually approach the optimization extreme value, according to equation (23), the trend of the objective function value should gradually decrease. When the numerical change is negligible, the objective function value converges, and the result vector set X is output.

[0014] In S6, according to Eqs. (27) and (28), the inclusion of the projection step restricts all solutions to the constraints given, i.e. ; The stress line segments overlap in the linear stage. According to equation (16), it is known that it has nothing to do with the stress change in the linear stage, and the stress magnitude is only related to the elastic modulus; when the stress curve enters the hyperbolic response stage, the upward trend of the optimized curve is smaller than that of the original data curve.

[0015] In S6, the size gap between the original data and the optimized derived data follows the rule of first large and then small, that is, the size change of the data gap is not monotonic; only the area size can truly reflect the size of the optimization loss; the larger the area, the greater the loss, and the smaller the area, the smaller the loss; the optimization accuracy is also controlled by the following equation, which is related to the size of the loss area: (29) (30) Using equation (30), the precision of the optimization algorithm is obtained from the results and the accuracy of the model simulation is demonstrated.

[0016] The main beneficial effects of the present invention are: Compared with traditional simulation, it is faster and more accurate. At the same time, according to the proposed loss area parameters, the accuracy of the model simulation can be effectively observed, and the material properties can be monitored based on previous data.

[0017] The convex optimization algorithm is used to solve the problem, thus obtaining the corresponding parameters of the material. These parameters can reflect important information such as the mechanical properties and deformation behavior of the material, providing strong support for the research and development and application of the material.

[0018] The material is monitored by defining the loss interval. When the stress-strain data of the material exceeds the preset loss interval, the algorithm will promptly issue an alarm to remind relevant personnel to inspect and maintain the material. This monitoring method can effectively prevent problems that may occur during the use of the material and improve the safety and reliability of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0020] Figure 1 Schematic diagram of the constitutive model of the present invention.

[0021] Figure 2 It is the stress-strain yield relationship diagram of the present invention.

[0022] Figure 3 It is the stress-strain cycle response diagram of the present invention.

[0023] Figure 4 This is a relationship diagram between the weight and loss value of the present invention.

[0024] Figure 5 This is a diagram of the golden section search method of the present invention.

[0025] Figure 6 It is the algebraic-objective function value diagram of the present invention.

[0026] Figure 7It is the distribution diagram of the vector set X of the present invention.

[0027] Figure 8 A model stress-strain diagram of optimized values ​​is used for the present invention.

[0028] Fig. 9 It is a comparison diagram of the stress-strain relationship between the algorithm model data of the present invention and the original data.

[0029] Fig.10 This is a loss area diagram of the present invention. DETAILED DESCRIPTION

[0030] like Figure 1 to Figure 10 In the present invention, an optimization algorithm for simulating and determining the response of a metal constitutive model based on convex optimization is provided, which comprises the following steps: S1, establish the constitutive model, establish a general constitutive model based on monotonic response, accurately model the algorithm, and conduct detailed and comprehensive modeling of the strain process; the core of the modeling process is to build an accurate and effective internal model to fully reflect the complex process of stress and strain changes with load; the entire strain process is divided into two main stages, each of which presents unique mechanical properties; S2, establish a cyclic response model, simulate the cyclic response, and perform secondary modeling on the cyclic response function; when studying the differences in the constitutive relations of materials under cyclic loading and monotonic loading, the cyclic skeleton curve is a key tool that intuitively and effectively reveals the similarities and differences in the mechanical responses of materials under these two loading conditions; the cyclic skeleton curve provides an overview of the performance of the material during cyclic loading by depicting the corresponding points of the maximum stress and strain reached by the material under each load level; S3, establish the optimization objective function; S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm revolves around machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the value of the loss function, the higher the accuracy of the model; to improve the accuracy of the machine learning model, it is necessary to reduce the value of the loss function; to reduce the value of the loss function, use the gradient descent method; there are two parameters in the loss function, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the weight and deviation are continuously adjusted by the gradient descent method to make the value of the loss function smaller and smaller; S5, golden search; assuming that the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search; S6, validation using the model; the step of simulating the response is to use the data to obtain the best Ck solution and incorporate it into the iterative model algorithm to output the stress-strain diagram; the entire optimization process is initiated by importing the experimental data into the optimization algorithm and inputting the known model parameters or estimated model parameters; the algorithm generates a loss in the objective function value when performing the optimization and outputs the optimized extreme values, i.e., the vector set X; the parameters required to create the artificial data and the model are created separately from the material parameters found and input.

[0031] Embodiment 1, In order to accurately model the algorithm, the strain process must be modeled in detail and comprehensively. The core of this modeling process is to build an accurate and effective internal model that can fully reflect the complex process of stress and strain changing with load. The entire strain process can usually be divided into two main stages, each of which presents unique mechanical properties.

[0032] In the initial stage of loading, especially before reaching the yield point, there is a linear relationship between stress and strain, which can be described by a simplified linear model. In this stage, the metal mainly exhibits elastic properties, that is, when the external force disappears, the material can return to its original state without permanent deformation.

[0033] When the load increases to a certain extent and the metal reaches the yield point, its mechanical behavior will change significantly. At this point, the relationship between stress and strain becomes nonlinear, showing the characteristics of a hyperbolic response. At this stage, the metal begins to undergo plastic deformation, and even if the external force is removed, it cannot completely return to its original state. As the load continues to increase, plastic deformation continues to accumulate, which may eventually lead to the destruction of the metal.

[0034] The objective function can be established through the metal stress-strain relationship: For elastic deformation: (1) The plastic deformation variables are: (2) From this we can get: (3) According to the tangent modulus: (4) From the yield function we can get: (5) in They represent tangent modulus, elastic modulus and plastic modulus respectively.

[0035] For the application case, the material accumulation effect can be simplified, and for the yield surface: (6) in is the yield starting stress intensity.

[0036] At the same time, according to the material properties, the yield stress k will change with plasticity. Because the yield surface formula should be equal to 0, the yield surface formula will maintain f=0 until the stress reaches the limit point after the yield point, so: (7) ; (8) (9) It is called the rate of change of yield stress. At the same time, knowing that the change of stress and the change of yield stress occur simultaneously, we can approximate the same formula and get: (10) Then, according to isotropic hardening, a relationship can be introduced: (11) is the maximum yield stress, is a material parameter and a constant, which indicates the hardening ability of the material. From this, the stress-strain yield relationship diagram can be obtained, such as Figure 2 .

[0037] Embodiment 2, Metal materials not only have linear changes, but also have hysteresis properties due to plastic deformation. Hysteresis performance refers to the fact that when a metal material is subjected to an external load, the relationship between its deformation and stress does not completely return to its original state, that is, it exhibits a certain degree of memory. This characteristic mainly reflects the higher sensitivity of metal materials to stress and the higher stability of corresponding deformation after exceeding their linear elastic range. Specifically, when a metal material is subjected to cyclic or reciprocating loads, its stress-strain relationship curve will form a closed loop, which is the hysteresis loop, which describes the energy dissipation and recovery ability of the material during loading and unloading.

[0038] In order to simulate the cyclic response, the cyclic response function should be modeled twice. When studying the differences in the constitutive relations of materials under cyclic loading and monotonic loading, the cyclic skeleton curve is a key tool that can intuitively and effectively reveal the similarities and differences in the mechanical responses of materials under these two loading conditions. The cyclic skeleton curve provides an overview of the performance of the material during cyclic loading by depicting the corresponding points of the maximum stress and strain reached by the material under each load level.

[0039] In order to fit and describe the characteristics of the cyclic skeleton curve more accurately, the Ramberg-Osgood model is usually used. This model is widely favored because it can better simulate the nonlinear stress-strain relationship of metal materials under cyclic loading. The Ramberg-Osgood model not only considers the elastic deformation part of the material, but also introduces nonlinear terms to capture the influence of plastic deformation, so that the model can more comprehensively reflect the true behavior of the material under cyclic loading.

[0040] (12) Introducing formula (12) as the plastic deformation detection part can effectively simulate the stress-strain relationship of the constitutive model.

[0041] Embodiment 3, For modeling, using an iterative algorithm is the choice of the present invention. According to existing formulas, the formulas related to stress changes are all related to the strain change rate, which can be obtained: (13) (14) (15) The model can then be built from the initial state:

[0042] At the same time, according to the linear and hyperbolic responses of the above line segments, the initial state of k can be obtained as the initial yield stress: Constant; (16) Yield strength is a general parameter of the material and can be determined based on the actual material. Therefore, the piecewise formula used for modeling can be obtained:

[0043] when : (17) when : (18) According to the established relationships (4), (10) and (11) in the model: (19) Substitute into equation (3) and equation (9): (20) It can be seen from formula (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters.

[0044] Therefore, you should choose To optimize the operation, we should first find the objective function. In order to achieve the expected goal of modeling, we can introduce artificial experimental data into the objective function: (twenty one) Add parameter space constraints: (twenty two) Among them is The scaling factor uses the least squares method to reduce the error between the model and the artificial data to achieve the optimization purpose.

[0045] Embodiment 4, In order to simplify and accurately optimize the result value, the algorithm should revolve around machine learning. The loss function is often used to measure the accuracy of the machine learning model. Generally, the smaller the value of the loss function, the higher the accuracy of the model. In order to improve the accuracy of the machine learning model, the value of the loss function needs to be reduced as much as possible. In order to reduce the value of the loss function, we usually use the gradient descent method. There are usually two parameters in the loss function, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value. This is achieved by continuously adjusting the weights and deviations through the gradient descent method to make the value of the loss function smaller and smaller. Assume that the value of the model loss in the loss function is related to the weight, such as Figure 3 shown.

[0046] The current position of the weights is at point A. At this point, if we find the gradient at point A, as we know, the value of the loss function may become smaller if the loss function moves to the right. At the same time, we can again think of the search for the least fixed point as an iterative process of generating points and the direction as the search direction from the previous point to the new point. The direction determines the direction of our next search, and the step size determines how far it will go in a specific direction. We can write this update formula as follows: (twenty three).

[0047] Embodiment 5, Assuming the function is convex in the domain, as shown in the figure, the minimum point interval has been determined in the iteration and can be found using the golden search. The golden section search is a method of finding the optimal value of a unimodal function by continuously narrowing the known range of its optimal value. The algorithm sets three points whose spacing has the properties of the golden mean.

[0048] like Figure 4 As can be seen from and The spacing is a+c, or and The golden section search requires these intervals to be equal. If they are not equal, wider intervals are used more often, which slows down the convergence rate. To ensure that b = a + c, the algorithm should follow = - + , and must satisfy the following functions: (twenty four) (25) From this we can get: (26) The method stops if and only if x resides. According to (16) and (19), the constraint set X has a relatively simple structure, which leads to a relatively simple projection operation: (27) That is, the projection of the components of vector x is determined by the following equations: (28).

[0049] Preferably, the following algorithm establishment logic should be satisfied for the cyclic response algorithm establishment:

[0050] Embodiment 6, The step of simulating the response is to use the data to obtain the best Ck solution and incorporate it into the iterative model algorithm to output the stress-strain diagram. The entire optimization process can be initiated by importing the experimental data into the optimization algorithm and inputting the known model parameters or estimated model parameters. According to the previous section, the algorithm produces a loss in the value of the objective function when performing the optimization and outputs the optimized extreme values, which is the vector set X. The parameters required to create the artificial data and model are created separately from the material parameters that can be found and input.

[0051] like Figure 6 The relationship between the value of the objective function and the number of generations is shown. The results show that as the number of generations of the iterative optimization algorithm increases, the value of the objective function decreases until it converges. As the number of generations increases, since the final result should gradually approach the optimization extreme value, according to equation (23), the trend of the objective function value should gradually decrease. When the numerical change is negligible, the objective function value converges and the result vector set X is the output.

[0052] The schematic diagram of the components of the vector set X is as follows Figure 7 According to equations (27) and (28), the inclusion of the projection step restricts all solutions to the constraints given, namely .

[0053] Comparison with the original data shows that the stress line segments overlap in the linear stage, which is known to be independent of the stress change in the linear stage according to equation (16), and the stress magnitude is only related to the elastic modulus. When the stress curve enters the hyperbolic response stage, the upward trend of the optimized curve is smaller than that of the original data curve.

[0054] The reasons for this can be analyzed from two aspects: optimization loss and the influence of practical factors. As mentioned earlier, the optimization process affects the size of the function, and a smaller function value leads to a smaller stress curve. In practice, metals undergo complex changes and isotropic hardening and softening. In addition, for actual test data, it is important to consider the error of numerical loss during the measurement process and the excessive numerical value or loss caused by external factors such as friction.

[0055] like Fig. 9 As shown in , the optimization curve encloses a region, namely the loss region. In addition, according to Figure 8 , it can be found that the size gap between the original data and the optimized derived data should follow the rule of first large and then small, that is, the size change of the data gap is not monotonic. Therefore, it can be concluded that only the size of the area can truly reflect the size of the optimization loss. The larger the area, the greater the loss, and the smaller the area, the smaller the loss.

[0056] Therefore, it can be concluded that the optimization accuracy is also controlled by the following equation, which is related to the size of the loss region: ; (29) (30) Using equation (30), the precision of the optimization algorithm can be obtained from the results and the accuracy of the model simulation can be demonstrated.

[0057] The above-mentioned embodiments are only preferred technical solutions of the present invention and should not be regarded as limitations of the present invention. The embodiments and features in the embodiments of the present application can be arbitrarily combined with each other without conflict. The protection scope of the present invention shall be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. An optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization, characterized in that: The steps include: S1, establish the constitutive model, establish a general constitutive model based on monotonic response, accurately model the algorithm, and conduct detailed and comprehensive modeling of the strain process; The core of the modeling process is to build an accurate and effective internal model to fully reflect the complex process of stress and strain changing with load; the entire strain process is divided into two main stages, each of which presents unique mechanical properties; S2, establish a cyclic response model, simulate the cyclic response, and perform secondary modeling on the cyclic response function; when studying the differences in the constitutive relations of materials under cyclic loading and monotonic loading, the cyclic skeleton curve is a key tool that intuitively and effectively reveals the similarities and differences in the mechanical responses of materials under these two loading conditions; the cyclic skeleton curve provides an overview of the performance of the material during cyclic loading by depicting the corresponding points of the maximum stress and strain reached by the material under each load level; S3, establish the optimization objective function; S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm revolves around machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the value of the loss function, the higher the accuracy of the model; to improve the accuracy of the machine learning model, it is necessary to reduce the value of the loss function; to reduce the value of the loss function, use the gradient descent method; there are two parameters in the loss function, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the weight and deviation are continuously adjusted by the gradient descent method to make the value of the loss function smaller and smaller; S5, golden search; assuming that the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search; S6, validation using the model; the step of simulating the response is to use the data to obtain the best Ck solution and incorporate it into the iterative model algorithm to output the stress-strain diagram; the entire optimization process is started by importing the experimental data into the optimization algorithm and inputting the known model parameters or estimated model parameters; the algorithm generates a loss in the objective function value when performing the optimization and outputs the optimized extreme value, that is, the vector set X; The parameters required to create the artificial data and the model are created separately from the material parameters found and entered.

2. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1 is characterized in that: In S1, at the initial stage of loading, before reaching the yield point, there is a linear relationship between stress and strain, and this stage is described by a simplified linear model.

3. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1 is characterized in that: In S1, the objective function is established through the metal stress-strain relationship: For elastic deformation: ；(1) For the amount of plastic deformation: ； (2) From this we can get: (3) According to the tangent modulus: ；(4) From the yield function we can get: (5) in They represent tangent modulus, elastic modulus and plastic modulus respectively; For application cases, the material accumulation effect can be simplified, and for the yield surface, there are; ；(6) in is the yield onset stress intensity; At the same time, according to the material properties, the yield stress k will change with plasticity; because the yield surface formula should be equal to 0, the yield surface formula will maintain f=0 until the stress reaches the limit point after the yield point, so: (7) (8) (9) is called the rate of change of yield stress; at the same time, the change of stress and the change of yield stress occur simultaneously, so they are approximately the same formula, and we get: (10) Then, according to isotropic hardening, a relationship is introduced: ；(11) is the maximum yield stress, is a material parameter and a constant, representing the hardening ability of the material.

4. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1, characterized in that: In S2, the Ramberg-Osgood model is used to fully reflect the true behavior of materials under cyclic loading and simulate the nonlinear stress-strain relationship of metal materials under cyclic loading: (12) Formula (12) is introduced as the plastic deformation detection part to effectively simulate the stress-strain relationship of the constitutive model.

5. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1, characterized in that: In S3, an iterative algorithm is used. According to the existing formulas, the formulas related to stress change are all related to the strain change rate, which can be obtained: ；(13) (14) (15) Then build the model from the initial state: ; At the same time, according to the linear and hyperbolic responses of the line segment, the initial state of k is obtained as the initial yield stress: constant; (16) Yield strength is a conventional material parameter, and its value is determined according to the actual material; the piecewise formula used for modeling is obtained: ; when : (17) when : (18) According to the established relationships (4), (10) and (11) within the model: (19) Substitute into equation (3) and equation (9): (20) It can be seen from formula (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters; Therefore, choose To optimize the operation, first find the objective function; to achieve the expected goal of modeling, introduce artificial experimental data into the objective function: (21) Add parameter space constraints: (22) Among them is The scaling factor uses the least squares method to reduce the error between the model and the artificial data to achieve the optimization purpose.

6. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1 is characterized in that: In S4, assume that the value of the model loss in the loss function is related to the weight, and the current position of the weight is at point A; if the gradient is found at point A, the loss function moves to the right, and the value of the loss function may become smaller; at the same time, the search for the minimum fixed point is again regarded as an iterative process of generating points, and the direction is regarded as the search direction from the previous point to the new point; the direction determines the direction of the next search, and the step size determines its distance in a specific direction; then write this update formula as follows: ；(23)。 7. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1 is characterized in that: In S5, the function is assumed to be convex in the domain, the minimum interval has been determined in the iteration, and the golden search is used to find it; the algorithm sets three points whose intervals have the properties of the golden mean; the new interval will be in and The spacing is a+c, or and The golden section search requires these intervals to be equal; if they are not equal, wider intervals are used multiple times, which reduces the convergence rate; to ensure that b = a + c, the algorithm should follow = - + , and must satisfy the following functions: ；(24) ； (25) From this we can get: (26) The method stops if and only if x resides; According to equations (16) and (19), the constraint set X has a relatively simple structure, which leads to a relatively simple projection operation: (27) That is, the projection of the components of vector x is determined by the following equation: (28)。 8. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1, characterized in that: In S6, as the number of times the iterative optimization algorithm is generated increases, the value of the objective function decreases continuously until it converges. As the number of generations increases, since the final result should gradually approach the optimization extreme value, according to equation (23), the trend of the objective function value should gradually decrease. When the numerical change is negligible, the objective function value converges, and the result vector set X is output.

9. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1 is characterized in that: In S6, according to Eqs. (27) and (28), the inclusion of the projection step restricts all solutions to the given constraints, i.e. ; The stress line segments overlap in the linear stage. According to equation (16), it is known that it has nothing to do with the stress change in the linear stage, and the stress magnitude is only related to the elastic modulus; when the stress curve enters the hyperbolic response stage, the upward trend of the optimized curve is smaller than that of the original data curve.

10. The optimization algorithm for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1, characterized in that: In S6, the size gap between the original data and the optimized derived data follows the rule of first large and then small, that is, the size change of the data gap is not monotonic; only the area size can truly reflect the size of the optimization loss; the larger the area, the greater the loss, and the smaller the area, the smaller the loss; the optimization accuracy is also controlled by the following equation, which is related to the size of the loss area: (29) (30) Using equation (30), the precision of the optimization algorithm is obtained from the results and the accuracy of the model simulation is demonstrated.

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