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

Abstract

An optimization algorithm based on convex optimization simulates and measures the response of metal constitutive models. By collecting and processing the stress and strain data of the material, the objective function and constraints of the convex optimization problem are constructed. Then, the convex optimization algorithm is used to solve the problem to obtain the corresponding material parameters. 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. In addition, the algorithm also monitors the material by defining a loss range. When the stress and strain data of the material exceeds the preset loss range, 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 arise during the use of the material and improve the safety and reliability of the material.

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 constitutive model of metals, also known as the stress-strain model of materials, describes how stress in metals changes with strain under certain conditions. It essentially describes the relationship between stress and strain, strain rate, and temperature during deformation. Deformation of metals is often accompanied by phenomena such as work hardening, recovery, and recrystallization, all of which are influenced by factors such as strain, strain rate, and temperature.

[0003] Metal constitutive models are widely used in fields such as materials science, mechanics, and engineering. They can predict the behavior of materials or structures under different conditions. These models can not only predict mechanical properties such as strength, stiffness, and wear resistance, but also thermal and electrical properties under different environmental conditions, such as high and low temperatures and humidity.

[0004] The core of the algorithm is to utilize the theory and methods of convex optimization to transform the material stress-strain data simulation problem and the material deformation problem into a convex optimization problem, thereby quickly and accurately calculating the corresponding material parameters. 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 that the global optimal solution is found, avoiding the problem of local optimal solutions 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, which have large errors, long calculation times, and insufficient numerical precision. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an optimization algorithm based on convex optimization to simulate and measure the response of metal constitutive models. According to the proposed loss area parameter, the accuracy of the model simulation is effectively observed, and the material properties are monitored based on previous data.

[0006] 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:

[0007] S1, establish a 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.

[0008] S2. Establish a cyclic response model and simulate the cyclic response. This involves performing secondary modeling on the cyclic response function. Cyclic skeleton curves are a key tool for studying the differences in material constitutive relations under cyclic loading and monotonic loading. They intuitively and effectively reveal the similarities and differences in the mechanical responses of materials under these two loading conditions. Cyclic skeleton curves provide an overview of the material's performance during cyclic loading by depicting the corresponding points of maximum stress and strain reached by the material at each load level.

[0009] S3, establish the optimization objective function;

[0010] S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm is based on machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the loss function value, the higher the accuracy of the model; to improve the accuracy of the machine learning model, the loss function value needs to be reduced; to reduce the loss function value, the gradient descent method is used; the loss function has two parameters, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the gradient descent method is used to continuously adjust the weight and deviation to achieve the desired result, making the loss function value smaller and smaller;

[0011] S5, golden search; assuming the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search;

[0012] 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 a stress-strain diagram; the entire optimization process is initiated by importing the experimental data into the optimization algorithm and inputting 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, namely the vector set X; the parameters required to create the artificial data and model are created separately from the material parameters found and input.

[0013] 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.

[0014] In S1, the objective function is established through the metal stress-strain relationship:

[0015] For elastic deformation:

[0016] ;(1)

[0017] For plastic deformation:

[0018] ;(2)

[0019] From this we can get:

[0020] (3)

[0021] According to the tangent modulus:

[0022] ;(4)

[0023] From the yield function we can get:

[0024] (5)

[0025] in represent tangent modulus, elastic modulus and plastic modulus respectively;

[0026] For application cases, the material accumulation effect can be simplified, and for the yield surface, there are;

[0027] ;(6)

[0028] in is the yield onset stress intensity;

[0029] 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:

[0030] (7)

[0031] (8)

[0032] (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:

[0033] (10)

[0034] Then, based on isotropic hardening, a relationship is introduced:

[0035] ;(11)

[0036] is the maximum yield stress, is a material parameter and a constant, which represents the hardening ability of the material.

[0037] In S2, the Ramberg-Osgood model is used to fully reflect the true behavior of materials under cyclic loading, simulating the nonlinear stress-strain relationship of metal materials under cyclic loading:

[0038] (12)

[0039] Formula (12) is introduced as the plastic deformation detection part to effectively simulate the stress-strain relationship of the constitutive model.

[0040] 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:

[0041] ; (13)

[0042] (14)

[0043] (15)

[0044] Then build the model from the initial state: ;

[0045] 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:

[0046] Constant; (16)

[0047] Yield strength is a common material parameter, and its value is determined based on the actual material. The piecewise formula used for modeling is obtained: ;

[0048] when :

[0049] (17)

[0050] when :

[0051] (18)

[0052] According to the established relationships (4), (10) and (11) within the model:

[0053] (19)

[0054] Substitute into equation (3) and equation (9):

[0055] (20)

[0056] It can be seen from Equation (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters;

[0057] Therefore, choose Optimize; To optimize the operation, first find the objective function; To achieve the expected goal of modeling, introduce artificial experimental data into the objective function:

[0058] (twenty one)

[0059] Add parameter space constraints:

[0060] (twenty two)

[0061] 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 purpose of optimization.

[0062] 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. The update formula is written as follows:

[0063] ;(twenty three).

[0064] 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 sets three points whose intervals have the properties of the golden mean; the new interval will be and The spacing between them is a+c, or and The golden section search requires that these intervals are 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 meet the following functions:

[0065] ;(twenty four)

[0066] ; (25)

[0067] From this we can get:

[0068] (26)

[0069] 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:

[0070] (27)

[0071] That is, the projection of the components of vector x is determined by the following equation:

[0072] (28).

[0073] In S6, as the number of iterations of the optimization algorithm increases, the value of the objective function decreases until it converges. As the number of generations increases, the final result should gradually approach the optimal extreme value. Therefore, 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.

[0074] 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 is independent of 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.

[0075] In S6, the size gap between the original data and the optimized derived data follows the rule of first getting larger and then getting smaller, that is, the change in the size of the data gap is not monotonic; only the area size can truly reflect the magnitude 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:

[0076] (29)

[0077] (30)

[0078] Using equation (30), the accuracy of the optimization algorithm is obtained from the results and the accuracy of the model simulation is demonstrated.

[0079] The main beneficial effects of the present invention are:

[0080] 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.

[0081] The convex optimization algorithm is used to solve the problem and obtain the corresponding material parameters. 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.

[0082] Materials are monitored by defining loss intervals. When stress and strain data exceed these limits, the algorithm promptly issues an alert, prompting personnel to inspect and maintain the material. This monitoring approach effectively prevents potential problems during material use and improves material safety and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The present invention will be further described below with reference to the accompanying drawings and examples.

[0084] Figure 1 Schematic diagram of the constitutive model of the present invention.

[0085] Figure 2 This is the stress-strain yield relationship diagram of the present invention.

[0086] Figure 3 This is the stress-strain cycle response diagram of the present invention.

[0087] Figure 4 This is a diagram showing the relationship between weight and loss value of the present invention.

[0088] Figure 5 This is a diagram of the golden section search method of the present invention.

[0089] Figure 6 It is the algebraic-objective function value diagram of the present invention.

[0090] Figure 7 It is the distribution diagram of the vector set X of the present invention.

[0091] Figure 8 Model stress-strain diagrams using optimized values ​​are used for the present invention.

[0092] Figure 9 This is a comparison diagram of the stress-strain relationship between the algorithm model data of the present invention and the original data.

[0093] Figure 10 This is a loss area diagram of the present invention. DETAILED DESCRIPTION

[0094] like Figures 1 to 10In [1], an optimization algorithm for simulating and measuring the response of metal constitutive models based on convex optimization includes the following steps:

[0095] S1, establish a 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.

[0096] S2. Establish a cyclic response model and simulate the cyclic response. This involves performing secondary modeling on the cyclic response function. Cyclic skeleton curves are a key tool for studying the differences in material constitutive relations under cyclic loading and monotonic loading. They intuitively and effectively reveal the similarities and differences in the mechanical responses of materials under these two loading conditions. Cyclic skeleton curves provide an overview of the material's performance during cyclic loading by depicting the corresponding points of maximum stress and strain reached by the material at each load level.

[0097] S3, establish the optimization objective function;

[0098] S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm is based on machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the loss function value, the higher the accuracy of the model; to improve the accuracy of the machine learning model, the loss function value needs to be reduced; to reduce the loss function value, the gradient descent method is used; the loss function has two parameters, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the gradient descent method is used to continuously adjust the weight and deviation to achieve the desired result, making the loss function value smaller and smaller;

[0099] S5, golden search; assuming the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search;

[0100] 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 a stress-strain diagram; the entire optimization process is initiated by importing the experimental data into the optimization algorithm and inputting 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, namely the vector set X; the parameters required to create the artificial data and model are created separately from the material parameters found and input.

[0101] Example 1,

[0102] To accurately model the algorithm, a detailed and comprehensive modeling of the strain process is essential. The core of this modeling process lies in constructing an accurate and effective internal model that fully reflects the complex process of stress and strain changes with load. The entire strain process can generally be divided into two main stages, each exhibiting unique mechanical properties.

[0103] During the initial loading phase, especially before reaching the yield point, the relationship between stress and strain is linear, which can be described by a simplified linear model. During this phase, the metal primarily exhibits elastic properties: when the external force disappears, the material returns to its original state without permanent deformation.

[0104] When the load increases to a certain level and the metal reaches its yield point, its mechanical behavior changes significantly. At this point, the relationship between stress and strain becomes nonlinear, exhibiting a hyperbolic response. At this stage, the metal begins to undergo plastic deformation, and even after the external force is removed, it cannot fully return to its original state. As the load continues to increase, the plastic deformation accumulates, potentially leading to the metal's failure.

[0105] The objective function can be established through the metal stress-strain relationship:

[0106] For elastic deformation:

[0107] (1)

[0108] The plastic deformation variables are:

[0109] (2)

[0110] From this we can get:

[0111] (3)

[0112] According to the tangent modulus:

[0113] (4)

[0114] From the yield function we can get:

[0115] (5)

[0116] in They represent tangent modulus, elastic modulus and plastic modulus respectively.

[0117] For application cases, the material accumulation effect can be simplified, and for the yield surface:

[0118] (6)

[0119] in is the yield starting stress intensity.

[0120] At the same time, the yield stress k will change with plasticity according to the material properties. Since 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:

[0121] (7)

[0122] ;(8)

[0123] (9)

[0124] 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 obtain:

[0125] (10)

[0126] Then, according to isotropic hardening, a relationship can be introduced:

[0127] (11)

[0128] is the maximum yield stress, is a material parameter and a constant, which represents the hardening ability of the material. From this, the stress-strain yield relationship diagram can be obtained, such as Figure 2 .

[0129] Example 2,

[0130] Metal materials not only exhibit linear changes but also exhibit hysteresis due to plastic deformation. Hysteresis refers to the fact that when a metal is subjected to an external load, the relationship between its deformation and stress does not completely return to its original state, exhibiting a certain degree of memory. This characteristic primarily reflects the metal's increased sensitivity to stress and increased stability to deformation after exceeding its linear elastic range. Specifically, when a metal is subjected to cyclic or reciprocating loads, its stress-strain curve forms a closed loop, known as the hysteresis loop, which describes the material's energy dissipation and recovery capabilities during loading and unloading.

[0131] To simulate cyclic response, a secondary modeling of the cyclic response function is required. Cyclic skeleton curves are a key tool for studying the differences between material constitutive relations under cyclic and monotonic loading. They can intuitively and effectively reveal the similarities and differences in the mechanical response of materials under these two loading conditions. By depicting the corresponding points of maximum stress and strain achieved by the material at each load level, the cyclic skeleton curve provides an overview of the material's performance during cyclic loading.

[0132] To more accurately fit and describe the characteristics of cyclic skeleton curves, the Ramberg-Osgood model is often used. This model is widely favored for its ability to effectively simulate the nonlinear stress-strain relationship of metal materials under cyclic loading. The Ramberg-Osgood model not only considers the elastic deformation of the material but also introduces nonlinear terms to capture the effects of plastic deformation, enabling the model to more comprehensively reflect the true behavior of the material under cyclic loading.

[0133] (12)

[0134] Introducing formula (12) as the plastic deformation detection part can effectively simulate the stress-strain relationship of the constitutive model.

[0135] Example 3,

[0136] For modeling, the use of 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:

[0137] (13)

[0138] (14)

[0139] (15)

[0140] The model can then be built from the initial state:

[0141] 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:

[0142] Constant; (16)

[0143] Yield strength is a common material parameter and can be determined based on the actual material. Therefore, a piecewise formula for modeling can be obtained:

[0144]

[0145] when :

[0146] (17)

[0147] when :

[0148] (18)

[0149] According to the established relationships (4), (10) and (11) within the model:

[0150] (19)

[0151] Substitute into equation (3) and equation (9):

[0152] (20)

[0153] It can be seen from Equation (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters.

[0154] 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:

[0155] (twenty one)

[0156] Add parameter space constraints:

[0157] (twenty two)

[0158] 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 purpose of optimization.

[0159] Example 4,

[0160] 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.

[0161] The current position of the weight is at point A. At this point, if we find the gradient at point A, as we know, if the loss function moves to the right, the value of the loss function may become smaller. 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:

[0162] (twenty three).

[0163] Example 5,

[0164] Assuming the function is convex in its domain, as shown in the figure, the minimum interval has been determined during iteration and can be found using a golden section search. Golden section search is a method for finding the optimal value of a unimodal function by continuously narrowing the known optimal range. The algorithm assumes three points, whose spacing has the properties of a golden mean.

[0165] like Figure 4 As can be seen in and The spacing between them is a+c, or and The golden section search requires that these intervals are 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 meet the following functions:

[0166] (twenty four)

[0167] (25)

[0168] From this we can get:

[0169] (26)

[0170] 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:

[0171] (27)

[0172] That is, the projection of the components of vector x is determined by the following equation:

[0173] (28).

[0174] Preferably, the following algorithm establishment logic should be satisfied for the cyclic response algorithm establishment:

[0175]

[0176] Example 6,

[0177] The step in simulating the response involves using the data to obtain the optimal Ck solution and incorporating it into an iterative modeling algorithm to output a stress-strain plot. The optimization process can be initiated by importing experimental data into the optimization algorithm and entering known or estimated model parameters. As described in the previous section, the algorithm generates a loss in the objective function value while performing the optimization and outputs the optimized extreme values, a vector set X. The parameters required to create the artificial data and model are created separately from the material parameters, which can be found and entered.

[0178] like Figure 6 The graph shows the relationship between the value of the objective function and the number of generations. The results show that as the number of iterations of the optimization algorithm increases, the value of the objective function decreases until convergence. As the number of generations increases, the final result should gradually approach the optimal extreme value, so 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.

[0179] 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, i.e. .

[0180] Comparison with the original data shows that the stress line segments overlap in the linear phase. According to Equation (16), it is known that this is independent of the stress change in the linear phase, and the stress magnitude is only related to the elastic modulus. When the stress curve enters the hyperbolic response phase, the upward trend of the optimized curve is smaller than that of the original data curve.

[0181] The reasons for this can be analyzed from two perspectives: optimization losses and the influence of practical factors. As previously mentioned, the optimization process affects the magnitude of the function; smaller function values ​​result in smaller stress curves. In practice, metals undergo complex changes and isotropic hardening and softening. Furthermore, for actual test data, it is important to account for errors caused by numerical losses during the measurement process, as well as excessive values ​​or losses due to external factors such as friction.

[0182] like Figure 9 As shown, the optimization curve encloses a region, namely the loss region. In addition, according to Figure 8, we can see that the size gap between the original data and the optimized derived data follows the rule of first increasing and then decreasing, that is, the change in the size of the data gap is not monotonic. Therefore, we can conclude that only the size of the area can truly reflect the magnitude of the optimization loss. The larger the area, the greater the loss, and the smaller the area, the smaller the loss.

[0183] 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:

[0184] ;(29)

[0185] (30)

[0186] 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.

[0187] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The embodiments and features in the embodiments of this application may be arbitrarily combined with each other unless they conflict. The scope of protection of the present invention shall be the technical solutions described in the claims, including equivalent alternatives to the technical features of the technical solutions described in the claims. Equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. An optimization method for simulating and measuring the response of a metal constitutive model based on convex optimization, characterized in that: The steps include: S1, establish a constitutive model. A general constitutive model is established based on the monotonic response, and the strain process is modeled in detail and comprehensively. 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 and simulate the cyclic response. This involves performing secondary modeling on the cyclic response function. Cyclic skeleton curves are a key tool for studying the differences in material constitutive relations under cyclic loading and monotonic loading. They intuitively and effectively reveal the similarities and differences in the mechanical responses of materials under these two loading conditions. Cyclic skeleton curves provide an overview of the material's performance during cyclic loading by depicting the corresponding points of maximum stress and strain reached by the material at each load level. S3, establish the optimization objective function; S4, establish the algorithm logic; to simplify and accurately optimize the result value, the algorithm is based on machine learning; the loss function is used to measure the accuracy of the machine learning model; the smaller the loss function value, the higher the accuracy of the model; to improve the accuracy of the machine learning model, the loss function value needs to be reduced; to reduce the loss function value, the gradient descent method is used; the loss function has two parameters, one controls the weight of the input signal, and the other adjusts the deviation of the function from the true value; the gradient descent method is used to continuously adjust the weight and deviation to achieve the desired result, making the loss function value smaller and smaller; S5, golden search; assuming the function is convex in the domain, the minimum point interval has been determined in the iteration and is found using golden search; S6, Use the model for validation; the step of simulating the response is to use the data to obtain the best The solution is incorporated into an iterative model algorithm to output a stress-strain diagram. The entire optimization process is initiated by importing experimental data into the optimization algorithm and inputting known or estimated model parameters. The algorithm generates a loss in the objective function value while performing the optimization and outputs the optimized extreme value, 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 entered.

2. The optimization method 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 method 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 steps to establish the objective function through the metal stress-strain relationship are as follows: For elastic deformation: ；(1) For plastic deformation: ；(2) From this we can get: (3) According to the tangent modulus: ；(4) From the yield function we can get: (5) in , and ; For application cases, the material accumulation effect can be simplified, and for the yield surface, there are; ；(6) 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 in stress and the change in yield stress occur simultaneously, so they are approximately the same formula, resulting in: (10) Then, based on isotropic hardening, a relationship is introduced: ；(11) is the maximum yield stress, is a material parameter and a constant, which represents the hardening ability of the material.

4. The optimization method 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, simulating 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 method 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 common material parameter, and its value is determined based on 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 Equation (19) that in the entire model construction, only one is an unconventional material parameter, while the other parameters are basic material parameters; Therefore, choose Optimize; 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 purpose of optimization.

6. The optimization method 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. The update formula is written as follows: ；(23)。 7. The optimization method 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, it is assumed that the function is 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 between them is a+c, or and The golden section search requires that these intervals are 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 meet 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 method 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 iterations of the optimization algorithm increases, the value of the objective function decreases until it converges. As the number of generations increases, the final result should gradually approach the optimal extreme value. Therefore, 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 method for simulating and measuring the response of a metal constitutive model based on convex optimization according to claim 1, 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 is independent of 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 method 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 getting larger and then getting smaller, that is, the change in the size of the data gap is not monotonic; only the area size can truly reflect the magnitude 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 accuracy of the optimization algorithm is obtained from the results and the accuracy of the model simulation is demonstrated.

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