Regression model generation method, regression model generation system, simulation method, simulation system, and program

Abstract

This makes it possible to easily simulate the behavior of materials in response to external forces. [Solution] The regression model generation method comprises: a stress-strain acquisition step of acquiring time-series stresses from 0 to N (where N is a natural number) and strains from 0 to N obtained by performing material tests or simulations on the material; an effective inelastic strain rate acquisition step of acquiring the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material, based on the nth stress (where n is a natural number between 1 and N) and the n-1 stress, and the nth strain and the n-1 strain; and a regression model generation step of generating a regression model that has learned the relationship between the nth strain information indicating the nth strain and the nth effective inelastic strain rate.

Description

[Technical Field]

[0001] The present invention relates to a regression model generation method, a regression model generation system, a simulation method, a simulation system, and a program. [Background technology]

[0002] When simulating the behavior of a material in response to external forces, a constitutive equation representing the relationship between stress and strain in the material is used. For example, when simulating the behavior of a tire in response to external forces generated by load, acceleration, braking, cornering, etc., a constitutive equation that models the viscoelastic behavior of the rubber that makes up the tire is used. [Overview of the Initiative] [Problems that the invention aims to solve]

[0003] When performing simulations, it is necessary to select or create a suitable constitutive equation from among the many existing material constitutive equations that best represent the relationship between stress and strain of the material being simulated, which is a time-consuming process.

[0004] Therefore, instead of using constitutive equations for materials, one could consider using a regression model that has learned the relationship between stress and strain in materials.

[0005] However, generating a regression model that learns the relationship between stress and strain in a material requires training data that shows this relationship, and preparing such training data is time-consuming. That is, both stress and strain are physical quantities (tensors) with six independent components. Therefore, obtaining data that shows the relationship between stress and strain in a material requires conducting material tests under various loading conditions (multi-axial fields), which is time-consuming.

[0006] The present invention has been made in view of the above problems, and one of its objectives is to provide a regression model generation method, a regression model generation system, a simulation method, a simulation system, and a program that enable the easy simulation of the behavior of a material in response to external forces. [Means for solving the problem]

[0007] A regression model generation method according to one embodiment of the present invention comprises: a stress-strain acquisition step of acquiring time-series stresses from 0 to N (where N is a natural number) and strains from 0 to N obtained by performing material testing or simulation on a material; an effective inelastic strain rate acquisition step of acquiring the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material, based on the nth stress (where n is a natural number between 1 and N) and the n-1th stress, and the nth strain and the n-1th strain; and a regression model generation step of generating a regression model that has learned the relationship between the nth strain information indicating the nth strain and the nth effective inelastic strain rate. [Brief explanation of the drawing]

[0008] [Figure 1] This figure shows an example of the hardware configuration of a tire design support system according to an embodiment of the present invention. [Figure 2] This figure shows an example of the functions realized by the regression model generation device according to an embodiment of the present invention. [Figure 3] This figure schematically shows the material composition formula according to an embodiment of the present invention. [Figure 4] This figure shows an example of the processing performed by the regression model generation device according to an embodiment of the present invention. [Figure 5] This figure shows an example of the process in S43 shown in Figure 4. [Figure 6] This figure shows an example of a function realized by the simulation device according to an embodiment of the present invention. [Figure 7]This is a diagram showing an example of a process executed by a simulation device according to an embodiment of the present invention. [Figure 8] This is a diagram showing an example of the process of S76 shown in FIG. 7. [Figure 9] This is a diagram showing an example of a process executed by a modified example of a regression model generation device according to an embodiment of the present invention. [Figure 10] This is a diagram showing an example of a process executed by a modified example of a simulation device according to an embodiment of the present invention. [Figure 11] This is a diagram showing an example of the process of S1008 shown in FIG. 10.

Embodiments for Carrying Out the Invention

[0009] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the present embodiment, when a regression model generation method, a regression model generation system, a simulation method, a simulation system, and a program according to the present invention are used for tire design, specifically, when used for analyzing the mechanical behavior of tire rubber (hereinafter sometimes simply referred to as "rubber"), this will be described as an example. That is, in the present embodiment, the case where the material is rubber is exemplified. However, the present invention is applicable to any material.

[0010] In the mathematical formulas described in this specification, physical quantities shown in bold are tensor quantities, and physical quantities shown in italics are scalar quantities.

[0011] [1. Hardware Configuration of Tire Design Support System] Figure 1 shows an example of the hardware configuration of a tire design support system 1 according to an embodiment of the present invention. As will be described later, the tire design support system 1 functions as a regression model generation device 2 and a simulation device 6. In this embodiment, the case in which the tire design support system 1 is implemented on a single computer is illustrated. That is, the regression model generation device 2 and the simulation device 6 are implemented on a single computer. The tire design support system 1 may be implemented on multiple computers connected to each other via a network such as the Internet or a LAN.

[0012] As shown in Figure 1, the tire design support system 1 includes a control unit 10, a storage unit 12, a communication unit 14, a display unit 16, and an operation unit 18. The control unit 10 is a program control device such as a CPU that operates according to a program stored in the storage unit 12. The storage unit 12 is a storage element such as ROM or RAM or a hard disk drive. The storage unit 12 stores programs executed by the control unit 10. The communication unit 14 is a communication interface such as a network board or a wireless LAN module. The display unit 16 is a display such as a liquid crystal display or an organic EL display. The operation unit 18 is an input device such as a keyboard, mouse, or touch panel.

[0013] The program stored in the storage unit 12 may be supplied via a network. Alternatively, the storage unit 12 may include a reading unit (e.g., a memory card slot) for reading computer-readable information storage media or an input / output unit (e.g., a USB terminal) for connecting to external devices. In this case, the program stored on the information storage media may be supplied via the reading unit or input / output unit.

[0014] [2. Functions realized by the regression model generator] Figure 2 shows an example of the functions realized by the regression model generation device 2 according to an embodiment of the present invention. As shown in Figure 2, the regression model generation device 2 realizes a stress-strain acquisition unit 200, a strain information acquisition unit 202, an effective inelastic strain rate acquisition unit 204, and a regression model generation unit 206.

[0015] The calculations performed by the regression model generation device 2 described below are based on the assumption that the deformation of the rubber is incompressible (the same applies to the simulation device 6). However, it is not always necessary to assume that the deformation of the material is incompressible.

[0016] [Stress-strain acquisition section] The stress-strain acquisition unit 200 acquires stresses from 0 to N (where N is a natural number) and strains from 0 to N in a time series, obtained by performing material testing on the material. In this embodiment, the stress-strain acquisition unit 200 acquires stresses from 0 to N and strains from 0 to N stored in the storage unit 12. Alternatively, the stress-strain acquisition unit 200 may acquire stresses from 0 to N and strains from 0 to N stored in an external information storage medium or device.

[0017] Material testing includes, for example, tensile tests, compression tests, shear tests, and other tests that can obtain stress and strain for a material. In this embodiment, we illustrate the case where stresses 0 to N and strains 0 to N are obtained by performing a uniaxial tensile test (material testing in a single deformation mode) on rubber. However, stresses 0 to N and strains 0 to N may also be obtained by performing material testing in multiple deformation modes.

[0018] Note that the zeroth stress and zeroth strain do not necessarily have to be the stress and strain at the start of measurement in an actual material test. Similarly, the nth stress and zeroth strain do not necessarily have to be the stress and strain at the end of measurement in an actual material test. That is, the zeroth stress (or strain) is the first data point of the stress (or strain) in the time series, and the nth stress (or strain) is the last data point of the stress (or strain) in the time series.

[0019] Furthermore, in this embodiment, the stress and strain acquired by the stress-strain acquisition unit 200 are assumed to be nominal stress and nominal strain, respectively. Nominal stress and nominal strain are scalar quantities. Therefore, in the following description, where "nominal stress" is written, it refers to the stress acquired by the stress-strain acquisition unit 200, and where "nominal strain" is written, it refers to the strain acquired by the stress-strain acquisition unit 200. Note that this is not an example, and the stress acquired by the stress-strain acquisition unit 200 may be, for example, true stress (Cauchy stress), Kirchhoff stress, second Piola-Kirchhoff stress, etc. Also, the strain acquired by the stress-strain acquisition unit 200 may be, for example, true strain (Henchy strain), Green-Lagrange strain, Euler-Almansi strain, etc.

[0020] Furthermore, in this embodiment, the stress-strain acquisition unit 200 acquires stresses from 0 to N and strains from 0 to N obtained by performing material testing. However, the stress-strain acquisition unit 200 may also acquire stresses from 0 to N and strains from 0 to N obtained by performing simulation. The simulation can also be any simulation that can acquire stress and strain for the material, similar to the material testing.

[0021] [Distortion Information Acquisition Department] The strain information acquisition unit 202 acquires strain information for the nth strain (where n is a natural number between 1 and N) based on the nth strain. Specifically, the strain information for the nth strain is a strain invariant related to the nth strain. The strain information for the nth strain may also be an equivalent strain related to the nth strain. In other words, the regression model generation device 2 does not necessarily have to be equipped with a strain information acquisition unit 202. Furthermore, the strain information acquisition unit 202 may acquire multiple pieces of strain information for the nth strain (for example, the strain invariant for the nth strain, the equivalent strain for the nth strain, and the nth strain).

[0022] More specifically, the strain information acquisition unit 202 acquires strain information for the first to N strains based on the strains for the first to N strains.

[0023] [Effective inelastic strain rate acquisition unit] The effective inelastic strain rate acquisition unit 204 acquires the nth effective inelastic strain rate based on the nth stress and the n-1th stress, and the nth strain and the n-1th strain.

[0024] The effective inelastic strain rate is a scalar quantity that indicates the magnitude of the deformation rate related to the inelastic deformation of a material (rubber in this embodiment). That is, the deformation rate related to the inelastic deformation of a material, which is a tensor quantity, is given by a component τ, which is a tensor quantity that indicates the direction of the deformation rate, as shown in equation (1) below. v / ||τ v || can be decomposed into a scalar component representing the magnitude of the deformation rate (i.e., the effective inelastic strain rate) γ dot. Equation (1) is sometimes called the advanced equation for inelastic deformation. The effective inelastic strain rate is also sometimes called the effective creep strain rate, effective plastic strain rate, or equivalent plastic strain rate.

[0025]

number

[0026] As shown in Figure 2, specifically, the effective inelastic strain rate acquisition unit 204 includes a time-dependent stress acquisition unit 2040, an elastic principal strain calculation unit 2041, a principal strain calculation unit 2042, a trial elastic principal strain calculation unit 2043, and an effective inelastic strain rate calculation unit 2044.

[0027] Note that, as will be described later with reference to FIGS. 4 to 5, the processing of the effective inelastic strain rate acquisition unit 204 (i.e., the processing of the time-dependent stress acquisition unit 2040, the elastic principal strain calculation unit 2041, the principal strain calculation unit 2042, the trial elastic principal strain calculation unit 2043, and the effective inelastic strain rate calculation unit 2044) is sequentially and repeatedly executed for each n from n = 1 to n = N. That is, the processing of the effective inelastic strain rate acquisition unit 204 is sequentially and repeatedly executed for the stress and strain of each n.

[0028] [Time-dependent stress acquisition unit] The time-dependent stress acquisition unit 2040 calculates the n-th time-dependent stress based on the n-th strain and the n-th stress.

[0029] Here, the time-dependent stress will be described. FIG. 3 is a diagram schematically showing a material constitutive equation according to an embodiment of the present invention. As shown in FIG. 3, in the present embodiment, the rubber as the material is represented by a material constitutive equation including a time-independent component T i and a time-dependent component T d The material constitutive equation is also called a material model. Note that the material constitutive equation shown in FIG. 3 is an example, and the material constitutive equation may include components other than the time-independent component T i and the time-dependent component T d or an arbitrary material constitutive equation may be used according to the mechanical properties of the material.

[0030] As shown in FIG. 3, the time-independent component T i is modeled by a spring. In the present embodiment, the time-independent component T i is a hyperelastic model. In the present embodiment, as an example of the hyperelastic model representing the time-independent component T i the Arruda-Boyce model is used, but the hyperelastic model may be other models such as the Neo-Hooke model, the Mooney-Rivlin model, or the Ogden model. Note that the time-independent component T i may be a simple elastic model.

[0031] On the other hand, as shown in FIG. 3, the time-dependent component Td This is modeled by a series connection of a spring and a dashpot (Maxwell model). In other words, in this embodiment, the time-dependent component T d This is a viscoelastic model.

[0032] Then, the stress of the rubber has a time-independent component T. i The stress is time-independent stress and time-dependent component T. d The stress is decomposed into time-dependent stresses.

[0033] Since the effective inelastic strain rate is a time-dependent quantity, the effective inelastic strain rate acquisition unit 204 of this embodiment calculates the effective inelastic strain rate using the time-dependent stress obtained by subtracting the time-independent stress from the stress, thus enabling the effective inelastic strain rate to be obtained with high accuracy.

[0034] In this embodiment, the strain energy density functions of the time-independent and time-dependent components are functions of the first invariant of strain. If the strain energy density function is a function of the second invariant of strain or the principal tension ratio, it is difficult to uniquely determine the parameters of the strain energy density function without using data obtained from material tests in multiple deformation modes. In this case, if the parameters of the strain energy density function are determined using material test data from a single deformation mode, the effective inelastic strain rate cannot be obtained with high accuracy. On the other hand, if the strain energy density function is a function of the first invariant, which does not include the second invariant or the principal tension ratio, the parameters of the strain energy density function can be uniquely determined using only material test data from a single deformation mode. That is, by making the strain energy density function a function of the first invariant of strain, the effective inelastic strain rate can be obtained with high accuracy even when only material test data from a single deformation mode (uniaxial tension) is available, as in this embodiment.

[0035] As shown in Figure 2, the time-dependent stress acquisition unit 2040 includes a deformation gradient calculation unit 20400, a time-independent stress calculation unit 20402, and a time-dependent stress calculation unit 20404.

[0036] The deformation gradient calculation unit 20400 calculates the nth deformation gradient based on the nth strain. Specifically, the deformation gradient calculation unit 20400 calculates the nth deformation gradient based on the following equation (2). In this embodiment, since the stress and strain data are obtained by a uniaxial tensile test, that is, since the deformation mode is a uniaxial tensile mode, the relationship between the deformation gradient and strain is expressed by the following equation (2). If the stress and strain data are obtained by a material test (or simulation) other than a uniaxial tensile test, the deformation gradient may be calculated using an appropriate equation according to the type of material test, that is, according to the type of deformation mode.

[0037]

number

[0038] The time-independent stress calculation unit 20402 calculates the nth stress, the nth deformation gradient, and the time-independent component T. i Based on the equation showing the relationship between stress and strain in the given region, the nth time-independent stress is calculated. In this embodiment, the time-independent component T i The equation showing the relationship between stress and strain in this context is given by equation (3) below.

number

[0039] The hydrostatic pressure p is calculated by solving equation (4) below, taking advantage of the fact that the component in the unloaded direction (e.g., the 33 direction) of the nth time-independent stress is 0. In equation (4) below, the subscript 33 means the 33 direction component.

[0040]

number

[0041] Furthermore, substituting the hydrostatic pressure p calculated by solving equation (4) into equation (3), the values ​​of the components other than the tensile component (component 11) of the nth time-independent stress become 0.

[0042] Initial values ​​are set for the material parameters μ and N. If the constraints described later are not met, the material parameters μ and N are reset, and the subsequent processing (processing from the time-dependent stress calculation unit 20404 to the effective inelastic strain rate calculation unit 2044) is repeatedly executed to optimize the material parameters μ and N (see Figure 5). Bayesian optimization may be used to optimize the material parameters μ and N. If experimental or simulation data that can be considered independent of time is available, the material parameters μ and N may be determined based on that data. Specifically, the material parameters μ and N in equation (3) above may be determined by a curve fitting process using stress data that can be considered independent of time.

[0043] The time-dependent stress calculation unit 20404 calculates the nth time-dependent stress based on the nth stress and the nth time-independent stress. Specifically, as shown in equation (5), the time-dependent stress calculation unit 20404 calculates the nth time-dependent stress by subtracting the tensile component of the nth time-independent stress from the nth Cauchy stress based on the nth nominal stress, thereby calculating the tensile component of the nth time-dependent stress. The nth time-dependent stress is a tensor quantity having 11 components, which are the tensile components of the nth time-dependent stress.

[0044]

number

[0045] The nth Cauchy stress is calculated based on equation (6) below. Cauchy stress is a scalar quantity, just like nominal stress.

[0046]

number

[0047] Furthermore, if experimental or simulation data that can be considered independent of time is available, the nth time-dependent stress may be calculated by subtracting the stress included in said experimental or simulation data from the nth Cauchy stress based on the nth nominal stress.

[0048] [Elastic principal strain calculation unit] The elastic principal strain calculation unit 2041 calculates the nth elastic principal strain based on the nth time-dependent stress. Specifically, the elastic principal strain calculation unit 2041 calculates the nth time-dependent stress and the time-dependent component T d Based on the equation showing the relationship between stress and strain in , the nth principal elastic strain is calculated. In this embodiment, the time-dependent component T d The equation showing the relationship between stress and strain in this region is given by equation (7) below. Note that a different mathematical model may be used to represent the relationship between stress and strain in the time-dependent component Td than the mathematical model representing the relationship between stress and strain in the time-independent component Ti.

[0049]

number

[0050] Similar to the material parameters μ and N, the material parameter μ v and N v Initial values ​​are set for this. If the constraints described later are not met, the material parameter μ v and N v By resetting and repeatedly executing the subsequent processes (from the main strain calculation unit 2042 to the effective inelastic strain rate calculation unit 2044), the material parameter μ is determined. v and N v This is optimized (see Figure 5). Material parameter μ v and N v For optimization, Bayesian optimization, for example, may be used.

[0051] The elastic principal strain calculation unit 2041 calculates the time-dependent component T based on the nth time-dependent stress. dThe nth left Cauchy-Green tensor relating to the elastic component is calculated. Specifically, the elastic principal strain calculation unit 2041 substitutes the nth time-dependent stress into equation (7) to calculate the nth left Cauchy-Green tensor relating to the elastic component. Then, the elastic principal strain calculation unit 2041 calculates the nth elastic principal strain based on the nth left Cauchy-Green tensor relating to the elastic component. Specifically, the elastic principal strain calculation unit 2041 calculates the nth elastic principal strain based on the following equations (8) and (9).

[0052]

number

[0053]

number

[0054] [Main Strain Calculation Unit] The principal strain calculation unit 2042 calculates the nth principal strain based on the nth strain. Specifically, the principal strain calculation unit 2042 calculates the nth left Cauchy-Green tensor based on the nth deformation gradient calculated by the deformation gradient calculation unit 20400 (see equation (2)). Then, the principal strain calculation unit 2042 calculates the nth principal strain based on the nth left Cauchy-Green tensor. Specifically, the principal strain calculation unit 2042 calculates the nth principal strain based on equations (10) and (11) below. Furthermore, the principal strain calculation unit 2042 calculates the 0th principal strain based on the 0th strain.

[0055]

number

[0056]

number

[0057] [Trial Elastic Principal Strain Calculation Unit] The trial elastic principal strain calculation unit 2043 calculates the nth trial elastic principal strain based on the sum of the nth principal strain increment and the (n-1)th elastic principal strain (see equation (12) below). The nth principal strain increment is the difference between the (n-1)th principal strain and the nth principal strain. When n=1, the trial elastic principal strain calculation unit 2043 calculates the first trial elastic principal strain based on the sum of the first principal strain increment and a given 0th elastic principal strain. However, the 0th elastic principal strain may be calculated by the elastic principal strain calculation unit 2041 based on the 0th time-dependent stress. In equations (12) and subsequent equations, a subscript (n or n-1) indicating the ordinal number of the data is placed in the upper left of each physical quantity.

[0058]

number

[0059] [Effective inelastic strain rate calculation unit] The effective inelastic strain rate calculation unit 2044 calculates the nth effective inelastic strain rate based on the following equation (13). Specifically, the effective inelastic strain rate calculation unit 2044 substitutes the nth time-dependent stress acquired by the time-dependent stress acquisition unit 2040, the nth elastic principal strain calculated by the elastic principal strain calculation unit 2041, and the nth trial elastic principal strain calculated by the trial elastic principal strain calculation unit 2043 into the following equation (13), and solves equation (13) for the nth effective inelastic strain rate to calculate the nth effective inelastic strain rate. The time increment is the difference between the time at which the nth stress and nth strain were measured in the material test and the time at which the (n-1)th stress and (n-1)th strain were measured.

[0060]

number

[0061] Furthermore, if the nth effective inelastic strain rate calculated by the effective inelastic strain rate calculation unit 2044 is less than 0, the second law of thermodynamics will not be satisfied. Therefore, in this embodiment, if the nth effective inelastic strain rate is less than 0, the constraint condition is not met, and the process returns to the time-independent stress calculation unit 20402, and the material parameters μ, N, μ v and N v Change at least one of the following and execute the process from the time-dependent stress calculation unit 20404 to the effective inelastic strain rate calculation unit 2044 again (see Figure 5).

[0062] [Regression Model Generation Unit] The regression model generation unit 206 generates a regression model that learns the relationship between the (n-1)th strain information and the nth strain information, and the nth effective inelastic strain rate. That is, the regression model generation unit 206 performs regression model learning with the (n-1)th strain information and the nth strain information as explanatory variables and the nth effective inelastic strain rate as the objective variable.

[0063] Furthermore, the regression model generation unit 206 does not need to train the regression model on the relationship between the (n-1)th strain information and the nth effective inelastic strain rate. In other words, the regression model generation unit 206 only needs to train the regression model on the relationship between each of the 1st to Nth strain information and each of the 1st to Nth effective inelastic strain rates.

[0064] The regression model generation unit 206 stores the generated regression model in the storage unit 12. Alternatively, the regression model generation unit 206 may store the generated regression model in an external information storage medium or device.

[0065] In this embodiment, we illustrate the case where the regression model is a neural network. However, the regression model may be any model, such as a linear regression model or a Gaussian process regression model. For generating the regression model, i.e., tuning the parameters of the regression model (learning the regression model), known learning algorithms such as backpropagation or stochastic gradient descent may be used.

[0066] [3. Processing performed by the regression model generator] Figure 4 shows an example of processing performed by the regression model generation device 2 according to an embodiment of the present invention. Figure 5 shows an example of processing S43 shown in Figure 4. The processing shown in Figures 4 and 5 is performed by the control unit 10 operating according to the program stored in the storage unit 12. For specific processing details of each step shown in Figures 4 and 5, please refer to the explanation in [2. Functions realized by the regression model generation device] above.

[0067] As shown in Figure 4, first the regression model generation device 2 acquires stresses 0 to N and strains 0 to N (S40). Next, the regression model generation device 2 acquires strain information 1 to N based on strains 1 to N (S41). The regression model generation device 2 initializes the variable n to 1 (S42) and acquires the nth effective inelastic strain rate based on the nth stress and the n-1 stress, and the nth strain and the n-1 strain (S43).

[0068] Moving on to Figure 5, the process in S43 will be explained. As shown in Figure 5, the regression model generation device 2 calculates the nth deformation gradient based on the nth strain (S430). Subsequently, the regression model generation device 2 calculates the nth stress, the nth deformation gradient, and the time-independent component T. i Based on the equation showing the relationship between stress and strain in the given region, the nth time-independent stress is calculated (S431). Furthermore, the regression model generation device 2 calculates the nth time-dependent stress based on the nth stress and the nth time-independent stress (S432).

[0069] The regression model generation device 2 calculates the nth principal elastic strain based on the nth time-dependent stress (S433). The regression model generation device 2 also calculates the nth principal strain based on the nth strain (S434). Then, the regression model generation device 2 calculates the nth trial principal elastic strain based on the sum of the nth principal strain increment and the (n-1)th principal elastic strain (S435). The regression model generation device 2 calculates the nth effective inelastic strain rate based on the aforementioned equation (13) (S436). The regression model generation device 2 determines whether the nth effective inelastic strain rate calculated in S436 satisfies the constraints (whether the nth effective inelastic strain rate is 0 or greater) (S437). If the regression model generator 2 determines that the nth effective inelastic strain rate does not satisfy the constraint (S437; No), it returns to S431 and processes the material parameters μ, N, μ v and N v The process is modified, and steps S431 through S437 are repeated. If the regression model generation device 2 determines that the nth effective inelastic strain rate satisfies the constraint (S437; Yes), it proceeds to step S44 shown in Figure 4.

[0070] Returning to Figure 4, the regression model generator 2 determines whether the variable n is equal to N (S44). That is, in S44, the regression model generator 2 determines whether the process in S43 has been executed for all n from the 1st to N. If the regression model generator 2 determines that the variable n is not equal to N (S44; No), it updates the variable n to n+1 (S45) and executes the process in S43 again. If the regression model generator 2 determines that the variable n is equal to N (S44; Yes), it trains the regression model to learn the relationship between the first strain information and the first effective inelastic strain rate, and generates a regression model that has learned the relationship between the set of the (n-1)th strain information and the nth strain information and the nth effective inelastic strain rate for each n from n=1 to n=N (S45), and then terminates this process.

[0071] Note that the processes shown in Figures 4 and 5 are examples, and the execution order of the processes is not limited to those shown in Figures 4 and 5. For example, the regression model generation device 2 may first acquire the effective inelastic strain rate and then acquire the strain information.

[0072] [4. Functions realized by the simulation device] Figure 6 shows an example of the functions realized in the simulation device 6 according to an embodiment of the present invention. As shown in Figure 6, the simulation device 6 realizes a simulation model generation unit 600, a virtual strain calculation unit 602, a virtual strain information acquisition unit 604, a virtual effective inelastic strain rate acquisition unit 606, and a virtual stress acquisition unit 608.

[0073] [Simulation Model Generation Unit] The simulation model generation unit 600 generates a tire model and a rubber model (virtual material) included in the tire model to be simulated. The rubber model, which is a material model, is a component of the tire model, which is a structural model. The tire model and the rubber model are simulation models based on the finite element method, for example, and consist of multiple small regions (elements) determined by multiple nodes. In other words, in this embodiment, the case in which the finite element method is used as the simulation method is described, but simulation methods such as the mesh-free method or the finite difference method may also be used.

[0074] [Virtual Strain Calculation Unit] The virtual strain calculation unit 602 calculates the m-th virtual strain, which is the m-th (where m is a natural number between 1 and M, and M is a natural number) strain of the rubber model. Specifically, in the m-th step, the virtual strain calculation unit 602 applies a virtual external force to the rubber model and calculates the m-th virtual deformation gradient based on the virtual displacements of each node that occur in response to the virtual external force. Then, the virtual strain calculation unit 602 calculates the m-th virtual strain based on the calculated m-th virtual deformation gradient. However, the procedure by which the virtual strain calculation unit 602 calculates the m-th virtual strain is not limited to this example. In this embodiment, the virtual strain calculation unit 602 also calculates the 0th virtual strain in the 0th step, i.e., in the stationary state, based on the virtual displacements of each node that occur in response to the virtual external force applied to the rubber model. In other words, in the simulation device 6 according to this embodiment, both static and dynamic analysis are performed. Note that static analysis may be omitted, and only dynamic analysis may be performed. Alternatively, you could perform a quasi-static analysis instead of a dynamic analysis.

[0075] As will be explained later using Figures 7 and 8, the processing of the virtual strain calculation unit 602, the virtual strain information acquisition unit 604, the virtual effective inelastic strain rate acquisition unit 606, and the virtual stress acquisition unit 608 is performed for each m from m=1 to m=M.

[0076] [Virtual Strain Information Acquisition Unit] The virtual strain information acquisition unit 604 acquires virtual strain information for the mth virtual strain based on the mth virtual strain. Specifically, the virtual strain information for the mth virtual strain is a strain invariant related to the mth virtual strain, similar to the strain information described above.

[0077] The virtual strain information must be the same physical quantity as the strain information used to generate the regression model. For example, if the strain information is equivalent strain, the virtual strain information must also be equivalent strain. Furthermore, if multiple strain information sources are used to generate the regression model, the virtual strain information acquisition unit 604 must acquire virtual strain information that is the same physical quantity as each of the multiple strain information sources.

[0078] [Virtual Effective Inelastic Strain Rate Acquisition Unit] The virtual effective inelastic strain rate acquisition unit 606 acquires the mth virtual effective inelastic strain rate, which is the mth effective inelastic strain rate of the rubber model, based on the mth virtual strain information and the regression model. Here, the regression model is a learned regression model generated by the regression model generation device 2 described above. Specifically, the virtual effective inelastic strain rate acquisition unit 606 inputs the mth virtual strain information into the regression model and acquires the mth virtual effective inelastic strain rate output from the regression model.

[0079] [Virtual stress acquisition unit] The virtual stress acquisition unit 608 acquires the mth virtual stress, which is the mth stress of the rubber model, based on the mth virtual strain and the mth virtual effective inelastic strain rate.

[0080] Specifically, the virtual stress acquisition unit 608 includes a virtual principal strain calculation unit 6080, a virtual trial elastic principal strain calculation unit 6081, a virtual elastic principal strain acquisition unit 6082, a virtual trial elastic principal strain calculation unit 6083, and a virtual stress calculation unit 6084.

[0081] [Virtual principal strain calculation unit] The virtual principal strain calculation unit 6080 calculates the mth virtual principal strain, which is the mth principal strain of the rubber model, based on the mth virtual deformation gradient. Specifically, the virtual principal strain calculation unit 6080 calculates the mth virtual left Cauchy-Green tensor based on the mth virtual deformation gradient (see equation (2)). Then, the virtual principal strain calculation unit 6080 calculates the mth virtual principal strain based on the mth virtual left Cauchy-Green tensor (see equations (10) and (11)). Furthermore, the virtual principal strain calculation unit 6080 calculates the 0th virtual principal strain based on the 0th virtual strain.

[0082] [Virtual trial elastic principal strain calculation unit] The virtual trial elastic principal strain calculation unit 6081 calculates the m-th virtual trial elastic principal strain based on the m-th virtual strain increment and the m-1-th virtual elastic strain. Specifically, the virtual trial elastic principal strain calculation unit 6081 calculates the m-th virtual trial elastic strain based on the sum of the m-th virtual strain increment and the m-1-th virtual elastic strain. Then, the virtual trial elastic principal strain calculation unit 6081 calculates the m-th virtual trial elastic principal strain by calculating the eigenvalue of the m-th virtual trial elastic strain. The m-th virtual strain increment is the difference between the m-1-th virtual strain and the m-th virtual strain.

[0083] In the case where m=1, first, the virtual trial elastic principal strain calculation unit 6081 obtains a given 0th virtual elastic strain, which is the 0th elastic strain of the rubber model. Then, the virtual trial elastic principal strain calculation unit 6081 calculates the first virtual trial elastic principal strain based on the sum of the first virtual strain increment and the given 0th virtual elastic strain. Then, the virtual trial elastic principal strain calculation unit 6081 calculates the first virtual trial elastic principal strain by calculating the eigenvalue of the first virtual trial elastic strain. In the case where m≧2, since the m-1th virtual elastic strain has already been calculated by the virtual elastic principal strain acquisition unit 6082, the virtual trial elastic principal strain calculation unit 6081 uses the calculated m-1th virtual elastic strain to calculate the mth virtual trial elastic principal strain.

[0084] [Virtual Elastic Principal Strain Acquisition Unit] The virtual elastic principal strain acquisition unit 6083 calculates the mth virtual elastic principal strain based on the following equation (14). Specifically, the virtual elastic principal strain acquisition unit 6083 calculates the mth virtual elastic principal strain by substituting the mth virtual effective inelastic strain rate acquired by the virtual effective inelastic strain rate acquisition unit 606, the mth virtual trial elastic principal strain calculated by the virtual trial elastic principal strain calculation unit 6081, and the mth virtual trial elastic strain into equation (14) and solving equation (14) for the mth virtual elastic principal strain. The time increment is the time interval between two consecutive steps in the simulation. The time increment may be determined appropriately by comprehensively considering the purpose of the simulation, the characteristics of the target material, the capacity of the computing resources, etc.

[0085]

number

[0086] Furthermore, the virtual elastic principal strain acquisition unit 6083 acquires a given 0th virtual elastic principal strain.

[0087] [Virtual stress calculation unit] The virtual stress calculation unit 6084 calculates the m-th virtual stress based on the m-th virtual elastic principal strain. Specifically, the virtual stress calculation unit 6084 calculates the m-th left Cauchy-Green tensor relating to the elastic component based on the m-th virtual elastic principal strain (see equations (8) and (9)). Then, the virtual stress calculation unit 6084 calculates the m-th virtual stress based on the m-th left Cauchy-Green tensor relating to the elastic component (see equation (7)). In this embodiment, the virtual stress is a time-dependent stress.

[0088] [5. Processes executed by the simulation generation device] Figure 7 shows an example of processing performed by the simulation device 6 according to an embodiment of the present invention. Figure 8 shows an example of processing S76 shown in Figure 7. The processing shown in Figures 7 and 8 is performed by the control unit 10 operating according to the program stored in the storage unit 12. For specific details of the processing content of each step shown in Figures 7 and 8, please refer to the explanation in [4. Functions realized by the simulation generation device] above.

[0089] As shown in Figure 7, first the simulation device 6 calculates the 0th virtual deformation gradient and calculates the 0th virtual strain based on the 0th virtual deformation gradient (S70). The simulation device 6 also obtains a given 0th virtual elastic principal strain (S71). The simulation device 6 initializes the variable m to 1 (S72), calculates the mth virtual deformation gradient, and calculates the mth virtual strain based on the mth virtual deformation gradient (S73). Next, the simulation device 6 obtains the mth virtual strain information based on the mth virtual strain (S74). Then, based on the mth virtual strain information and the regression model, it obtains the mth virtual effective inelastic strain rate (S75). The simulation device 6 obtains the mth virtual stress based on the mth virtual strain and the mth virtual effective inelastic strain rate (S76).

[0090] Moving on to Figure 8, the process in S76 will be explained. As shown in Figure 8, the simulation device 6 acquires the (m-1)th virtual elastic strain (S760). The simulation device 6 also calculates the (m)th virtual strain increment, which is the difference between the (m)th virtual strain and the (m-1)th virtual strain (S761). Next, the simulation device 6 calculates the (m)th virtual trial elastic strain based on the sum of the (m)th virtual strain increment and the (m-1)th virtual elastic strain (S762). The simulation device 6 also calculates the (m)th virtual trial principal elastic strain based on the (m)th virtual trial elastic strain (S763). Then, the simulation device 6 calculates the (m)th virtual principal elastic strain based on equation (14) (S764). The simulation device 6 calculates the (m)th virtual stress based on the (m)th virtual principal elastic strain (S765), and then proceeds to the process in S77 shown in Figure 7.

[0091] Returning to Figure 7, the simulation device 6 determines whether the variable m is equal to M (S77). That is, in S77, the simulation device 6 determines whether it has performed the processes S73 to S76 for all of 1 to M. If the simulation device 6 determines that the variable m is not equal to M (S77; No), it updates the variable m to m+1 (S78) and performs the processes S73 to S76 again. If the simulation device 6 determines that the variable m is equal to M (S77; Yes), it terminates this process.

[0092] Note that the processes shown in Figures 7 and 8 are just examples, and the execution order of the processes is not limited to the examples shown in Figures 7 and 8. For example, the simulation device 6 may first acquire the 0th virtual elastic principal strain and then calculate the 0th virtual strain.

[0093] [6. Summary] When directly training a regression model on the relationship between stress and strain, which are both tensors of six independent components, preparing the training data for such a regression model requires conducting material tests or simulations under various loading conditions (multi-axial fields), which is time-consuming.

[0094] In contrast, the regression model generation device 2 according to this embodiment generates a regression model that learns the relationship between the nth strain information, which indicates the nth strain, and the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material. This reduces the effort required to prepare training data compared to the case where the relationship between stress and strain, both of which are tensors with six independent components, is directly trained into the regression model. Therefore, according to this embodiment, it becomes possible to easily simulate the behavior of a material in response to an external force.

[0095] As mentioned above, the effective inelastic strain rate is a scalar quantity that indicates the magnitude of the deformation rate related to the inelastic deformation of a material, and therefore can be treated independently of the effects of different deformation modes. Consequently, even if a regression model is trained using the effective inelastic strain rate calculated based on stress and strain data obtained from material tests or simulations (e.g., uniaxial tensile tests) under a single or small number of loading conditions, a regression model with good accuracy can be obtained.

[0096] Furthermore, in this embodiment, a strain invariant, which is a scalar quantity, is used as strain information. That is, the regression model generation device 2 according to this embodiment generates a regression model that has learned the relationship between the nth strain information, which is a scalar quantity, and the nth effective inelastic strain rate, which is a scalar quantity. This further reduces the effort required to prepare the training data.

[0097] Furthermore, in this embodiment, the nth time-dependent stress is used as the nth stress. Specifically, the nth principal elastic strain is calculated based on the nth time-dependent stress, and the nth effective inelastic strain rate is calculated by substituting the nth time-dependent stress, the nth principal elastic strain, and the nth trial principal elastic strain into equation (13) and solving equation (13) for the nth effective inelastic strain rate. Since the effective inelastic strain rate is a time-dependent quantity, according to this embodiment, the effective inelastic strain rate is calculated based only on the time-dependent component of the stress, which includes both a time-dependent component (time-dependent stress) and a time-independent component (time-independent stress), and the regression model is trained using this effective inelastic strain rate, thus enabling the acquisition of a highly accurate regression model.

[0098] [7. Variant] It should be noted that the present invention is not limited to the embodiments described above. The present invention can be modified as appropriate without departing from the spirit of the invention. Furthermore, the specific strings and numbers described above, as well as the specific strings and numbers in the drawings, are illustrative examples and the invention is not limited to these strings and numbers.

[0099] Hereinafter, a modified example of the above embodiment will be described using Figures 9 to 11. Figure 9 is a diagram showing an example of processing performed in a modified example of the regression model generation device 2 according to the embodiment of the present invention. Figure 10 is a diagram showing an example of processing performed in a modified example of the simulation device 6 according to the embodiment of the present invention. Figure 11 is a diagram showing an example of processing S1008 shown in Figure 10. Note that configurations (processes) similar to those in the above embodiment will not be described unless specifically mentioned.

[0100] The regression model in the modified example shown in Figures 9 to 11 was learned using the nth stress as input (explanatory variable) as well as the nth strain, and the nth effective inelastic strain rate as output (dependent variable). On the other hand, in the simulation, the mth virtual stress, which is necessary to estimate the mth virtual effective inelastic strain rate, is unknown at the time of the mth step. The purpose of the simulation is to determine the mth virtual stress from the mth virtual strain. Therefore, in this modified example, the simulation cannot be performed in the same way as in the above embodiment.

[0101] Therefore, in this modified example, a provisional value (trial stress) of the m-th virtual stress is obtained, and this trial stress information of the m-th trial stress is input into the regression model to obtain a provisional virtual effective inelastic strain rate of the m-th virtual stress. Subsequently, the trial stress of the m-th virtual stress is updated so that the absolute value of the residual Ra in equation (15), described later, becomes small, and the updated trial stress of the m-th virtual stress is obtained as the m-th virtual stress. In this way, even if the n-th stress is included in the explanatory variables of the regression model, it is possible to perform a simulation to determine the m-th virtual stress from the m-th virtual strain.

[0102] Now, as shown in Figure 9, the regression model generation device 2 according to the modified example not only acquires strain information for the first to N (S91), but also acquires stress information for the first to N, each representing the stress for the first to N (S92). Specifically, the regression model generation device 2 according to the modified example acquires stress information for the first to N based on the stresses for the first to N. In this embodiment, the nth stress information is the equivalent stress related to the nth stress. The nth stress information may also be a stress invariant related to the nth stress. Alternatively, the nth stress information may be the nth stress itself.

[0103] Then, in S97, the regression model generation device 2 for the modified example generates a regression model that has learned the relationship between the set of the (n-1)th strain information, the nth strain information, the (n-1)th stress information, and the nth stress information, and the nth effective inelastic strain rate. In other words, the regression model for this modified example is learned with the (n-1)th strain information, the nth strain information, the (n-1)th stress information, and the nth stress information as explanatory variables, and the nth effective inelastic strain rate as the objective variable.

[0104] As shown in Figure 10, in the modified simulation device 6, in S1003, the mth trial stress, which is a provisional value of the mth virtual stress, is obtained. The mth trial stress obtained in S1003 is set to, for example, a given initial value. Also, in S1005, the simulation device 6 obtains the mth trial stress information based on the mth trial stress. In this embodiment, the mth trial stress information is the equivalent stress related to the mth trial stress. The trial stress information needs to be the same physical quantity as the stress information used to generate the regression model, similar to the relationship between the virtual strain information and the strain information described above.

[0105] In S1007, the simulation device 6 acquires the m-th virtual effective inelastic strain rate based on the m-1 virtual strain information, the m-th virtual strain information, the m-1 virtual stress information, the m-th trial stress information, and the regression model. Specifically, in S1007, the simulation device 6 inputs the m-1 virtual strain information, the m-1 virtual strain information, the m-1 virtual stress information, and the m-th trial stress information into the regression model and acquires the m-th virtual effective inelastic strain rate output from the regression model.

[0106] Moving on to Figure 11, the process in S1008 will be explained. In S10080, the simulation device 6 calculates the m-th virtual elastic principal strain based on the m-th trial stress. Specifically, in S10080, the simulation device 6 calculates the m-th virtual elastic strain based on the m-th virtual elastic principal strain. The simulation device 6 also calculates the m-th virtual strain increment, which is the difference between the m-th virtual strain and the m-th virtual strain (S10081). Subsequently, the simulation device 6 calculates the m-th virtual trial elastic strain based on the sum of the m-th virtual strain increment and the m-th virtual elastic strain (S10082). The simulation device 6 also calculates the m-th virtual trial elastic principal strain based on the m-th virtual trial elastic strain (S10083).

[0107] In S10084, the simulation device 6 calculates the mth virtual elastic principal strain based on the mth trial stress. Specifically, in S10084, the simulation device 6 calculates the nth elastic principal strain based on the mth trial stress and an equation showing the relationship between stress and strain. The equation showing the relationship between stress and strain may be of the same form as equation (7). More specifically, the simulation device 6 calculates the mth left Cauchy-Green tensor relating to the elastic component based on the mth trial stress. Then, the simulation device 6 calculates the mth virtual elastic principal strain based on the mth left Cauchy-Green tensor relating to the elastic component.

[0108] In S10085, the simulation device 6 calculates the residual R in the following equation (15). a Specifically, the simulation device 6 calculates the residual Ra by substituting the m-th virtual effective inelastic strain rate calculated in S1007, the m-th virtual elastic principal strain calculated in S10084, the m-th virtual trial elastic principal strain calculated in S10083, and the m-th virtual trial elastic strain calculated in S10082 into equation (15).

[0109]

number

[0110] In S10086, the simulation device 6 determines whether the absolute value of the residual Ra in equation (15) is less than or equal to a predetermined threshold. If the simulation device 6 determines that the absolute value of the residual Ra exceeds the predetermined threshold (S10086; No), it updates the value of the m-th trial stress and repeats the process from S1003 to S10086 (see Figures 10 and 11). If the simulation device 6 determines that the absolute value of the residual Ra is less than or equal to a predetermined threshold (S10086; Yes), it acquires the m-th trial stress as the m-th virtual stress (S10087) and proceeds to the process in S1009.

[0111] In addition, instead of determining whether the absolute value of the residual Ra is less than or equal to a predetermined threshold in S10086, it may be possible to determine whether the process from S1003 to S10086 has been repeated a predetermined number of times.

[0112] In addition to the modifications shown in Figures 9 to 11, the present invention can be implemented in various other forms.

[0113] For example, the regression model generation apparatus 2 according to this embodiment uses a time-independent component T as the material constitutive equation representing the material. i and time-dependent component T d Although a formula including the time-dependent component was used (see Figure 3), a material constitutive formula including only the time-dependent component may also be used. In that case, the regression model generation device 2 may use the stress acquired by the stress-strain acquisition unit 200 as is to calculate the effective inelastic strain rate. In other words, the regression model generation device 2 does not need to be equipped with a time-dependent stress acquisition unit 2040.

[0114] Furthermore, in this embodiment, the regression model was trained to learn the relationship between strain information and effective inelastic strain rate. However, instead of training the regression model to learn the relationship between strain information and effective inelastic strain rate, the regression model may be trained to learn only the relationship between stress information and effective inelastic strain rate. In other words, the explanatory variable of the regression model may be stress information only. In that case, the operation of the regression model generation device 2 and the simulation device 6 may be the same as the modified examples shown in Figures 9 to 11.

[0115] Instead of the effective inelastic strain rate, the effective inelastic strain increment, obtained by multiplying the effective inelastic strain rate by the time increment, may be used. In this case, the equation can be appropriately modified using the relationship in equation (16) below.

[0116]

number

[0117] 1 Tire design support system, 2 Regression model generation device, 6 Simulation device, 10 Control unit, 12 Memory unit, 14 Communication unit, 16 Display unit, 18 Operation unit, 200 Stress-strain acquisition unit, 202 Strain information acquisition unit, 204 Effective inelastic strain rate acquisition unit, 206 Regression model generation unit, 2040 Time-dependent stress acquisition unit, 20400 Deformation gradient calculation unit, 20402 Time-independent stress calculation unit, 20404 Time-dependent stress calculation unit, 2041 Elastic principal strain calculation unit, 2042 Principal strain calculation unit, 2043 Trial elastic principal strain calculation unit, 2044 Effective inelastic strain rate calculation unit, 600 Simulation model generation unit, 602 Virtual strain calculation unit, 604 Virtual strain information acquisition unit, 606 Virtual effective inelastic strain rate acquisition unit, 608 Virtual stress acquisition unit, 6080 Virtual principal strain calculation unit, 6081 Virtual trial elastic principal strain calculation unit, 6082 Virtual trial elastic strain calculation unit, 6083 Virtual elastic principal strain acquisition unit, 6084 Virtual stress calculation unit.

Claims

1. A stress-strain acquisition step to obtain time-series stresses from 0 to N (where N is a natural number) and strains from 0 to N obtained by performing material testing or simulation on the material, An effective inelastic strain rate acquisition step to acquire the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material, based on the nth stress (where n is a natural number between 1 and N) and the n-1th stress, and the nth strain and the n-1th strain; A regression model generation step of generating a regression model that learns the relationship between the nth strain information representing the nth strain and the nth effective inelastic strain rate, A regression model generation method having the following characteristics.

2. In the regression model generation method described above, For each n from n=1 to n=N, the effective inelastic strain rate acquisition step is sequentially and repeatedly performed. In the regression model generation step, the regression model is made to learn the relationship between each of the first to N strain information and each of the first to N effective inelastic strain rates. The regression model generation method according to claim 1.

3. The aforementioned step of obtaining the effective inelastic strain rate is: A principal elastic strain calculation step, which calculates the nth principal elastic strain based on the nth stress, A principal strain calculation step of calculating the nth principal strain based on the nth strain, A trial elastic principal strain calculation step for calculating the nth trial elastic principal strain based on the sum of the nth principal strain increment, which is the difference between the (n-1)th principal strain and the nth principal strain, and the (n-1)th elastic principal strain, An effective inelastic strain rate calculation step is performed to calculate the nth effective inelastic strain rate based on the following equation 1, including, The regression model generation method according to claim 2. [Math 1]

4. The aforementioned material is represented by a material constitutive formula that includes a time-independent component and a time-dependent component, The stress includes a time-independent stress, which is the stress of the time-independent component, and a time-dependent stress, which is the stress of the time-dependent component. The aforementioned step of obtaining the effective inelastic strain rate is: A deformation gradient calculation step that calculates the nth deformation gradient based on the nth strain, A time-independent stress calculation step for calculating the nth time-independent stress based on the nth stress, the nth deformation gradient, and an equation showing the relationship between stress and strain in the time-independent component, A time-dependent stress calculation step in which the nth time-dependent stress is calculated based on the nth stress and the nth time-independent stress, It further includes, In the step of calculating the principal elastic strain, the nth principal elastic strain is calculated based on the nth time-dependent stress, In the effective inelastic strain rate calculation step, the nth effective inelastic strain rate is calculated by taking the nth stress in Equation 1 as the nth time-dependent stress. The regression model generation method according to claim 3.

5. The stresses 0 to N and strains 0 to N were obtained by performing material tests or simulations on the material in a single deformation mode. The strain energy density function of the time-independent component or the time-dependent component is a function of the first invariant of strain. The regression model generation method according to claim 4.

6. In the regression model generation step, the regression model is generated by further learning the relationship between the (n-1)th strain information and the nth effective inelastic strain rate. The regression model generation method according to claim 2.

7. The aforementioned strain information is equivalent strain or strain invariant. A method for generating a regression model according to claim 1 or 2.

8. In the regression model generation step, the regression model is generated by further learning the relationship between the nth stress information representing the nth stress and the nth effective inelastic strain rate. The regression model generation method according to claim 2.

9. In the regression model generation step, the regression model is generated by further learning the relationship between the (n-1) stress information and the nth effective inelastic strain rate. The regression model generation method according to claim 8.

10. The aforementioned stress information is equivalent stress or stress invariant. The regression model generation method according to claim 8.

11. A simulation method using the regression model described in claim 1, A virtual strain calculation step to calculate the virtual strain of the mth (where m is a natural number between 1 and M, and M is a natural number) of the virtual material to be simulated, A virtual effective inelastic strain rate acquisition step, which acquires the virtual effective inelastic strain rate of the virtual material, based on the virtual strain information of the mth virtual strain and the regression model, the effective inelastic strain rate of the mth virtual material, A virtual stress acquisition step to acquire the m virtual stress, which is the m stress of the virtual material, based on the m virtual strain and the m virtual effective inelastic strain rate, A simulation method having the following characteristics.

12. The regression model is generated by sequentially performing the effective inelastic strain rate acquisition step for each n from n=1 to n=N, and learning the relationship between each of the first to N strain information and each of the first to N effective inelastic strain rates in the regression model generation step. In the above simulation method, For each m from m=1 to m=M, the virtual strain calculation step, the virtual effective inelastic strain rate acquisition step, and the virtual stress acquisition step are sequentially and repeatedly executed. The simulation method according to claim 11.

13. A virtual deformation gradient calculation step involves applying a virtual external force to the virtual material and calculating the mth virtual deformation gradient based on the virtual displacement of the virtual material that occurs in response to the virtual external force. A virtual elastic strain acquisition step to acquire a given zero virtual elastic strain, which is the zero elastic strain of the virtual material, It further possesses, In the virtual stress acquisition step, Based on the aforementioned virtual deformation gradient of the mth, the virtual principal strain of the mth virtual material is calculated. The virtual trial elastic strain of the mth is calculated based on the sum of the virtual strain increment of the mth, which is the difference between the virtual strain of the m-1th and the virtual strain of the mth, and the virtual elastic strain of the m-1th. Based on the aforementioned virtual trial elastic strain of the mth, the virtual trial principal elastic strain of the mth is calculated. Based on the following equation 2, the m-th virtual elastic principal strain is calculated, Based on the aforementioned virtual elastic principal strain of the mth, the aforementioned virtual stress of the mth is calculated. The simulation method according to claim 12. [Math 2]

14. The regression model is generated by further learning the relationship between the nth stress information based on the nth stress and the nth effective inelastic strain rate in the regression model generation step. The aforementioned simulation method is A virtual deformation gradient calculation step involves applying a virtual external force to the virtual material and calculating the mth virtual deformation gradient based on the virtual displacement of the virtual material that occurs in response to the virtual external force. A virtual elastic strain acquisition step to acquire a given zero virtual elastic strain, which is the zero elastic strain of the virtual material, A trial stress acquisition step to obtain the trial stress, which is a provisional value of the m-th virtual stress, It further possesses, In the virtual effective inelastic strain rate acquisition step, the mth virtual effective inelastic strain rate is acquired based on the mth trial stress information indicating the mth trial stress, In the virtual stress acquisition step, Based on the aforementioned trial stress of the mth, the mth virtual elastic principal strain, which is the mth elastic principal strain of the virtual material, is calculated. Based on the aforementioned virtual deformation gradient of the mth, the virtual principal strain of the mth virtual material is calculated. The virtual trial elastic strain of the mth is calculated based on the sum of the virtual strain increment of the mth, which is the difference between the virtual strain of the m-1th and the virtual strain of the mth, and the virtual elastic strain of the m-1th. Based on the aforementioned virtual trial elastic strain of the mth, the virtual trial principal elastic strain of the mth is calculated. Residual R in the following equation 3 ａ The value of the m-th trial stress is updated so that its absolute value becomes smaller, and the updated m-th trial stress is obtained as the m-th virtual stress. The simulation method according to claim 12. [Math 3]

15. A stress-strain acquisition means for acquiring time-series stresses from 0 to N (where N is a natural number) and strains from 0 to N obtained by performing material testing or simulation on a material, An effective inelastic strain rate acquisition means for acquiring the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material, based on the nth stress (where n is a natural number between 1 and N) and the n-1th stress, and the nth strain and the n-1th strain; A regression model generation means for generating a regression model that learns the relationship between the nth strain information based on the nth strain and the nth effective inelastic strain rate, A regression model generation system having the following features.

16. A simulation system using the regression model described in claim 15, A virtual strain calculation means for calculating the m-th virtual strain, which is the m-th strain of the virtual material that is the subject of the simulation (where m is a natural number between 1 and M, and M is a natural number), A virtual effective inelastic strain rate acquisition means for acquiring the virtual effective inelastic strain rate of the virtual material, which is the effective inelastic strain rate of the virtual material, based on the virtual strain information of the mth virtual strain and the regression model, A virtual stress acquisition means for acquiring the m virtual stress, which is the m stress of the virtual material, based on the m virtual strain and the m virtual effective inelastic strain rate, A simulation system having the following features.

17. A stress-strain acquisition means for obtaining time-series stresses from 0 to N (where N is a natural number) and strains from 0 to N, obtained by performing material testing or simulation on a material. Effective inelastic strain rate acquisition means for acquiring the nth effective inelastic strain rate, which is a scalar quantity indicating the magnitude of the deformation rate related to the inelastic deformation of the material, based on the nth stress (where n is a natural number between 1 and N) and the n-1th stress, and the nth strain and the n-1th strain. Regression model generation means for generating a regression model that learns the relationship between the nth strain information based on the nth strain and the nth effective inelastic strain rate. A program that makes a computer function.

18. A program using the regression model described in claim 17, A virtual strain calculation means for obtaining the virtual strain of the mth (where m is a natural number between 1 and M, and M is a natural number) of the virtual material that is the subject of the simulation. A virtual effective inelastic strain rate acquisition means for acquiring the virtual effective inelastic strain rate of the virtual material, which is the effective inelastic strain rate of the virtual material, based on the virtual strain information of the mth virtual strain and the regression model. A virtual stress acquisition means that acquires the mth virtual stress, which is the mth stress of the virtual material, based on the mth virtual strain and the mth virtual effective inelastic strain rate. A program that makes a computer function.

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