A constitutive model construction method and system for rail fastener elastic pad

Abstract

The present invention discloses a constitutive model construction method and system for a rail fastener elastic pad, the method comprising: constructing a hyperelastic constitutive model of the fastener elastic pad considering temperature variables, and determining the viscoelastic constitutive model and the plastic constitutive model of the fastener elastic pad; fitting the first parameter of the hyperelastic constitutive model, the second parameter of the viscoelastic constitutive model and the third parameter of the plastic constitutive model, respectively obtaining a target hyperelastic constitutive model, a target viscoelastic constitutive model and a target plastic constitutive model; unifying the physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model, and superimposing the unified target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model to obtain the final target constitutive model of the fastener elastic pad. When simulating the pad, the various mechanical properties of the pad can be more comprehensively reflected, effectively improving the accuracy of the numerical simulation of the pad.

Description

Technical Field

[0001] The present invention belongs to the technical field of constitutive model construction, and in particular relates to a method and system for constructing a constitutive model of an elastic pad of a rail fastener. Background Art

[0002] The fastener system is an indispensable component of the high-speed railway track structure. It can elastically absorb the force of the rail and transmit it to the sleeper, suppress the vibration and impact generated by the train as much as possible, maintain the accuracy of the track structure, and have a significant impact on driving safety, passenger comfort, track structure vibration, wheel-rail rolling noise, etc. The dynamic support performance of the rail fastener system mainly depends on the elastic pad of rubber material. In order to scientifically evaluate the dynamic support performance of the rail fastener system, it is first necessary to accurately establish the constitutive model of the real dynamic service performance of the rail fastener elastic pad.

[0003] The dynamic behavior of rubber materials often changes nonlinearly with ambient temperature and load frequency, and exhibits both viscous liquid characteristics and elastic solid mechanical characteristics, namely viscoelastic mechanical characteristics. In addition, the elastic pad of the fastener will also show a nonlinear stress-strain relationship under elastic deformation, namely hyperelastic mechanical characteristics; due to the plastic deformation caused by carbon black additives, the pad also has plastic mechanical characteristics.

[0004] In general, the mechanical response behavior of elastic pads of high-speed railway fasteners is very complex. Stress is not only nonlinearly related to temperature, loading rate, and strain, but also related to the deformation process. Obtaining an accurate constitutive model of elastic pads is one of the keys to studying the mechanical properties of pads and the dynamic response of the entire track structure. At present, linear viscoelastic constitutive models or hyperelastic constitutive models are mostly used in the analysis and calculation of fastener elastic pads and track structures. These two constitutive models are obviously unable to fully and accurately describe the hyperelastic, viscoelastic and plastic properties of fastener elastic pads. The mechanical responses calculated using these two constitutive models will also have accuracy problems. Therefore, the study of the nonlinear viscoelastic-plastic constitutive model of fastener elastic pads is very important. Summary of the invention

[0005] The present invention provides a method and system for constructing a constitutive model of an elastic pad of a rail fastener, which is used to solve the technical problem that the hyperelasticity, viscoelasticity and plastic properties of the elastic pad of the fastener cannot be fully and accurately described, and the mechanical response calculated using the existing constitutive model has low precision.

[0006] In a first aspect, the present invention provides a method for constructing a constitutive model of an elastic pad of a rail fastener, comprising:

[0007] Construct a hyperelastic constitutive model of the elastic pad of the fastener considering the temperature variable, and determine the viscoelastic constitutive model and plastic constitutive model of the elastic pad of the fastener;

[0008] Fitting a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively;

[0009] The physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model are unified, and the unified target hyperelastic constitutive model, target viscoelastic constitutive model and target plastic constitutive model are superimposed to obtain the final target constitutive model of the fastener elastic pad.

[0010] In a second aspect, the present invention provides a rail fastener elastic pad constitutive model construction system, comprising:

[0011] A construction module configured to construct a hyperelastic constitutive model of the elastic pad of the fastener considering temperature variables, and determine a viscoelastic constitutive model and a plastic constitutive model of the elastic pad of the fastener;

[0012] A fitting module, configured to fit a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model, to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively;

[0013] The superposition module is configured to unify the physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model, and to superimpose the unified target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model to obtain the final target constitutive model of the fastener elastic pad.

[0014] According to a third aspect, an electronic device is provided, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the steps of the method for constructing a constitutive model of an elastic pad of a rail fastener according to any embodiment of the present invention.

[0015] In a fourth aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor executes the steps of the method for constructing a constitutive model of an elastic pad of a rail fastener according to any embodiment of the present invention.

[0016] The constitutive model construction method and system of the rail fastener elastic pad of the present application take into account the hyperelasticity, viscoelasticity and plasticity of rubber. When simulating the pad, it can more comprehensively reflect the various mechanical properties of the pad, effectively improving the accuracy of the numerical simulation of the pad. In addition, the hyperelasticity, viscoelasticity and plasticity models of the pad can be independently changed according to the different types of fastener elastic pads, so as to achieve the purpose of effectively characterizing the elastic pad according to different actual conditions. When simulating the pad, it can more comprehensively reflect the various mechanical properties of the pad, effectively improving the accuracy of the numerical simulation of the pad. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 A flow chart of a method for constructing a constitutive model of an elastic pad of a rail fastener provided in one embodiment of the present invention;

[0019] Figure 2 A structural block diagram of a rail fastener elastic pad constitutive model building system provided by an embodiment of the present invention;

[0020] Figure 3 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] See also Figure 1 , which shows a flow chart of a method for constructing a constitutive model of an elastic pad of a rail fastener of the present application.

[0023] like Figure 1 As shown in FIG. 1 , the constitutive model construction method of the rail fastener elastic pad specifically includes the following steps:

[0024] Step S101, constructing a hyperelastic constitutive model of the elastic pad of the fastener taking into account the temperature variable, and determining the viscoelastic constitutive model and the plastic constitutive model of the elastic pad of the fastener.

[0025] In this step, the strain energy function expression of the hyperelastic constitutive model is:

[0026] ,

[0027] ,

[0028] In the formula, is the strain energy, and is a material constant, determined by relevant tests, and are the principal strain invariants, is the change in strain energy caused by temperature change, is the surface integral, the surface integral object is the pad temperature, and the upper limit of the integral is the highest temperature reached by the pad during the test The lower limit of the integral is the lowest temperature reached by the pad during the test , For The natural logarithm of base , The contour integral is the temperature of the pad, and the upper limit of the integral is the highest temperature reached by the pad during the test. The lower limit of the integral is the lowest temperature reached by the pad during the test , is the specific heat capacity constant of the rubber material, is the actual temperature of the pad, is the standard reference temperature, is the volume thermal expansion coefficient of rubber, is the second Lamé constant of the material.

[0029] The time domain constitutive equation of the viscoelastic constitutive model is:

[0030] ,

[0031] In the formula, , , , are the viscosity parameters of the viscoelastic constitutive model, is the stress varying with time, is the temperature coefficient, are the fractional derivative orders, , are the elastic parameters of the viscoelastic constitutive model, is the strain that varies with time;

[0032] The time domain constitutive equation of the viscoelastic constitutive model is transformed by Fourier transform to obtain:

[0033] ,

[0034] In the formula, is the strain varying with frequency, is an imaginary unit, is the stress varying with frequency, is the frequency;

[0035] The complex modulus of the viscoelastic constitutive model is obtained by rearranging the transformation, and the expression is:

[0036] ,

[0037] In the formula, is the complex modulus that varies with frequency;

[0038] Will Substitute it into the complex modulus of the viscoelastic constitutive model, separate the real part and the imaginary part and calculate the energy storage model of the viscoelastic constitutive model. , Energy consumption model , and the loss factor , the expression is:

[0039] ,

[0040] ,

[0041] ,

[0042] In the formula, is the storage modulus that varies with frequency, is the energy loss modulus that varies with frequency.

[0043] The expression of the plastic constitutive model is:

[0044] ,

[0045] In the formula, is the plastic friction force, is the friction force at the reference point each time the displacement direction changes, is the displacement of the pad, is the displacement of the reference point each time the displacement direction changes, is the maximum friction force, for The corresponding displacement, , and varies within the interval (-1,1).

[0046] Step S102, fitting the first parameter of the hyperelastic constitutive model, the second parameter of the viscoelastic constitutive model and the third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model and a target plastic constitutive model respectively.

[0047] In this step, a static uniaxial compression test is performed on the elastic pad of the fastener to obtain a static force-displacement curve of nonlinear change of the elastic pad, and the first parameter of the hyperelastic constitutive model is fitted according to the static force-displacement curve;

[0048] The elastic pad of the fastener is subjected to extremely low frequency cyclic loading to obtain the dynamic load-dynamic displacement curve of the elastic pad under the action of extremely low frequency load. The third parameter of the plastic constitutive model is fitted according to the dynamic load-dynamic displacement curve after deducting the static nonlinear mechanical curve.

[0049] A constant-frequency variable-temperature test was carried out on the elastic pad of the fastener, and the constant-frequency variable-temperature dynamic load-dynamic displacement curve of the elastic pad was obtained. After deducting the static nonlinear mechanics curve and the dynamic plastic mechanics curve, the second parameter of the viscoelastic constitutive model was fitted.

[0050] It should be noted that for the case of uniform strain, the Cauchy principal stress of the elastic pad of the fastener is expressed as:

[0051] ,

[0052] In the formula, is the Cauchy principal stress of the pad, is the strain energy, and are the principal strain invariants, The main elongation, is the hydrostatic pressure;

[0053] Calculate the principal stress difference in three directions, the expression is:

[0054] ,

[0055] Substituting the stress-strain relationship of the uniaxial compression test into the expression of the principal stress difference in the three directions, the relationship between the principal stress and the principal strain under the unit test is obtained;

[0056] The relationship between the principal stress and the principal elongation ratio under uniaxial compression is:

[0057] ,

[0058] ,

[0059] ,

[0060] ,

[0061] In the formula, is the main elongation ratio, and are the vertical and transverse Cauchy principal stresses, and is the principal elongation in vertical and horizontal directions;

[0062] Since the compressive strain is negative, the principal extension ratio ,Will and Eliminate and get:

[0063] ,

[0064] The corresponding nominal stress for:

[0065] ,

[0066] Substituting the nominal stress into the strain energy function of the hyperelastic constitutive model, the characterization equation of the hyperelastic constitutive model is obtained, which is expressed as follows:

[0067] ,

[0068] In the formula, , and is the unknown coefficient of the equation, , , and is the material constant.

[0069] Step S103, unifying the physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model, and superimposing the unified target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model to obtain the final target constitutive model of the fastener elastic pad.

[0070] In this step, the expression of the target constitutive model is:

[0071] ,

[0072] ,

[0073] ,

[0074] In the formula, is the hyperelastic element stress, is the total stress after superposition of M plastic units, is the total stress after superposition of N viscoelastic units, is the stress of the jth plastic element, is the stress of the kth viscoelastic unit, is the total number of plastic elements, is the total number of viscoelastic units.

[0075] It should be noted that, due to the inconsistency of physical quantities in the process of model superposition, it is necessary to uniformly convert the load-displacement relationship in the model into a stress-strain relationship so that superposition can be performed. The stress of the pad can be expressed as:

[0076] ,

[0077] in, is the nominal compressive stress, is the load acting on the pad, It is the compression area of ​​the pad, which is equal to half of the sum of the upper and lower compression areas of the pad.

[0078] The strain of the pad can be expressed as:

[0079] ,

[0080] in, is the compressive strain, is the compression deformation of the pad, is the compression thickness of the pad.

[0081] In summary, the method of the present application takes into account the hyperelasticity, viscoelasticity and plasticity of rubber, and can more comprehensively reflect the various mechanical properties of the pad when simulating the pad, thereby effectively improving the accuracy of the numerical simulation of the pad. In addition, the hyperelasticity, viscoelasticity and plasticity models of the pad can be independently changed according to the different types of fastener elastic pads, thereby achieving the purpose of effectively characterizing the elastic pad according to different actual conditions, and can more comprehensively reflect the various mechanical properties of the pad when simulating the pad, thereby effectively improving the accuracy of the numerical simulation of the pad.

[0082] See also Figure 2 , which shows a structural block diagram of a rail fastener elastic pad constitutive model building system of the present application.

[0083] like Figure 2 As shown, the rail fastener elastic pad constitutive model construction system 200 includes a construction module 210 , a fitting module 220 and a superposition module 230 .

[0084] Among them, the construction module 210 is configured to construct a hyperelastic constitutive model of the fastener elastic pad considering the temperature variable, and determine the viscoelastic constitutive model and the plastic constitutive model of the fastener elastic pad; the fitting module 220 is configured to fit the first parameter of the hyperelastic constitutive model, the second parameter of the viscoelastic constitutive model and the third parameter of the plastic constitutive model, and obtain the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model respectively; the superposition module 230 is configured to unify the physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model, and superimpose the unified target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model to obtain the final target constitutive model of the fastener elastic pad.

[0085] It should be understood that Figure 2 Modules and references documented in Figure 1 Therefore, the operations and features described above for the method and the corresponding technical effects are also applicable to Figure 2 The modules in it will not be described in detail here.

[0086] In some other embodiments, the embodiments of the present invention further provide a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor is caused to execute the constitutive model construction method of the elastic pad of the rail fastener in any of the above method embodiments;

[0087] As an implementation mode, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are configured as follows:

[0088] Construct a hyperelastic constitutive model of the elastic pad of the fastener considering the temperature variable, and determine the viscoelastic constitutive model and plastic constitutive model of the elastic pad of the fastener;

[0089] Fitting a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively;

[0090] The physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model are unified, and the unified target hyperelastic constitutive model, target viscoelastic constitutive model and target plastic constitutive model are superimposed to obtain the final target constitutive model of the fastener elastic pad.

[0091] The computer-readable storage medium may include a program storage area and a data storage area, wherein the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the rail fastener elastic pad constitutive model construction system, etc. In addition, the computer-readable storage medium may include a high-speed random access memory, and may also include a memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the rail fastener elastic pad constitutive model construction system via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0092] Figure 3 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention, such as Figure 3 As shown, the device includes: a processor 310 and a memory 320. The electronic device may also include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330 and the output device 340 may be connected via a bus or other means. Figure 3 In the example, the connection through the bus is taken as an example. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running the non-volatile software programs, instructions and modules stored in the memory 320, that is, the method for constructing the constitutive model of the elastic pad of the rail fastener in the above-mentioned method embodiment is realized. The input device 330 can receive input digital or character information, and generate key signal input related to the user settings and function control of the constitutive model construction system of the elastic pad of the rail fastener. The output device 340 may include a display device such as a display screen.

[0093] The electronic device can execute the method provided by the embodiment of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the method provided by the embodiment of the present invention.

[0094] As an implementation mode, the electronic device is applied to a rail fastener elastic pad constitutive model construction system, and is used for a client, and includes: at least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can:

[0095] Construct a hyperelastic constitutive model of the elastic pad of the fastener considering the temperature variable, and determine the viscoelastic constitutive model and plastic constitutive model of the elastic pad of the fastener;

[0096] Fitting a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively;

[0097] The physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model are unified, and the unified target hyperelastic constitutive model, target viscoelastic constitutive model and target plastic constitutive model are superimposed to obtain the final target constitutive model of the fastener elastic pad.

[0098] Through the description of the above implementation modes, those skilled in the art can clearly understand that each implementation mode can be implemented by means of software plus a necessary general hardware platform, or of course by hardware. Based on such an understanding, the above technical solution can essentially or in other words be embodied in the form of a software product that contributes to the prior art. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiment.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a constitutive model of an elastic pad of a rail fastener, characterized in that: include: A hyperelastic constitutive model of the elastic pad of the fastener considering the temperature variable is constructed, and the viscoelastic constitutive model and the plastic constitutive model of the elastic pad of the fastener are determined, wherein the strain energy function expression of the hyperelastic constitutive model is: ， ， In the formula, is the strain energy, and is the material constant, and are the principal strain invariants, is the change in strain energy caused by temperature change, is the surface integral, the surface integral object is the pad temperature, and the upper limit of the integral is the highest temperature reached by the pad during the test The lower limit of the integral is the lowest temperature reached by the pad during the test , For The natural logarithm of base , The contour integral is the temperature of the pad, and the upper limit of the integral is the highest temperature reached by the pad during the test. The lower limit of the integral is the lowest temperature reached by the pad during the test , is the specific heat capacity constant of the rubber material, is the actual temperature of the pad, is the standard reference temperature, is the volume thermal expansion coefficient of rubber, is the second Lamé constant of the material; Fitting a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively; The physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model are unified, and the unified target hyperelastic constitutive model, target viscoelastic constitutive model and target plastic constitutive model are superimposed to obtain the final target constitutive model of the fastener elastic pad.

2. A method for constructing a constitutive model of a rail fastener elastic pad according to claim 1, characterized in that: The time domain constitutive equation of the viscoelastic constitutive model is: ， In the formula, , , , are the viscosity parameters of the viscoelastic constitutive model, is the stress varying with time, is the temperature coefficient, , , are the fractional derivative orders, , are the elastic parameters of the viscoelastic constitutive model, is the strain that varies with time; The time domain constitutive equation of the viscoelastic constitutive model is transformed by Fourier transform to obtain: ， In the formula, is the strain varying with frequency, is an imaginary unit, is the stress varying with frequency, is the frequency; The complex modulus of the viscoelastic constitutive model is obtained by rearranging the transformation, and the expression is: ， In the formula, is the complex modulus that varies with frequency; Will Substitute it into the complex modulus of the viscoelastic constitutive model, separate the real part and the imaginary part and calculate the energy storage model of the viscoelastic constitutive model. , Energy consumption model , and the loss factor , the expression is: ， ， ， In the formula, is the storage modulus that varies with frequency, is the energy loss modulus that varies with frequency.

3. The method for constructing a constitutive model of a rail fastener elastic pad according to claim 1, characterized in that: The expression of the plastic constitutive model is: ， In the formula, is the plastic friction force, is the friction force at the reference point each time the displacement direction changes, is the displacement of the pad, is the displacement of the reference point each time the displacement direction changes, is the maximum friction force, for The corresponding displacement, , and varies within the interval (-1,1).

4. The method for constructing a constitutive model of a rail fastener elastic pad according to claim 1, characterized in that: The fitting of the first parameter of the hyperelastic constitutive model, the second parameter of the viscoelastic constitutive model and the third parameter of the plastic constitutive model to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model and a target plastic constitutive model respectively includes: Performing a static uniaxial compression test on the elastic pad of the fastener to obtain a static force-displacement curve of nonlinear change of the elastic pad, and fitting a first parameter of the hyperelastic constitutive model according to the static force-displacement curve; The elastic pad of the fastener is subjected to extremely low frequency cyclic loading to obtain the dynamic load-dynamic displacement curve of the elastic pad under the action of extremely low frequency load. The third parameter of the plastic constitutive model is fitted according to the dynamic load-dynamic displacement curve after deducting the static nonlinear mechanical curve. A constant-frequency variable-temperature test was carried out on the elastic pad of the fastener, and the constant-frequency variable-temperature dynamic load-dynamic displacement curve of the elastic pad was obtained. After deducting the static nonlinear mechanics curve and the dynamic plastic mechanics curve, the second parameter of the viscoelastic constitutive model was fitted.

5. A method for constructing a constitutive model of a rail fastener elastic pad according to claim 4, characterized in that: The fitting of the first parameter of the hyperelastic constitutive model according to the static force-displacement curve comprises: For the case of uniform strain, the Cauchy principal stress of the elastic pad of the fastener is expressed as: ， In the formula, is the Cauchy principal stress of the pad, is the strain energy, and are the principal strain invariants, The main elongation, is the hydrostatic pressure; Calculate the principal stress difference in three directions, the expression is: ， Substituting the stress-strain relationship of the uniaxial compression test into the expression of the principal stress difference in the three directions, the relationship between the principal stress and the principal strain under the unit test is obtained; The relationship between the principal stress and the principal elongation ratio under uniaxial compression is: ， ， ， ， In the formula, is the main elongation ratio, and are the vertical and transverse Cauchy principal stresses, and is the principal elongation in vertical and horizontal directions; Since the compressive strain is negative, the principal extension ratio ,Will and Eliminate and get: ， The corresponding nominal stress for: ， Substituting the nominal stress into the strain energy function of the hyperelastic constitutive model, the characterization equation of the hyperelastic constitutive model is obtained, which is expressed as follows: ， In the formula, , and is the unknown coefficient of the equation, , , and is the material constant.

6. A method for constructing a constitutive model of a rail fastener elastic pad according to claim 1, characterized in that: The expression of the target constitutive model is: ， ， ， In the formula, is the hyperelastic element stress, is the total stress after superposition of M plastic units, is the total stress after superposition of N viscoelastic units, is the stress of the jth plastic element, is the stress of the kth viscoelastic unit, is the total number of plastic elements, is the total number of viscoelastic units.

7. A rail fastener elastic pad constitutive model construction system, characterized in that: include: The construction module is configured to construct a hyperelastic constitutive model of the elastic pad of the fastener considering the temperature variable, and determine the viscoelastic constitutive model and the plastic constitutive model of the elastic pad of the fastener, wherein the strain energy function expression of the hyperelastic constitutive model is: ， ， In the formula, is the strain energy, and is the material constant, and are the principal strain invariants, is the change in strain energy caused by temperature change, is the surface integral, the surface integral object is the pad temperature, and the upper limit of the integral is the highest temperature reached by the pad during the test The lower limit of the integral is the lowest temperature reached by the pad during the test , For The natural logarithm of base , The contour integral is the temperature of the pad, and the upper limit of the integral is the highest temperature reached by the pad during the test. The lower limit of the integral is the lowest temperature reached by the pad during the test , is the specific heat capacity constant of the rubber material, is the actual temperature of the pad, is the standard reference temperature, is the volume thermal expansion coefficient of rubber, is the second Lamé constant of the material; A fitting module, configured to fit a first parameter of the hyperelastic constitutive model, a second parameter of the viscoelastic constitutive model, and a third parameter of the plastic constitutive model, to obtain a target hyperelastic constitutive model, a target viscoelastic constitutive model, and a target plastic constitutive model, respectively; The superposition module is configured to unify the physical quantities of the target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model, and to superimpose the unified target hyperelastic constitutive model, the target viscoelastic constitutive model and the target plastic constitutive model to obtain the final target constitutive model of the fastener elastic pad.

8. An electronic device, characterized in that: include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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