A simulation method for nonlinear loading and unloading hysteresis stiffness of rubber materials

Abstract

This invention relates to the field of performance analysis of rubber materials, specifically providing a simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials, comprising the following steps: S1: Conducting basic mechanical experiments on the rubber material to obtain the original experimental data; S2: Obtaining the loaded hyperelastic constitutive parameters, unloading hyperelastic constitutive parameters, and plastic constitutive parameters of the rubber material based on the original experimental data in step S1; S3: Selecting temperature-dependent data when creating the material's hyperelastic constitutive parameters, and setting different virtual temperatures for the loaded and unloading hyperelastic constitutive parameters; S4: In the load setting step, creating a temperature preset field and calling appropriate hyperelastic constitutive parameters; S5: Refining the calculation settings, executing the calculation, and obtaining the hysteresis curve. This scheme characterizes the loading and unloading characteristics of the material based on the acquisition of rubber material parameters, and simultaneously considers the loading and unloading curve segments, resulting in high accuracy of the analysis results.

Description

Technical Field

[0001] This invention relates to the field of performance analysis technology for rubber materials, and in particular to a simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials. Background Technology

[0002] Rubber, as the main material for elastic vibration damping components, possesses excellent hyperelastic properties and has been widely used in vibration damping and noise reduction components in fields such as rail transportation, oil fields, aerospace, and marine engineering. In the early design stage of elastic components, finite element simulation technology is typically used to evaluate and analyze the performance of the product to ensure its mechanical and overall performance. Material parameters, as crucial inputs to the simulation calculations, are key factors in determining the accuracy of the simulation results; therefore, accurately characterizing the material's mechanical behavior through appropriate material parameters and simulation methods is essential. The following patents in the prior art relate to the mechanical analysis of rubber material products:

[0003] 1. The invention patent with patent number "202010165052.X" and patent title "A Method for Identifying Parameters of Restoring Force Model for Lead-Core Rubber Bearings Based on Genetic Algorithm" includes the following steps: inputting the third-cycle hysteresis curve of the lead-core rubber bearing obtained from the experiment; taking two points each from the loading and unloading segments of the third-cycle hysteresis curve to obtain the value range of the bearing's restoring force model parameters; inputting the terminal performance index function of the genetic algorithm, and combining it with the obtained parameter value range, performing parameter identification through the genetic algorithm; obtaining the identification results of reloading stiffness, unloading stiffness, and yield force, and constructing its restoring force model; comparing the hysteresis loop obtained by the restoring force model with the measured first-cycle hysteresis curve of the lead-core rubber bearing to obtain the slippage during the experiment. This patent simplifies the method for identifying parameters of the restoring force model of lead-core rubber bearings and can calculate the slippage of the lead-core rubber bearing during the experiment.

[0004] 2. The invention patent with patent number "200810162668.0" and patent title "Method and Special Equipment for Testing Mechanical Properties of Tire Rubber under Complex Stress State" includes material tests such as uniaxial tensile tests, biaxial tensile tests, and planar tensile tests. The test data are recorded as CCD images, tensile force, and time curves. A digital image processing program is used to obtain the strain-time relationship curve. The stress-strain curve data is obtained through the time correspondence, and then a regression analysis program is used to obtain the smoothed stress-strain curve. This method can perform stress-deformation tests on rubber specimens under uniaxial, biaxial, and pure shear conditions to evaluate the mechanical properties of tire rubber under complex stress states.

[0005] However, the aforementioned existing technology has the following problems:

[0006] 1. Rubber is a nonlinear elastic material. During large deformation, part of the energy absorbed is converted into mechanical energy and the other part into thermal energy, which causes the loading curve and unloading curve to be inconsistent, thus exhibiting hysteresis characteristics. At present, the stiffness simulation of products is usually obtained by fitting the loading curve segment of the basic mechanical performance test, without considering the unloading curve segment.

[0007] 2. Although the aforementioned patents relate to the hysteresis properties of rubber, they achieve hysteresis performance fitting through specific experiments on elastic element products. They are applied to specific products rather than characterizing material properties based on parameters obtained from the rubber material itself, which limits the accuracy of the performance analysis results. Furthermore, different product applications require different hysteresis stiffness. Appropriate hysteresis stiffness should be designed according to the product's application and performance requirements to achieve a balance between vibration reduction, noise reduction, and fatigue performance. The aforementioned technologies do not perform relevant performance analysis on the rubber material before product manufacturing, based on the product's intended use.

[0008] In summary, designing a simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials based on the acquisition of rubber material parameters to characterize the loading and unloading characteristics of the material, and fitting the loading and unloading curve segments of the basic mechanical performance test respectively, is an urgent problem to be solved. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials. By fitting hyperelastic parameters to the loading and unloading curve segments of basic mechanical property tests and then setting a virtual temperature field, the static hysteresis stiffness curve of the elastic element can be characterized, allowing for the study of the hysteresis stiffness performance of rubber materials.

[0010] To achieve the above objectives, the present invention proposes the following technical solution: a simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials, comprising the following steps:

[0011] S1: Conduct basic mechanical experiments on rubber materials to obtain raw experimental data of the rubber materials;

[0012] S2: Obtain the loaded hyperelastic constitutive parameters, unloaded hyperelastic constitutive parameters, and plastic constitutive parameters of the rubber material based on the original experimental data in step S1;

[0013] S3: When creating hyperelastic constitutive parameters for materials, select temperature-dependent data and set different virtual temperatures for loading and unloading hyperelastic constitutive parameters;

[0014] S4: In the load setting step, create a temperature preset field and call the appropriate hyperelastic constitutive parameters;

[0015] S5: Improve calculation settings, execute calculations, and obtain hysteresis curves.

[0016] Preferably, the raw experimental data in step S1 includes: conducting uniaxial tensile tests, biaxial tensile tests, and planar tensile tests on the material, and obtaining raw experimental data for different tensile strain levels under uniaxial tensile, biaxial tensile, and planar tensile deformation modes. The loaded hyperelastic constitutive parameters and unloaded hyperelastic constitutive parameters in step S2 are obtained according to the following method:

[0017] Preferably, based on the original experimental data from uniaxial tensile tests, biaxial tensile tests, and planar tensile tests of the material, the Mooney-Rivlin model is used to fit the original data curves, fitting the hyperelastic constitutive models for the loading and unloading curve segments respectively, thereby obtaining the loading and unloading hyperelastic constitutive parameters. The fitting formulas are as follows:

[0018] W MR =C 10 (I1-3)+C 01 (I2-3)

[0019] Among them, W MR For strain energy density, C 10 C 01 The material parameters are used to characterize the elastic behavior, and I1 and I2 are strain invariants.

[0020] Preferably, in step S3, when creating the material hyperelastic constitutive parameters, the loading hyperelastic constitutive parameters and the unloading hyperelastic constitutive parameters are input into the calculation software, and temperature-dependent data is selected; wherein different virtual temperature settings are made for the loading hyperelastic constitutive parameters and the unloading hyperelastic constitutive parameters, specifically, a normal temperature is set in the loading stage and a high temperature is set in the unloading stage.

[0021] Preferably, step S4 includes the following sub-steps:

[0022] S41: Define the loading and unloading steps of the elastic element product, and determine the loading load displacement and unloading load displacement;

[0023] S42: Create a preset field, input the virtual temperature set in the loading hyperelastic constitutive parameters and unloading hyperelastic constitutive parameters according to the defined loading and unloading steps, and call the appropriate hyperelastic constitutive parameters in the loading and unloading phases.

[0024] Preferably, the original experimental data in step S1 also includes: performing a uniaxial tensile test on the material and obtaining the relationship curve between the total strain and the plastic strain of the material.

[0025] Preferably, the plastic constitutive parameters of the rubber material are obtained based on uniaxial tensile test data under different strains.

[0026] Preferably, the data of plastic strain and stress of the rubber material are obtained based on the plastic constitutive parameters of the rubber material and then input into the computer software.

[0027] Preferably, the calculation settings are improved, the calculation is performed, and the hysteresis curve is obtained.

[0028] Preferably, the ambient temperature during the loading stage is set to 23°C, and the high temperature during the unloading stage is set to 50°C.

[0029] The beneficial effects of this invention are: by characterizing the hyperelastic constitutive parameters of the rubber material in stages for loading and unloading curve segments, and superimposing the permanent deformation effect of the rubber material, and by setting a virtual temperature field in the calculation software to realize the staged calling of the hyperelastic constitutive parameters, the invention can accurately simulate the hysteresis curve of elastic element products based on rubber materials, obtain the loading and unloading hysteresis stiffness, accurately characterize the mechanical behavior of rubber materials, and achieve high accuracy of simulation results. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the stress-strain curves of rubber material under different tensile strain levels.

[0031] Figure 2 This is an implementation flowchart provided in the embodiments of the present invention.

[0032] Figure 3 This is a table of experimental conditions for uniaxial tensile tests, biaxial tensile tests, and planar tensile tests provided in the embodiments of the present invention.

[0033] Figure 4 These are experimental data curves for uniaxial tension, biaxial tension, and planar tension provided in the embodiments of the present invention.

[0034] Figure 5 This is a table of uniaxial tensile test conditions for a certain formulation provided in an embodiment of the present invention.

[0035] Figure 6 This is a graph showing the relationship between total strain and plastic strain of a material under different strain levels in a uniaxial tensile test provided by an embodiment of the present invention.

[0036] Figure 7 This is a data table of loading hyperelastic constitutive parameters and unloading hyperelastic constitutive parameters C10 and C01 provided in the embodiments of the present invention.

[0037] Figure 8 This is a table showing the relationship between plastic strain and stress in rubber materials provided in the embodiments of the present invention.

[0038] Figure 9This is a table of hyperelastic constitutive parameters provided in an embodiment of the present invention.

[0039] Figure 10 This is the temperature preset field setting parameter table in the calculation software provided in this embodiment of the invention.

[0040] Figure 11 This is a hysteresis curve obtained through simulation, provided in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with the appendix. Figure 1-11 The present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and do not constitute a limitation thereof.

[0042] A simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials includes the following steps:

[0043] S1: Conduct basic mechanical experiments on rubber materials to obtain raw experimental data.

[0044] The aforementioned raw experimental data includes: uniaxial tensile tests, biaxial tensile tests, and planar tensile tests on the material, and the raw experimental data of different tensile strain levels under the deformation modes of uniaxial tensile, biaxial tensile, and planar tensile; the experimental conditions of the uniaxial tensile test, biaxial tensile test, and planar tensile test are described here.

[0045] like Figure 3 As shown, the strain rate is 1% / sec; the test temperature is 20℃-30℃, preferably 23℃; the experimental strain levels for uniaxial and planar tension are 25%-200%, and the experimental strain levels for biaxial tension are 10%-100%. Figure 4 As shown, Figure 4 Figures a, b, and c in the figure represent the experimental data curves for uniaxial tension, biaxial tension, and planar tension, respectively.

[0046] The aforementioned original experimental data also includes: uniaxial tensile tests on the material, and obtaining the relationship curve between the total strain and plastic strain of the material.

[0047] like Figure 1 As shown, L1 is the loading curve segment and L2 is the unloading curve segment. Existing simulation methods mostly only consider the loading curve segment and do not consider the unloading curve segment. This scheme considers both the loading curve segment and the unloading curve segment.

[0048] like Figure 5As shown, the strain rate is 1% / sec; the test temperature is 20℃-30℃, preferably 23℃; and the test strain level is 50%-450%. The relationship between total strain and plastic strain in the uniaxial tensile test at different strain levels is shown in the graph below. Figure 6 As shown.

[0049] S2: Obtain the loaded hyperelastic constitutive parameters, unloaded hyperelastic constitutive parameters, and plastic constitutive parameters of the rubber material based on the original experimental data in step S1.

[0050] The loaded and unloaded hyperelastic constitutive parameters are obtained using the following method:

[0051] Based on the original experimental data from uniaxial tensile tests, biaxial tensile tests, and planar tensile tests of the material, the Mooney-Rivlin model was used to fit the original data curves. The hyperelastic constitutive models for the loading and unloading curve segments were fitted respectively, thereby obtaining the loading and unloading hyperelastic constitutive parameters. The fitting formulas are as follows:

[0052] W MR =C 10 (I1-3)+C 01 (I2-3)

[0053] Among them, W MR For strain energy density, C 10 C 01 The parameters are material parameters that characterize elastic behavior, and I1 and I2 are strain invariants.

[0054] The loading hyperelastic constitutive parameters and unloading hyperelastic constitutive parameters C10 and C01 of the rubber material in this embodiment are obtained by fitting the hyperelastic constitutive models of the loading curve segment and the unloading curve segment, respectively. Figure 7 As shown.

[0055] Simultaneously, based on uniaxial tensile test data under different strains, the plastic constitutive parameters of the rubber material were obtained, and finally, the relationship between the plastic strain and stress of the rubber material was derived. The table showing the relationship between the plastic strain and stress of the rubber material is as follows: Figure 8 As shown.

[0056] S3: When creating hyperelastic constitutive parameters for materials, select temperature-dependent data and set different virtual temperatures for loading and unloading hyperelastic constitutive parameters.

[0057] The Mooney-Rivlin parameters for the hyperelastic constitutive model of the rubber material are created by inputting the loaded and unloaded hyperelastic constitutive parameters into the calculation software, selecting temperature-dependent data when creating the material's hyperelastic constitutive parameters. Different virtual temperatures are set for the loaded and unloaded hyperelastic constitutive parameters: a room temperature is set during the loading phase, and a high temperature is set during the unloading phase. In this embodiment, the room temperature set during the loading phase is 23°C, and the high temperature set during the unloading phase is 50°C. The hyperelastic constitutive parameters are as follows: Figure 9 As shown, Figure 9 D1 in the figure is a material parameter characterizing volumetric behavior. In actual experiments, rubber is usually considered to be incompressible, and the value of D1 is set to 0.0001.

[0058] Data on plastic strain and stress of rubber materials are obtained based on the plastic constitutive parameters of the rubber materials and then input into computer software.

[0059] S4: In the load setting step, create a temperature preset field and call up the appropriate hyperelastic constitutive parameters.

[0060] S41: Define the loading and unloading steps of the elastic element product, and determine the loading load displacement and unloading load displacement;

[0061] S42: Create a preset field, input the virtual temperature set in the loading hyperelastic constitutive parameters and unloading hyperelastic constitutive parameters according to the defined loading and unloading steps, and call the appropriate hyperelastic constitutive parameters in the loading and unloading phases.

[0062] Temperature preset field setting parameters in the calculation software, such as Figure 10 As shown:

[0063] In the software, the analysis steps are set up, and the calculation is performed in two steps: Step 1 is the loading step, where the deformation is set to 0-10mm and the temperature to 23℃. The temperature of 23℃ set here is a virtual temperature entered when setting the loading hyperelastic constitutive parameters, which is used to retrieve the loading hyperelastic constitutive parameters in the loading step; Step 2 is the unloading step, where the deformation is set to 10-0mm and the temperature to 50℃. The temperature of 50℃ set here is a virtual temperature entered when setting the unloading hyperelastic constitutive parameters, which is used to retrieve the unloading hyperelastic constitutive parameters in the unloading step.

[0064] S5: Refine calculation settings, execute calculations, and obtain results. Figure 11 The hysteresis curve shown is shown in the figure.

[0065] Complete the calculation settings, execute the calculation, and obtain the hysteresis curve; the calculation settings include model structure, mesh generation, mesh type, contact settings, work submission, etc.

[0066] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0067] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials, characterized in that, Includes the following steps: S1: Conduct basic mechanical experiments on rubber materials to obtain raw experimental data of the rubber materials; S2: Obtain the loaded hyperelastic constitutive parameters, unloaded hyperelastic constitutive parameters, and plastic constitutive parameters of the rubber material based on the original experimental data in step S1; S3: When creating hyperelastic constitutive parameters for materials, select temperature-dependent data and set different virtual temperatures for loading and unloading hyperelastic constitutive parameters; S4: In the load setting step, create a temperature preset field and call the appropriate hyperelastic constitutive parameters; S5: Improve calculation settings, execute calculations, and obtain hysteresis curves; The raw experimental data in step S1 includes: conducting uniaxial tensile tests, biaxial tensile tests and planar tensile tests on the material, and obtaining raw experimental data of different tensile strain levels under uniaxial tensile, biaxial tensile and planar tensile deformation modes; The loading and unloading hyperelastic constitutive parameters in step S2 are obtained as follows: Based on the original experimental data from uniaxial tensile tests, biaxial tensile tests, and planar tensile tests of the material, the Mooney-Rivlin model was used to fit the original data curves. The hyperelastic constitutive models for the loading and unloading curve segments were fitted respectively, thereby obtaining the loading and unloading hyperelastic constitutive parameters. The fitting formulas are as follows: ； in, For strain energy density, , Material parameters characterizing elastic behavior, , For strain invariants; In step S3, when creating the hyperelastic constitutive parameters of the material, the loading and unloading hyperelastic constitutive parameters are input into the calculation software, and temperature-dependent data is selected. Different virtual temperatures are set for the loading and unloading hyperelastic constitutive parameters, specifically, a normal temperature is set during the loading stage and a high temperature is set during the unloading stage.

2. The simulation method for nonlinear loading and unloading hysteresis stiffness of rubber materials according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41: Define the loading and unloading steps of the elastic element product, and determine the loading load displacement and unloading load displacement; S42: Create a preset field, input the virtual temperature set in the loading hyperelastic constitutive parameters and unloading hyperelastic constitutive parameters according to the defined loading and unloading steps, and call the appropriate hyperelastic constitutive parameters in the loading and unloading phases.

3. The simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials according to any one of claims 1-2, characterized in that, The original experimental data in step S1 also include: conducting a uniaxial tensile test on the material and obtaining the relationship curve between the total strain and the plastic strain of the material.

4. The simulation method for nonlinear loading and unloading hysteresis stiffness of rubber materials according to claim 3, characterized in that, Based on uniaxial tensile test data under different strains, the plastic constitutive parameters of the rubber material were obtained.

5. The simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials according to claim 4, characterized in that, Data on plastic strain and stress of rubber materials are obtained based on the plastic constitutive parameters of the rubber materials and then input into computer software.

6. The simulation method for the nonlinear loading and unloading hysteresis stiffness of rubber materials according to claim 5, characterized in that, Optimize the calculation settings, execute the calculation, and obtain the hysteresis curve.

7. The simulation method for nonlinear loading and unloading hysteresis stiffness of rubber materials according to claim 6, characterized in that, The ambient temperature is set at 23℃ during the loading phase, and the high temperature is set at 50℃ during the unloading phase.

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