CN115329644A - Accurate simulation method for large-deformation rubber material superelasticity composite behavior - Google Patents
Accurate simulation method for large-deformation rubber material superelasticity composite behavior Download PDFInfo
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Abstract
The invention provides an accurate simulation method for the superelastic composite behavior of a large-deformation rubber material, which belongs to the technical field of simulation and comprises the following steps: s1, carrying out uniaxial tension, biaxial tension and plane tension tests on materials with different strain levels to obtain original data; s2, constructing an auxiliary main curve family which takes strain history loading test data under different strain levels as characterization damage; s3, building a group of virtual super-elastic main curves, and respectively representing uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors; and S4, fitting the virtual super-elastic main curve and the auxiliary main line group to obtain super-elastic constitutive parameters and mullins effect parameters. The simulation material parameters obtained by the method can more accurately represent the super-elastic composite mechanical behavior of the elastic element, and the accuracy of the rigidity simulation of the elastic element product is improved.
Description
Technical Field
The invention relates to the technical field of simulation, in particular to a method for accurately simulating the superelastic composite behavior of a large-deformation rubber material.
Background
The rubber material is used as a main material of an elastic vibration reduction element due to good super-elastic performance, and is widely applied to the vibration reduction and noise reduction fields of rail transit, oil fields, aerospace and the like. In the early design stage of the elastic element, the stiffness performance of the product is usually evaluated by adopting a finite element simulation technology. The material parameters are used as important input of the rigidity simulation calculation, whether the mechanical behavior of the material can be completely represented or not is a key factor for determining whether the simulation result is accurately output or not. Therefore, how to obtain the simulation material parameters capable of completely representing the mechanical behavior of the material is important through reasonable material experimental design and innovative consideration of the superelastic composite mechanical behavior of the rubber material and fitting of the superelastic composite mechanical behavior.
Through the analysis of experimental data, the rubber material is found to have the following characteristics: the material has a large deformation and super-elastic behavior; the material has the maximum strain history effect behavior, namely different strain histories correspond to completely different experimental data; the material has a material softening behavior that manifests itself as a strain history. Therefore, to completely characterize the mechanical behavior of the material, a material constitutive function matched with the behavior needs to be built. For the buffer rubber shock absorber, a product bears the reciprocating circulation effect, so the invention particularly builds the following steps for establishing the rigidity simulation material parameters of the rubber material:
(1) Constructing a secondary main curve family which takes strain history unloading experimental data under different strain levels as the characteristic damage;
(2) Building a group of virtual super-elastic main curves, and respectively representing uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors;
(3) The material parameters characterizing the above behavior are fitted by simulation.
The existing elastic element is used for acquiring material parameters of rigidity simulation calculation, and is obtained by fitting the maximum and single tensile experiment stress-strain curve at present. The method has the following technical problems:
1. because the rubber material has obvious maximum strain history effect and different stress-strain curves under different strain history working conditions, it is difficult to replace all the strain history experimental curves with one curve. At present, the stress-strain curve of the maximum strain history is usually selected for fitting the material parameters (as shown in fig. 1, the stress-strain curve of only 200% strain level is selected for fitting), and during the loading process of the elastic element, the strain degree of each region inside the rubber material is inconsistent, so that the calculation result of the stiffness has an error from the actual result.
2. For the buffer rubber shock absorber, a product bears a reciprocating circulation effect, a rubber material has a stress softening phenomenon after cyclic loading, the superelasticity and Marins effect of the rubber material are not comprehensively considered in the current rigidity simulation, and the difference exists between the traditional rigidity simulation and the application condition of an actual product.
Patent 200810162668.0 provides a method and special equipment for testing the mechanical properties of tire rubber in a complex stress state, mainly including uniaxial tensile test, equibiaxial tensile test, and plane tensile (pure shear) test, and provides accurate material parameters for tire numerical analysis. The invention focuses on a test method and a device for a specific test.
Patent 201711005543.2 discloses an elastic constitutive model suitable for rubber materials and application thereof. The accurate model of the rubber incompressible superelasticity material can be obtained only by adopting a single type of test data, the precision and the reliability are higher than those of the existing model, and the accurate and comprehensive rubber material characteristic model can be obtained by only carrying out simple uniaxial tension test without adopting equal biaxial tension and plane tension tests which are difficult to carry out at home at present. The invention only considers the super-elastic stretching behavior of rubber materials and simplifies the acquisition of the super-elastic constitutive parameters.
Patent 201810777738.7 provides a new method for evaluating the Marins effect of a rubber material. The evaluation method provided by the invention can more accurately reflect the damage state of the Marins effect. The method only considers the acquisition method of the material damage, and does not comprehensively evaluate and fit the material damage and the superelastic constitutive behavior of the material.
Through careful analysis of the above patents, all of them involve obtaining the parameters of the rubber material simulation material. However, only the superelasticity behavior of the rubber material is considered, and the maximum strain history effect behavior shown in the rubber material experiment is not considered, namely different strain histories correspond to completely different experimental data, and the damage behavior (Marins effect) of the rubber material is not comprehensively considered. Therefore, the invention analyzes the superelastic composite behavior of the rubber material and builds the material parameters matched with the superelastic composite behavior of the rubber material.
Disclosure of Invention
The invention aims to provide an accurate simulation method for the superelastic composite behavior of a large-deformation rubber material, so that the obtained simulation material parameters can more accurately represent the superelastic composite mechanical behavior of an elastic element, and the accuracy of the rigidity simulation of the elastic element product is improved.
The technical scheme of the invention is realized as follows:
the invention provides a method for accurately simulating the superelastic composite behavior of a large-deformation rubber material, which is characterized by comprising the following steps of:
s1, carrying out uniaxial tension, biaxial tension and plane tension tests on materials with different strain levels to obtain original data;
s2, building an auxiliary main curve family which takes strain history loading test data under different strain levels as characteristic damage;
s3, building a group of virtual super-elastic main curves, and respectively representing uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors;
and S4, fitting the virtual super-elastic main curve and the auxiliary main line family by utilizing an Ogden-N model and a Mullins effect formula to obtain super-elastic constitutive parameters and Mullins effect parameters.
As a further improvement of the present invention, step S2 specifically includes:
(1) Extracting the last loading curve obtained by the uniaxial tensile test under different strain levels by using a software module, and carrying out zero setting treatment on the curve, namely the initial zero strain corresponds to the initial zero stress to form different strain history uniaxial tensile data families representing the superelasticity;
(2) Extracting the last loading curve under different strain histories obtained by a biaxial stretching test, and then carrying out zeroing treatment on the curve so as to form biaxial stretching data families with different strain histories for representing the superelasticity;
(3) And extracting the last loading curve under different strain histories obtained by the plane tensile test, and then carrying out zero setting treatment on the curve, thereby forming different strain history plane tensile data families representing the superelasticity behavior.
As a further improvement of the present invention, the software module is a calibration module in the ABAQUS software.
As a further improvement of the present invention, the last loading curve is a stabilized loading curve.
As a further improvement of the present invention, step S3 specifically includes:
(1) For the uniaxial tension main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a uniaxial tension-stress-strain data curve;
(2) For the main super-elastic behavior of biaxial stretching, extracting and adjusting maximum stress-strain data points under different strain levels to form a biaxial stretching stress-strain data curve;
(3) For the plane stretching main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a plane stretching stress-strain data curve;
(4) Together, a set of virtualized superelastic principal curves for the rubber material is constructed from the 3 sets of virtualized stress-strain data curves.
As a further improvement of the present invention, step S4 specifically includes:
(1) Fitting the virtual group of main superelastic curves by using an Ogden-N model to obtain a superelastic constitutive parameter mu i 、α i ；
(2) And (3) characterizing the strain history effect of the uniaxial stretching, biaxial stretching and plane stretching behaviors by using a Mullins effect formula to obtain material parameters r, m and beta for characterizing the damage, wherein the calculation formula is shown as the following formula (2).
As a further improvement of the invention, the Ogden-N model formula is as follows (1):
wherein W is the strain energy density; alpha i and mu i are super-elastic constitutive parameters representing the deformation behavior of the material; λ 1, λ 2 and λ 3 are the elongations of the material in three main directions.
As a further improvement of the invention, the Mullins effect formula is as follows (2):
wherein eta is the damage variable, W (I) 1 ) Strain energy density for superelastic deformation, W (I) 1,max ) Is W (I) 1 ) Maximum value in the deformation history; r beta and m are material parameters for representing damage; erf (x) is an error function.
As a further improvement of the invention, the method specifically comprises the following steps:
s1, carrying out material stretching experiments with different strain levels, including uniaxial stretching, biaxial stretching and plane stretching experiments, and obtaining original experiment data of different stretching strain levels in three basic deformation modes;
s2, constructing a secondary main curve family taking strain history loading test data under different strain levels as characterization damage:
(1) Extracting stable loading curves obtained by a uniaxial tensile test under different strain levels by using a calibration module in ABAQUS software, and carrying out zero setting treatment on the stable loading curves, namely the initial zero strain corresponds to the initial zero stress to form different strain history uniaxial tensile data groups representing the superelasticity;
(2) Extracting stable loading curves under different strain histories obtained by a biaxial tension test, and then carrying out zero setting treatment on the curves so as to form biaxial tension data families with different strain histories and representing the superelasticity;
(3) Extracting stable loading curves under different strain histories obtained by a plane tensile test, and carrying out zero setting treatment on the stable loading curves so as to form plane tensile data families with different strain histories for representing the superelasticity;
s3, a group of virtual super-elastic main curves is built, and uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors are represented respectively: virtualizing a superelastic stress-strain data curve for uniaxial tensile behavior, biaxial tensile behavior and planar tensile behavior:
(1) For the uniaxial tension main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a uniaxial tension-stress-strain data curve;
(2) For the main super-elastic behavior of biaxial stretching, extracting maximum stress-strain data points under different strain levels to form a biaxial stretching stress-strain data curve;
(3) For the plane stretching main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a plane stretching stress-strain data curve;
(4) A group of virtualized superelastic main curves of the rubber material are constructed by the 3 groups of virtualized stress-strain data curves;
s4, fitting the virtual super-elastic main curve and the auxiliary main line family by utilizing an Ogden-N model and a Mullins effect formula to obtain super-elastic constitutive parameters and Mullins effect parameters:
(1) Fitting the virtual group of main superelastic curves by using an Ogden-N model to obtain a superelastic constitutive parameter mu i 、α i The calculation formula is shown as formula (1):
wherein W is the strain energy density; alpha i and mu i are super-elastic constitutive parameters representing the deformation behavior of the material; λ 1, λ 2 and λ 3 are the elongations of the material in three main directions.
(2) Characterizing the strain history effect of uniaxial stretching, biaxial stretching and plane stretching behaviors by using a Mullins effect formula to obtain material parameters r, m and beta for characterizing damage, wherein the calculation formula is as shown in formula (2):
wherein eta is the damage variable, W (I) 1 ) Strain energy density for superelastic deformation, W (I) 1,max ) Is W (I) 1 ) Maximum value in the deformation history; r beta and m are material parameters for representing damage; erf (x) is an error function.
The invention has the following beneficial effects:
1. the invention relates to a material parameter acquisition method for simulating the rigidity of an elastic element product, which completely represents the maximum strain history effect behavior of a rubber material by a virtual main curve made of maximum stress strain points with different tensile strain levels and better accords with the characteristic that the strain levels of rubber areas are different when the elastic element product bears the load.
2. According to the material parameter acquisition method for the rigidity simulation of the elastic element product, disclosed by the invention, the damage behavior of a rubber material is represented by fitting a stable post-loading curve segment, and the reciprocating bearing characteristic of the elastic element is better met.
3. The invention relates to a method for acquiring material parameters for simulating the rigidity of an elastic element product, which is suitable for all super-elastic materials with mechanical behaviors (maximum strain history effect and Mullins effect) similar to those of rubber materials.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a stress-strain curve for different tensile strain levels;
FIG. 2 is a flow chart of an embodiment of the present invention;
FIG. 3 is a graph of uniaxial 5 strain levels in an example of the invention;
FIG. 4 is a graph of biaxial stretching 4 strain levels in an example of the invention;
FIG. 5 is a graph of the in-plane tensile 5 strain level in an example of the invention;
FIG. 6 is a graph showing the stress relief curves of 5 uniaxial tensions in accordance with an embodiment of the present invention;
FIG. 7 is a graph of strain history unload for 4 sets of biaxial stretching;
FIG. 8 is a graph of the stress-history unload curves for the 5 sets of planar tensile members;
FIG. 9 is a main curve of a virtualized superelastic device according to embodiments of the present invention;
FIG. 10 is a plot fitted with the mullins effect according to an embodiment of the present invention;
fig. 11 is a graph comparing a stiffness simulation result of a material parameter obtained in the embodiment of the present invention with an experimental result.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 2, the invention provides a design method of accurate simulation parameters of the superelastic composite behavior of a large-deformation rubber material, which comprises the following specific implementation steps:
s1, carrying out uniaxial tension, biaxial tension and plane tension tests on materials with different strain levels to obtain original data: and developing material stretching experiments with different strain levels, including uniaxial stretching, biaxial stretching and plane stretching experiments, and obtaining original experiment data of different stretching strain levels in three basic deformation modes. The specific experimental arrangement is as follows:
TABLE 1 basic mechanics experimental conditions for a certain formulation
The raw experimental data curves obtained are shown in FIGS. 3-5 below:
s2, establishing an auxiliary main curve family taking strain history loading test data under different strain levels as characteristic damage:
1) Extracting the last loading curve (stabilized loading curve) under different strain levels obtained by the uniaxial tensile test in the figure 3 by utilizing a calibration module in ABAQUS software, and carrying out zero setting treatment on the curve, namely the initial zero strain corresponds to the initial zero stress to form different strain history uniaxial tensile data groups (figure 6) representing the superelasticity;
2) Extracting the last loading curve under different strain histories obtained by the biaxial tension test in the figure 4, and then carrying out zero setting treatment on the curve, thereby forming biaxial tension data groups (figure 7) with different strain histories and representing the superelasticity;
3) And extracting the last loading curve under different strain histories obtained in the plane tensile test in the figure 5, and carrying out zero setting treatment on the curve, thereby forming different strain history plane tensile data families (figure 8) representing the superelasticity behavior.
S3, a group of virtual super-elastic main curves is built, and uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors are represented respectively: a superelastic stress-strain data curve is virtualized for uniaxial stretching behavior, biaxial stretching behavior and plane stretching behavior.
1) For the uniaxial tension main superelasticity behavior, extracting and adjusting the maximum stress-strain data points under 5 different strain levels to form a uniaxial tension-strain data curve;
2) For the biaxial stretching main superelasticity behavior, extracting and adjusting 4 maximum stress-strain data points under different strain levels to form a biaxial stretching stress-strain data curve;
3) For the plane stretching main superelasticity behavior, extracting and adjusting the maximum stress-strain data points under 5 different strain levels to form a plane stretching stress-strain data curve;
4) Together, a set of virtualized superelastic master curves for the rubber material was constructed from these 3 sets of virtualized stress-strain data curves (fig. 9).
S4, fitting the virtual super-elastic main curve and the auxiliary main line family by utilizing an Ogden-N model and a Mullins effect formula to obtain super-elastic constitutive parameters and Mullins effect parameters:
1) Fitting the virtual group of main superelastic curves by using an Ogden-N model to obtain a superelastic constitutive parameter mu i 、α i 。
Obtaining the superelastic constitutive parameter mu of a certain formula in the embodiment i 、α i The following were used:
TABLE 2Ogden-3 model fitting of certain formulation Material parameters
| μ i | α i |
| 1.221 | 2.407 |
| 0.043 | -2.407 |
| 6.46e-07 | 3.678 |
2) And characterizing the strain history effect of the uniaxial stretching, biaxial stretching and plane stretching behaviors by using a Mullins effect formula to obtain the parameters r, m and beta of the material for characterizing the damage.
The parameters r, m, β of the material characterizing the damage in this example were obtained as follows:
TABLE 3 Mullins parameters for certain formulations
The typical strain history of the test data as a carrier is shown in fig. 10, which characterizes the overall fit effect of uniaxial, biaxial and planar stretching modes.
And S5, simultaneously inputting the superelastic constitutive parameters and the Mullins effect parameters in the calculation software, and calculating the rigidity of a certain elastic element. FIG. 11 shows the calculation results of the stiffness of the elastic element using different material parameters, FEA-1 using the material parameters obtained by the original fitting method, and FEA-2 using the material parameters obtained by the scheme of the present invention. As can be seen from the figure, the calculation curve of the FEA-2 is more consistent with the experimental curve, the error is within 12 percent, and the curve is similar in form, so that the load-displacement corresponding relation of the product can be more accurately reflected.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (9)
1. A method for accurately simulating the superelastic composite behavior of a large-deformation rubber material is characterized by comprising the following steps of:
s1, carrying out uniaxial tension, biaxial tension and plane tension tests on materials with different strain levels to obtain original data;
s2, constructing an auxiliary main curve family which takes strain history loading test data under different strain levels as characterization damage;
s3, building a group of virtual super-elastic main curves, and respectively representing uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors;
and S4, fitting the virtual super-elastic main curve and the auxiliary main line family by utilizing an Ogden-N model and a Mullins effect formula to obtain super-elastic constitutive parameters and Mullins effect parameters.
2. The method for accurately simulating the superelastic compounding behavior of the large-deformation rubber material according to claim 1, wherein the step S2 specifically comprises the following steps:
(1) Extracting the last loading curve obtained by the uniaxial tensile test under different strain levels by using a software module, and carrying out zero setting treatment on the curve, namely the initial zero strain corresponds to the initial zero stress to form different strain history uniaxial tensile data families representing the superelasticity;
(2) Extracting the last loading curve under different strain histories obtained by the biaxial tension test, and then carrying out zero setting treatment on the curve so as to form biaxial tension data families with different strain histories and representing the superelasticity;
(3) And extracting the last loading curve under different strain histories obtained by the plane tensile test, and then carrying out zero setting treatment on the curve, thereby forming different strain history plane tensile data families representing the superelasticity behavior.
3. The method for accurately simulating the superelastic composite behavior of the large-deformation rubber material according to claim 2, wherein the software module is a calibration module in ABAQUS software.
4. The method for accurately simulating the superelastic composite behavior of the large-deformation rubber material according to claim 2, wherein the last loading curve is a stabilized loading curve.
5. The method for accurately simulating the superelastic compounding behavior of the large-deformation rubber material according to claim 1, wherein the step S3 specifically comprises the following steps:
(1) For the uniaxial tension main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a uniaxial tension-strain data curve;
(2) For the main super-elastic behavior of biaxial stretching, extracting and adjusting maximum stress-strain data points under different strain levels to form a biaxial stretching stress-strain data curve;
(3) For the plane stretching main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a plane stretching stress-strain data curve;
(4) Together, a set of virtualized superelastic principal curves for the rubber material is constructed from the 3 sets of virtualized stress-strain data curves.
6. The method for accurately simulating the superelastic composite behavior of the large-deformation rubber material according to claim 1, wherein the step S4 specifically comprises the following steps:
(1) Fitting the virtual group of main superelastic curves by using an Ogden-N model to obtain a superelastic constitutive parameter mu i 、α i ；
(2) And (3) characterizing the strain history effect of the uniaxial stretching, biaxial stretching and plane stretching behaviors by using a Mullins effect formula to obtain material parameters r, m and beta for characterizing the damage, wherein the calculation formula is shown as the following formula (2).
7. The method for accurately simulating the superelastic composite behavior of the large-deformation rubber material according to claim 6, wherein the Ogden-N model formula is as shown in formula (1):
wherein W is the strain energy density; alpha i and mu i are super-elastic constitutive parameters representing the deformation behavior of the material; λ 1, λ 2 and λ 3 are the elongations of the material in three main directions.
8. The method for accurately simulating the superelastic composite behavior of the large-deformation rubber material according to claim 6, wherein the Mullins effect formula is as shown in formula (2):
wherein eta is the damage variable, W (I) 1 ) Strain energy density for superelastic deformation, W (I) 1,max ) Is W (I) 1 ) Maximum in deformation history; r beta and m are material parameters characterizing the damage; erf (x) is an error function.
9. The method for accurately simulating the superelastic compounding behavior of the large-deformation rubber material according to claim 1, is characterized by comprising the following steps of:
s1, carrying out material stretching experiments with different strain levels, including uniaxial stretching, biaxial stretching and plane stretching experiments, and obtaining original experiment data of different stretching strain levels in three basic deformation modes;
s2, constructing a secondary main curve family taking strain history loading test data under different strain levels as characterization damage:
(1) Extracting stable loading curves obtained by uniaxial tensile test under different strain levels by using a calibration module in ABAQUS software, and carrying out zero setting treatment on the stable loading curves, wherein the initial zero strain corresponds to the initial zero stress to form different strain history uniaxial tensile data families representing the superelasticity;
(2) Extracting stable loading curves under different strain histories obtained by a biaxial tension test, and then carrying out zero setting treatment on the curves so as to form biaxial tension data families with different strain histories and representing the superelasticity;
(3) Extracting stable loading curves under different strain histories obtained by a plane tensile test, and then carrying out zero setting treatment on the stable loading curves so as to form different strain history plane tensile data families representing the superelasticity;
s3, a group of virtual super-elastic main curves is built, and uniaxial stretching, biaxial stretching and plane stretching super-elastic behaviors are represented respectively: virtualizing a superelastic stress-strain data curve for uniaxial tensile behavior, biaxial tensile behavior and planar tensile behavior:
(1) For the uniaxial tension main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a uniaxial tension-stress-strain data curve;
(2) For the main super-elastic behavior of biaxial stretching, extracting and adjusting maximum stress-strain data points under different strain levels to form a biaxial stretching stress-strain data curve;
(3) For the plane stretching main superelasticity behavior, extracting and adjusting maximum stress-strain data points under different strain levels to form a plane stretching stress-strain data curve;
(4) A group of virtualized superelastic main curves of the rubber material are jointly constructed by the 3 groups of virtualized stress-strain data curves;
s4, fitting the virtual super-elastic main curve and the auxiliary main line family by utilizing an Ogden-N model and a Mullins effect formula to obtain super-elastic constitutive parameters and Mullins effect parameters:
(1) Fitting the virtual group of main superelastic curves by using an Ogden-N model to obtain a superelastic constitutive parameter mu i 、α i The calculation formula is as shown in formula (1):
wherein W is the strain energy density; alpha i and mu i are super-elastic constitutive parameters representing the deformation behavior of the material; λ 1, λ 2 and λ 3 are the elongations of the material in three main directions.
(2) The strain history effect of uniaxial stretching, biaxial stretching and plane stretching behaviors is characterized by using a Mullins effect formula to obtain material parameters r, m and beta for representing damage, and the calculation formula is as shown in a formula (2):
wherein eta is the damage variable, W (I) 1 ) Strain energy density for superelastic deformation, W (I) 1,max ) Is W (I) 1 ) Maximum value in the deformation history; r beta and m are material parameters for representing damage; erf (x) is an error function.
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| CN116502480A (en) * | 2022-11-21 | 2023-07-28 | 北京化工大学 | Super-elasticity constitutive model construction and simulation method for stress steep rise characteristic under small strain |
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