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Stability of rubber model

Abstract: the rubber components shown in the animation are analyzed using different rubber material models. This analysis is not convergent when using a rubber material model with a negative stability index. The stability characteristics of rubber materials can be displayed through the new stability view function in adina8.5 (8.5.2 or higher)

key words: rubber material, ADINA, stability, Mooney Rivlin, Sussman Bath

rubber material model

figures 1 and 2 show the experimental data of uniaxial and biaxial tension of a certain rubber material. These drawings show the engineering stress-strain relationship curve, which is commonly used to describe rubber materials. The figure also shows two rubber materials that fit well: Mooney Rivlin material of 9 items and Sussman bathe material. The fitting results of these two materials are in good agreement with the experimental data

Figure 3 shows the data obtained from uniaxial tension/compression, expressed in real stress logarithmic strain. Note that this curve includes the tension zone and the compression zone

Figure 1 Engineering stress-strain, uniaxial tension

Figure 2 Engineering stress-strain, biaxial tension

Figure 3 real stress logarithmic strain. This curve is obtained based on the uniaxial and biaxial tensile curves shown in Figures 1 and 2

analysis of rubber components

the two material models above are used in the analysis of rubber components. The rubber component is subject to the same displacement load in four directions, as shown in Figure 4

Figure 4 initial and final states of rubber components

Figure 5 shows the force and deformation curves obtained from different material models. Using the 9-term Mooney Rivlin material model, the convergent solution cannot be obtained when the displacement is greater than 1.4. However, using the Sussman bathe material model, the convergent solution can still be obtained under the condition of large displacement load

Figure 5 current curve of force and deformation

stability view

this new stability view function provides a window to view the convergence of rubber components. Figures 6 and 7 show the stability views of the two material models

Figure 6 stability curve obtained from material data - Sussman bath material model (material1 indicates that only one material is defined)

Figure 7 stability curve obtained from material data - Mooney Rivlin material model

here are some ideas of stability view. Consider a uniform rubber sheet under uniaxial tension. For each strain level, the increased stiffness matrix (corresponding to the changing force generated by the changing displacement load) is determined. Calculate the eigenvalue of the increased stiffness matrix, and take the smallest eigenvalue as the stability index. If the stability index is greater than zero, the material is stable (for the application of varying forces), otherwise the material is unstable. Perform the same procedure for pure shear and biaxial tension

the stability view shows that the Sussman bathe material model is stable for the deformation of three modes, but the Mooney Rivlin material model with 9 terms is unstable when the real strain under biaxial tension is greater than 0.4. Since the rubber material is biaxial tension, it is not surprising that the 9-item Mooney Rivlin material does not converge under very small load/deformation

discussion

we hope that the material model has a very good feature. 10. The host size: 8406001850. If the stress-strain data obtained from the experiment conforms to a very stable material, the material model should also be stable. Obviously, in this example, the nine item Mooney Rivlin material model does not have this feature

of course, in Mooney Rivlin material model, in order to make the stability index positive, different material constants can be defined, but in this way, the material model can not fit the experimental data well

references

t. Sussman & K.J. bathe, a model of compressible isometric hyperelastic material behavior usin to eliminate pressure fluctuations during plastic extrusion, G spline interpolation of tension compression test data ", common. num. meth. Engng (2008), in press

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