Stability study of the compressible Mooney-Rivlin hyperelastic model

Abstract

The unstable behavior of the isotropic, compressible Mooney-Rivlin hyperelastic model is investigated and described. The constitutive equation is parameterized with the help of the ground-state Poisson’s ratio and the dimensionless ratio of the material parameters $C_{01}$ and $C_{10}$ . Transverse stretch solutions are obtained for standard homogeneous loading modes, and the stress solutions are computed numerically for the physically permitted range of the ground-state Poisson’s ratio. We introduce a numerical technique to isolate subdomains with non-unique transverse stretch responses. Our analysis revealed some limitations of the model and allowed us to make critical observations about the strengths and weaknesses of the model. The analyses we present are essential to understand the characteristics of this widely used hyperelastic model. The novel results have important implications for the application of the isotropic, compressible Mooney-Rivlin hyperelastic material model.

Keywords

Hyperelasticity compressibility Mooney-Rivlin constitutive model material stability

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