One-parameter family of equations of state for isotropic compressible solids

Abstract

Applying the theorem proved by the authors in [10], we established the hyperbolicity of non-stationary equations of hyperelastic isotropic solids for a one-parameter family of equations of state containing, in particular, generalized neo-hookean solids. The hyperbolicity is equivalent to the rank-one convexity of the corresponding stored energy. The influence of the parameter on the solution properties is shown in the case of a strong shear test