Non-linear anisotropic hyperelasticity for granular materials

Abstract

We describe a non-linear anisotropic hyperelastic model appropriate for geomaterials, deriving the full stress-strain response from strain energy or complementary energy functions. Specific forms of the functions are chosen so that the stiffness and compliance matrices have the appropriate minor symmetries. The model employs two material parameters to describe basic volumetric and shear response, one to express nonlinearity of stiffness as a function of mean stress, and two more (together with the directions of the principal axes of anisotropy) to express the degree of anisotropy. The model is modular, so that non-linearity and anisotropy can be included separately or in combination. For specific parameter settings it reduces to simpler cases such as linear isotropic elasticity. Because the model employs hyperelasticity, thermodynamic acceptability is ensured and all appropriate cross-coupling terms are included between the shear and volumetric behaviour.