A State Dependent Thermo-Hyperelastic Model for Geomaterials

Abstract

A hyperelastic model for the state dependent and thermo-mechanical coupled nonlinear elastic behavior of geomaterials is developed in this paper. In the model the stress-density state dependent elastic moduli and the elastic instability are predicted by the high order terms of elastic strain invariants in the elastic potential function. The effects of true cohesion on the elastic potential of bonded geomaterials such as bonded sands, natural structured clays and rocks are also taken into account. As a result, unified relations between the density, the degradable cohesion, the confining stress and the elastic moduli can be derived for different geomaterials. Meanwhile, such an approach theoretically results in a state boundary and thus a strength criterion for geomaterials from the stability of elasticity. Based on such a hyperelastic approach, the nonlinear thermo-elastic coupled behavior is further considered by defining an equivalent elastic volumetric strain and taking into account a volumetric elastic thermal expansion coefficient dependent on both the volume fraction and thermal property of bound water absorbed on mineral surfaces.