Elastic moduli of soils dependent on pressure: a hyperelastic formulation

The elastic behaviour of granular materials is non-linear, in that the small-strain tangent stiffness depends on the stress level. The elastic moduli typically vary as power functions of the mean stress. Simple models of this nonlinearity can result in behaviour that violates the laws of thermodynamics. To guarantee that an elasticity model is thermodynamically acceptable it must be possible to derive the elastic behaviour from a free energy potential (or alternatively from a complementary energy potential). In this paper elasticity models are derived that allow for variation of elastic moduli as power functions of mean stress, while guaranteeing thermodynamic acceptability. The important issue of the dependence of secant stiffness on strain amplitude (a phenomenon related to dissipation processes in the soil) is acknowledged but not addressed here.