A nonlinear model for describing the mechanical behaviour of rock

In this paper, a nonlinear constitutive relation is proposed to model the behaviour of sandstone. The model is based on a relatively new class of constitutive relations proposed recently in the literature, which cannot be classified as Cauchy or Green elastic bodies. A specific expression for the constitutive relation is proposed on the basis of some experimental data for the compression of a sample of rock, and several boundary value problems are analysed, considering homogeneous distributions of strains, as well as a problem wherein one has a non-homogeneous distribution of strains. Finally, the behaviour of the P- and S-waves is studied for a sample of rock under compression, and it is discovered that the wave speed depends on the compressive load, a result supported by experiments.