A bimodular nonlinear constitutive equation for rock

Abstract

Experimental data for the strains and stresses is obtained for some classes of rock, for the compression and tension of a cylindrical sample without lateral loads, and for the triaxial load of a bar. A nonlinear constitutive equation is proposed to fit the data, wherein the infinitesimal strain tensor is assumed to be a nonlinear function of the stress tensor. The constitutive equation requires two sets of materials constants, namely the Young’s modulus and Poisson ratio in tension and compression. Some boundary value problems are studied to see the predictions of the above constitutive theory.

Keywords

• Nonlinear elasticity
• Wave propagation
• Small strains
• Elastic bodies
• Isotropic bodies