An iteration method to study nonlinear wave propagation for a non-Green elastic 1D bar

Abstract

The problem of propagation of nonlinear waves in a 1D bar is studied, wherein the linearized strain tensor is considered as a function of the Cauchy stress tensor. Specifically, two constitutive equations for non-Green elastic solids are investigated, introducing a novel numerical iterative method capable to obtain approximate solutions of one nonlinear constitutive equation for rock, and one constitutive equation that shows a strain limiting behaviour. The numerical results are compared with exact solutions for the case of a linearized elastic solid.