Bi-modulus materials consistent with a stored energy function: Theory and numerical implementation

Abstract

Many materials present different behavior in tension and compression. Within the infinitesimal isotropic theory, the widely used approach based on the Ambartsumyan theory presents only three independent constants to preserve symmetry of the elasticity tensor. The reported finite element implementation of this and similar theories are complex and often lack the convergence properties expected for a bi-linear material. In this work we address the problem through a hyperelastic approach, obtaining a simple and consistent framework which retains the four independent constants and yields the expected convergence characteristics of a bi-linear material. The Ambartsumyan model is obtained as a particular case within this framework.