Influence of residual stress in failure of soft materials

Abstract

Engineering and biological materials are very commonly subject to residual stresses or initial stresses. The source of residual stress can be processes like growth, remodeling, etc., in biological materials, and various manufacturing processes in engineering materials. Initial/residual stress would unequivocally influence the failure of soft materials. However, this influence of residual stress was never investigated earlier. Here we develop the first failure model for the residually stressed rubber-like materials using softening hyperelasticity. This model developed in a residually stressed configuration is consistent with Volokh’s model in a virtual stress-free configuration. Since the stress-free configuration is usually unknown, the present framework based on a stressed reference is useful for problem solving. We use a semi-inverse method to obtain the constitutive relation of the stressed reference configuration. The required parameters like the strain energy density and Lagrange multiplier of the same configuration are also evaluated in an intricate manner. Finally, we apply the developed model to demonstrate the influence of residual stress in arterial failure under inflation and failure of a block under simple shear. The strain energy density in the stressed reference is used to represent a measure of residual stress in the artery.