A general non-local constitutive relation for residually stressed solids

Abstract

In this paper, we propose a novel phenomenological constitutive modeling framework which enables incorporating damage and residually stress capabilities for solids. In particular, a non-local gradient-enhanced damage model has been formulated using the Internal State Variables (ISV) approach in the finite strain setting with the preclusion of mesh sensitivity pathologies. Owing to its modular format, it is shown that constitutive relations can be expressed in a closed form. We formulate the constitutive relations for residual stressed models in various co-ordinate systems, pinpointing the versatility of the modeling approach at hand. Based on these main attributes, it is mentionable that the developed formulation is suitable for cord–rubber composite application like tires, airsprings, and soft tissues in biomechanics, among others, leading to multi-field a variational formalism and finite element implementation.