Constitutive Modeling Framework for Residually Stressed Viscoelastic Solids at Finite Strains

This article presents a novel three-dimensional constitutive modeling framework for residually stressed viscoelastic solids undergoing finite strains. Within the current of phenomenological approach, the constitutive relations are derived for a viscoelastic matrix whereas residual stresses are considered in the constitutive law in terms of a set of invariants. In particular, we analyze the bifurcation of a residually stressed viscoelastic solids using the finite element method (FEM). In-plane residual stresses are introduced in the constitutive relation that satisfy the balance of momentum. The implementation is discussed with regard to commercial finite element code Abaqus. Furthermore, the robustness of the proposed user material is illustrated emphasizing the dependence of bifurcation and viscoelastic parameters of tubes under torsion upon the residual stresses. The proposed formulation is also suitable for cord-rubber composite application like tires, airsprings, and soft tissues in biomechanics, among others, being such applications particular extensions to anisotropic materials