A new approach to modeling the thermomechanical, orthotropic, elastic-inelastic response of soft materials

Abstract

This paper generalizes six previously developed nonlinear distortional deformation invariants for general hyperelastic orthotropic materials to model the thermomechanical, orthotropic, elastic-inelastic response of soft materials. These new invariants depend on two independent functions of elastic dilatation and temperature and characterize elastic distortional deformations from Hydrostatic States of Stress (HSS). When the Helmholtz free energy depends on these invariants, elastic dilatation and temperature, the correct response in HSS is automatically satisfied so the determination of the functional form of the Helmholtz free energy is simplified and can focus on modeling the response causing deviatoric stress. In addition, the new invariants are based on an Eulerian formulation of evolution equations for microscructural vectors that describe elastic deformation and directions of anisotropy. In contrast with the standard Lagrangian formulation, the Eulerian formulation is unaffected by arbitrary choices of the reference configuration, an intermediate configuration, a total deformation measure, and an inelastic deformation measure.