Rheological model for stress-softened visco-hyperelastic materials

A rate-dependent thermodynamically consistent constitutive model for hyperelastic materials in finite strain regime is presented on the basis of multiplicative split of deformation gradient tensor into elastic and viscous parts. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the Zener rheological model. To incorporate the Mullins stress-softening phenomenon in viscoelastic material, an invariant-based stress-softening function is also proposed. An analytical scheme based on Clausius-Duhem inequality is proposed that ascertains thermodynamic consistency with the fundamental relation between the viscous strain rate and the overstress tensor with some limited elastic parent material models. The proposed softening model is validated with uniaxial stress relaxation test data and the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena.