Damage-induced stress-softening and viscoelasticity of limited elastic materials

The rate-dependent behavior of filled natural rubber (NR) is investigated in tensile regime. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity is proposed on the basis of the multiplicative decomposition of the 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 rheological models of Poynting–Thomson and Zener types. To incorporate the Mullins stress-softening phenomenon into a viscoelastic material, an invariant-based stress-softening function is also proposed. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme is proposed that ascertains the fundamental relation between the viscous strain rate and the overstress tensor with limited elastic parent material model. Evaluation of the experimental results using 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. Based on this, an evolution equation is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated into the finite-strain viscoelasticity model in a thermodynamically consistent way.