Viscoelastoplastic Damage with Maximum Rate of Dissipation-Based Growth Criterion and Tri-Component Lie Rate Decomposition

Abstract

Maximization of the rate of dissipation is applied to develop a viscoelastoplastic damaging material model with anisotropic properties and finite deformation. The thermodynamic framework suggests a new damage activation criterion based on the sum of stress and an energy release rate based on a damage-based strain measure. The framework combines the usually disjointed ideas of effective stress and damage strain kinematics to track the dimensional changes attributed to damage while retaining the physical link to load-bearing area reduction. Potential applications include large volume change oxidation of SiC CMC composites, high temperature creep and relaxation influences on damage processes in reinforced polymers and ceramics, and opening/closing of cracks via natural elastic behavior as opposed to treatments based on loading criteria.

Maximum rate of dissipation analysis is applied to develop a framework corresponding to a material model incorporating three strain elements characterized by viscoelastic, damage, and viscoplastic behaviors. A push-pull framework associates these behaviors with respective multiplicative deformation gradients with rates determined by Lie material derivatives.