A computational model for simulating thermo-elasto-plastic failures using non-localizing and localizing gradient damage

The conventional strategy for simulating thermo-mechanical failures using localizing gradient damage is based on an elastic material-model. It does not incorporate the physics of plastically-driven failures under combined thermal and mechanical loads. Moreover, the conventional formulation neglects the effect of damage on heat-capacity and avoids certain essential physics-based couplings among the deformations, damage and temperature. Therefore, in this work, a novel computational framework based on non-localizing and localizing gradient damage is developed for simulating thermo-elasto-plastic failure of materials, under the influences of both mechanical and thermal loads. The present strategy is derived from the law of thermodynamic power-balance and the free-energy density function. Unlike previous works, the present framework considers the effect of damage-based degradation on both thermal conductivity and heat-capacity. A new set of constitutive relations for thermo-elasto-plastic damage are developed in incremental form to incorporate the stress fields, local and non-local equivalent plastic strains, damage and temperature. Using these constitutive equations, new formulations of coupled-stiffness matrices and heat-capacity matrices are derived in the context of gradient damage. The cross-influences of damage, temperature and deformation on each other are incorporated through these matrices. The capability of the present framework is demonstrated by solving several examples on thermo-elasto-plastic ductile failures using finite element approach.