An incremental variational method to the coupling between gradient damage, thermoelasticity and heat conduction

In this work, we propose an incremental variational approach to study the coupling between gradient damage, thermoelasticity and heat conduction phenomena. To this end, we first extend the thermodynamics of linear thermoelasticity to incorporate gradient damage phenomena. After carefully introducing the concept of kinetic entropy to describe the interaction between thermoelasticity and heat conduction, this extension is implemented to establish a four-field incremental energy minimization procedure. By considering a suitable kinetic entropy approximation, the latter is then consistently reduced to a three-field (displacement, damage, and absolute temperature) dependency, numerically implemented by means of a staggered optimization algorithm. Applications consisting in a study of the cracking of a plate under thermal shocks are considered. The approach is shown to deliver reliable predictions, based on comparison to available experimental observations which is also provided.