Application of the Müller–Liu entropy principle to gradient-damage models in the thermo-elastic case

Abstract

A general damage-gradient model is developed within the framework of continuum mechanics, using balance relations. As a new item, a balance relation for totally damaged material is introduced, leading to a partial differential equation for the damage variable. The obtained model is evaluated using the Müller–Liu approach, yielding necessary and sufficient conditions for thermodynamic consistency. The widely spread damage model with a scalar damage variable is obtained as a special case of the general model considered here. As a special case, we deal with a thermo-elastic material, avoiding splitting of the strain as well as introduction of internal variables connected with inelastic behaviour.