Thermodynamically based concept for the modelling of continua with microstructure and evolving defects

The aim of the paper is to present a thermodynamically based concept for the analysis of defect evolution in continua with microstructure. In classical models of continua with microstructure, balance laws for linear and angular momentum are formulated for macroforces and microforces, which can be called deformational macroforces and microforces. Characteristic feature of macrodefects and microdefects such as cracks and voids is the fact, that they can migrate relative to the moving body and this relative motion of defects is caused by so-called con®gurational forces. Therefore, in a continuum with microstructure and evolving macrodefects and microdefects we have to deal with deformational and con®gurational macroforces and microforces. To formulate a reliable theory for material bodies with microstructure and migrating macrodefects and microdefects, a continuum is considered, where each particle is equipped with an arbitrary number of deformable directors. We distinguish then between directors undergoing a convective deformation leading to deformational (physical) microforces, and directors describing a set of defects migrating relative to the underlying lattice, where this migration is caused by con®gurational (material) microforces. For deformational and con®gurational macroforces and microforces corresponding balance laws are presented and the macro- and micro-Eshelby stress tensors are derived. Next, deformational and con®gurational heatings and entropy ¯uxes are introduced and the ®rst and second law of thermodynamics for the microcontinuum with evolving macrodefects and microdefects are formulated. Finally, we present the most general form of the ®rst order constitutive equations satisfying the second law of thermodynamics for migrating defects