A multiscale model for dislocations: From mesoscopic elasticity to macroscopic plasticity

Abstract

A multiscale model for dislocations in single crystals is proposed. The aim of this paper is to provide homogenization of dislocations from the meso- to the macro-scale. In particular we prove a new formula relating macroscopic strain incompatibility and dislocation density. Moreover, it is shown that plasticity is recovered from homogenization of purely elastic mesoscopic crystals with dislocations, where the appropriate functional space of Special functions of Bounded Deformation appears as a natural choice. Nonstandard defect and deformation internal variables and their evolution in time appear while novel differential relations are sketched in the non-Riemannian crystal with a thermodynamical model as based on those results, A multiscale model for dislocations in single crystals is proposed. The aim of this paper is to provide homogenization of dislocation clusters from the meso- to the macro-scale. In particular we prove a new formula relating macroscopic strain incompatibility and dislocation density. Moreover, it is shown that plasticity is recovered from homogenization of purely elastic mesoscopic crystals with dislocations, where the appropriate functional space of Special functions of Bounded Deformation appears as a natural choice. Nonstandard defect and deformation internal variables and their evolution in time appear while novel differential relations are sketched in the non-Riemannian crystal with a thermodynamical model as based on those results. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.