Coarse-Graining Methodologies for Dislocation Energetics and Dynamics

Abstract

Recent computational advances have permitted mesoscale simulations, wherein individual dislocations are the objects of interest, of systems containing on the order of 106 dislocation [1–4]. While such simulations are beginning to to elucidate important energetic and dynamical features, it is worth noting that the large-scale deformation response in, for example, well-worked metals having dislocation densities ranging between 1010–1014/m2 can be accurately described by a relatively small number of macrovariables. This reduction in the number of degrees of freedom required to characterize plastic deformation implies that a homogenization, or coarse-graining, of variables is appropriate over some range of length and time scales. Indeed, there is experimental evidence that, at least in some cases, the mechanical response of materials depends most strongly on the macroscopic density of dislocations [5] while, in others, the gross substructural details may also be of importance.