Continuous Dislocation Dynamics Made Simple

This book presents an easy-to-read introduction to Continuous Dislocation Dynamics (CDD). By treating dislocations which are carriers of crystal deformation as continuously spread defects represented by a density, CDD aims at filling the mesoscopic gap in multi-scale materials modelling. CDD is more coarse-grained than discrete dislocation dynamics (DDD) which models dislocations as discrete lines represented by nodes, and is less coarse-grained than slip-system based FEM crystal plasticity (CPFEM) which models plastic deformation as resulting from slip of crystal planes without important dislocation physics incorporated. Therefore, compared with DDD, CDD can treat much bigger problems involving real quantities of dislocations in engineering applications, yet compared with CPFEM, key dislocation physics are preserved.

This book aims at introducing CDD as an exact approach to crystal plasticity. The starting point is Maxwell's equation for moving lines, which is generalized to densities of parallel dislocation quantities, and then to an "all-dislocation" density (ADD) defined on both the spatial and dislocation-character domains. The ADD is a representation of dislocation density of a coarse-grained resolution suitable for handling large systems, and yet an exact kinematics law is available.

Written in a style which aims to facilitate understanding of the difficult mathematical concepts of dislocation dynamics, the book provides simple illustrations and key computer codes. Suitable readers would be senior undergraduates or starting graduate students with basic understanding of dislocations and engineering mathematics.