A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations

This paper develops a finite-deformation, gradient theory of single crystal plasticity. The theory is based on a system of microscopic force balances, one balance for each slip system, derived from the principle of virtual power, and a mechanical version of the second law that includes, via the microscopic forces, work performed during plastic flow. When combined with thermodynamically consistent constitutive relations the microscopic force balances become flow rules for the individual slip systems. Because these flow rules are in the form of partial differential equations requiring boundary conditions, they are nonlocal. The chief new ingredient in the theory is a free energy dependent on (geometrically necessary) edge and screw dislocation-densities as introduced in Gurtin [Gurtin, 2006. The Burgers vector and the flow of screw and edge dislocations in finite-deformation plasticity. Journal of Mechanics and Physics of Solids 54, 1882].