A framework and finite element formulation for incompatibility tensor‐based gradient plasticity

Abstract

AbstractThe present contribution deals with a gradient plasticity formulation that accounts for energetic contributions of plastic incompatibilities that are interpreted in terms of dislocation densities. At the outset of the theory, an extended form of the dissipation inequality in terms of a nonlocality residual is assumed in accordance with [1]. Taking into account dislocation density tensors as additional arguments of the free energy density function, this form naturally gives rise to the balance equation of a generalised (quasi) nonlocal stress field that is energetically conjugated to the plastic deformation. Against this background one furthermore observes that the energetic dual to the dislocation density tensor is closely related to a back stress‐type part of the generalised stress field. For the solution of the resulting system of coupled partial differential equations, a multi‐field finite element approach is taken, with the plastic consistency conditions being accounted for on global level by means of Fischer‐Burmeister complementarity functions.