Some theoretical and computational aspects of single-crystal strain-gradient plasticity

Abstract

Variational formulations are constructed for rate-independent problems in single-crystal strain-gradient plasticity. The framework makes use of the flow rule expressed in terms of a dissipation function. The formulation extends to the finitedeformation context earlier work on this problem. Provision is made for energetic and dissipative microstresses, and a range of defect energies is accounted for. The minimization problem corresponding to the time-discrete formulation is derived. Two special cases are then treated: first, for the small-strain problem with energetic microstresses, results on wellposedness, convergence of finite element approximations, the associated algorithms, and computational examples, are discussed. Secondly, recent computational work on the the related large-deformation viscoplastic problem, with both energetic and dissipative effects, is presented and discussed for problems involving ensembles of grains.