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

Abstract

AbstractVariational 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 finite‐deformation 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 well‐posedness, 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.