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Mixed Variational Principles and Robust Finite Element Design of Gradient Plasticity at Finite Strains

The modeling of size effects in elastic‐plastic solids, such as the width of shear bands or the grain size dependence in polycrystals, must be based on non‐standard theories which incorporate length‐scales. This is achieved by models of strain gradient plasticity, incorporating spatial gradients of selected micro‐structural fields which describe the evolving dissipative mechanisms. The key aspect of this work is to provide a rigorous incremental variational formulation and mixed finite element design of additive finite gradient plasticity in the logarithmic strain space. We start from a mixed saddle point principle for metric‐type plasticity, which is specified for the important model problem of isochoric plasticity with gradient‐extended hardening/softening response. To this end, we propose a novel finite element design of the coupled problem incorporating a local‐global solution strategy of short‐ and long‐range fields. This includes several new aspects, such as extended Q1P0‐type and MINI‐type finite elements for gradient plasticity [4]. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)