Multiscale Modeling of Anisotropies in Single Crystals and Polycrystals at Finite Strains

Abstract

The paper provides an overview about recent developments in the multiscale analysis of the anisotropic material behavior of single crystals and polycrystals. We outline a distinct incremental variational formulation for the local constitutive response of standard dissipative materials where an incremental stress potential is obtained from a local minimization problem with respect to the internal variables. This potential allows for the formulation of IBVPs for standard dissipative solids as a sequence of incremental minimization problems. Particular emphasis is put on crystal plasticity where we develop alternative stress update algorithms for Schmid-type single crystal plasticity with potential hardening. Furthermore the variational setting provides for the formulation of a canonical framework of nonlinear homogenization of standard dissipative microstructures where a quasi-hyperelastic incremental macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. Finally we extend the framework of standard local crystal plasticity to the setting of dislocation density based gradient plasticity for inhomogeneously deforming crystals. Here we equip the formulation with a sound micromechanical basis where an incompatibility induced storage of geometrically necessary dislocations results in a scale dependent material behavior. The performance of the formulations is demonstrated for benchmarks of single crystal and polycrystal plasticity as well as thin films.