A Two—Scale Micro—Macro—Approach to Anisotropic Finite Plasticity of Polycrystals

Abstract

We discuss elements of a two—scale micro—macro—approach to the modelling of the elastic—plastic material response of polycrystals at finite strains. The underlying key idea is a direct analysis of a homogenized macro—continuum with a locally attached micro—structure, which represents a representative aggregate of single crystal grains. The first part of the paper focuses on the formulation and numerical implementation of an average—type micro—macro—transition and points out a discinct closed—form representation of the overall elastic—plastic tangent moduli. The second part adresses a computational model of finite crystal plasticity for the modelling of the grains in the microstructure and proposes a characteristic stress update algorithm based on an incremental minimizing problem.