Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials

The paper presents a framework for the treatment of a homogenized macro-continuum with locally attached micro-structure, which undergoes non-isothermal inelastic deformations at large strains. The proposed concept is applied to the simulation of texture evolution in polycrystalline metals, where the micro-structure consists of a representative assembly of single crystal grains. The deformation of this micro-structure is coupled with the local deformation at a typical material point of the macro-continuum by three alternative constraints of the microscopic fluctuation field. In a deformation driven process, extensive macroscopic variables, like stresses and dissipation are defined as volume averages of their microscopic counterparts in an accompanying local equilibrium state of the micro-structure. The proposed numerical implementation is based in the general setting on a finite element discretization of the macro-continuum which is locally coupled at each Gauss point with a finite element discretization of the attached micro-structure. In the first part of the paper we set up the two coupled boundary value problems associated with the macro-continuum and the pointwise attached micro-structure and consider aspects of their finite element solutions. The second part presents details of a robust algorithmic model of finite plasticity for single crystals which governs the response of the grains in a typical micro-structure. The paper concludes with some representative numerical examples by demonstrating the performance of the proposed concept with regard to the prediction of texture evolution in polycrystals.