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. (C) 1999 Elsevier Science S.A. All rights reserved.