Computational homogenization analysis in finite plasticity - Simulation oftexture development in polycrystalline materials

The paper presents a framework for the treatment of a homogenized macro-con tinuum with locally attached micro-structure, which undergoes non-isotherma l 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 gr ains. The deformation of this micro-structure is coupled with the local def ormation at a typical material point of the macro-continuum by three altern ative constraints of the microscopic fluctuation field. In a deformation dr iven process, extensive macroscopic variables, like stresses and dissipatio n are defined as volume averages of their microscopic counterparts in an ac companying local equilibrium state of the micro-structure. The proposed num erical implementation is based in the general setting on a finite element d iscretization 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 p roblems associated with the macro-continuum and the pointwise attached micr o-structure and consider aspects of their finite element solutions. The sec ond part presents details of a robust algorithmic model of finite plasticit y for single crystals which governs the response of the grains in a typical micro-structure. The paper concludes with some representative numerical ex amples 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.