Computational micro-macro transitions and overall moduli in the analysis of polycrystals at Large strains

This paper presents a numerical procedure for the computation of the overall moduli of polycrystalline materials based on a direct evaluation of a micro-macro transition. We consider a homogenized macro-continuum with locally attached representative micro-structure, which consists of perfectly bonded single crystal grains. The deformation of the microstructure is assumed to be coupled with the local deformation at a typical point on the macro-continuum by three alternative constraints of the microscopic fluctuation field. The underlying key approach is a finite-element discretization of the boundary value problem for the fluctuation held on the micro-structure of the polycrystal. This results in a new closed-form representation of the overall elastoplastic tangent moduli or so-called generalized Prandtl-Reuss-tensors in terms of a Taylor-type upper bound term. and a characteristic softening term which depends on global fluctuation stiffness matrices of the discretized micro-structure. (C) 1999 Published by Elsevier Science B.V. All rights reserved.