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 micro-structure 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 field 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.