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 overal l moduli of polycrystalline materials based on a direct evaluation of a mic ro-macro transition. We consider a homogenized macro-continuum with locally attached representative micro-structure, which consists of perfectly bonde d single crystal grains. The deformation of the microstructure is assumed t o be coupled with the local deformation at a typical point on the macro-con tinuum by three alternative constraints of the microscopic fluctuation fiel d. The underlying key approach is a finite-element discretization of the bo undary value problem for the fluctuation held on the micro-structure of the polycrystal. This results in a new closed-form representation of the overa ll elastoplastic tangent moduli or so-called generalized Prandtl-Reuss-tens ors in terms of a Taylor-type upper bound term. and a characteristic soften ing term which depends on global fluctuation stiffness matrices of the disc retized micro-structure. (C) 1999 Published by Elsevier Science B.V. All ri ghts reserved.