Consistent micro–macro transitions at large objective strains in curvilinear convective coordinates

Abstract

AbstractThis paper presents a computational homogenization scheme that is of particular interest for problems formulated in curvilinear coordinates. The main goal of this contribution is to generalize the computational homogenization scheme to a formulation of micro–macro transitions in curvilinear convective coordinates, where different physical spaces are considered at the homogenized macro‐continuum and at the locally attached representative micro‐structures. The deformation and the coordinate system of the micro‐structure are assumed to be coupled with the local deformation and the local coordinate system at a corresponding point of the macro‐continuum. For the consistent formulation of micro–macro transitions, the operations scale‐up and scale‐down are introduced, considering the rotated representation of tensor variables at the different physical reference frames of micro‐ and macro‐structure. The second goal of this paper is to use objective strain measures like the Green–Lagrange strain tensor for the solution of boundary value problems on the micro‐ and macro‐scale by providing the required transformations for the work‐conjugate stress, strain and tangent tensors into variables admissible for the considered micro–macro transitions and satisfying the averaging theorem. Copyright © 2007 John Wiley & Sons, Ltd.