RVE computations with error control and adaptivity: the power of duality

Journal article, 2007

The goal of computational homogenization is to obtain the macro-scale response, normally in terms of macro-scale stress for given macro-scale deformation, via RVE-computations. In this paper we investigate, in a systematic manner, the effects of Dirichlet and Neumann boundary conditions on the RVE. Adaptive computations are carried out with respect to, in particular, control of the error in the macro-scale stress tensor. This requires the corresponding dual solutions. As a new result, it is shown how the same dual solutions can be conveniently used in computing the algorithmic tangent stiffness tensor, thereby demonstrating the "power of duality". © Springer Verlag 2007.