The heterogeneous multiscale finite element method FE‐HMM for the homogenization of linear elastic solids

Abstract

The objective of the present paper is a formulation of the Heterogeneous Multiscale Finite Element Method (FE‐HMM) for the homogenization of linear elastic solids in a geometrical linear frame, and doing so, for the first time, of a vector‐valued field problem. The macro stiffness is estimated by stiffness sampling on heterogeneous microdomains in terms of a modified quadrature formula, which implies an equivalence of energy densities of the microscale with the macroscale. Existing a‐priori estimates are assessed and used for optimal micro‐macro refinement strategies in the H 1 ‐norm and the L 2 ‐norm. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)