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

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 H¹-norm and the L²-norm. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)