Novel formulations of microscopic boundary-value problems in continuous multiscale finite element methods

This article explores the use of a homogenization method inspired by the classical Irving–Kirkwood procedure in the continuous multiscale modeling of elastic solids within the context of the finite element method. This homogenization method gives rise to a broad range of allowable boundary conditions for the RVE, which, in turn, yield a rich spectrum of estimates of the macroscopic stress response for two representative problems involving heterogeneous elastic bodies.