The edge smoothed finite element for multiscale homogenization

Computational homogenization provides an effective method for the design of material microstructures and the exploration of new materials with superior performances. Nevertheless, the homogenization method often relies on finite element (FE) discretization, which may act as a computational constriction in terms of its efficiency and accuracy. The smoothed FE variant exhibits attractive mathematical/numerical properties, which are further explored in this study. We combined edge-smoothed finite elements with periodic boundary conditions treated via the Nitsche and mortar methods on a non-matching boundary mesh aimed at improving the estimation of the homogenized elasticity properties. The convergence and size effect benchmarks revealed that the smoothed finite element method provides for greater accuracy and efficiency than does regular FE.