A k-medoids-based partitioned method for computational homogenization of heterogeneous materials

Although they are very interesting for structural simulations involving heterogeneous materials, Finite Element (FE) squared approaches, often coined FE², are well-known to require great computational resources. The main challenge is that, for each integration point of the coarse structure, a so-called fine scale problem should be solved. In this work, a k-medoids-based partitioned FE² approach is proposed to directly tackle this challenge by effectively reducing the number of fine scale solves. At each coarse scale nonlinear iteration, coarse scale integration points are partitioned a priori based on the current coarse scale displacement gradient and fine scale internal variables using the k-medoids-based clustering algorithm. Stresses and tangent moduli are computed only for cluster medoids, and are then extended to the remaining non-medoid coarse scale integration points. Results with nonlinear material behavior such as hyperelasticity and elasto-plasticity show that the proposed method is a promising candidate for reducing the computational cost of FE² simulations.