Multi-scale computational homogenization of heterogeneous materials

The mechanical response of a heterogeneous medium results from the interactions of mechanisms spanning several length scales. The computational homogenization method captures direct influence of underlying constituents and morphology with a numerically efficient framework. This study reviews the performance of first order computational homogenization technique with a flat punch indentation problem. Results obtained are benchmarked against those using direct numerical simulations (DNS) with full microstructural details. It is shown that the computational homogenization method is able to capture structural response adequately, even for constituent materials with nonlinear behavior. However, the first order computational homogenization method becomes problematic when localized macroscopic deformation occurs. In this context, some re- cent trends addressing the issues are discussed.