Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Abstract

This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two-scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High-performance parallel multiscale implementations of the CH scheme are addressed in more detail.