Homogenization of elastic-plastic periodic materials by FVDAM and FEM approaches - An assessment

The standard computational approach for the homogenization of elastic-plastic response of periodic materials is the finite-element method. Amongst the emerging alternatives, the finite-volume direct averaging micromechanics (FVDAM) theory has shown promise. Herein, we present a systematic comparison of the predictive capabilities of both approaches in the context of two technologically important material systems, each of which exhibits interesting plasticity-driven local and global responses in its own right, which have not been well-documented. This comparison is conducted for the first time on the same footing using an in-house developed finite-element code which closely mimics the homogenization framework, displacement field approximation and unit cell discretization employed by the parametric FVDAM theory. A new stress measure is introduced which highlights the fundamental differences in the variational-based and direct averaging-based solution approaches employed by the two methods. The comparison provides firm support for the parametric FVDAM theory's ability to capture highly localized plasticity effects in different classes of heterogeneous materials, which lead to interesting and technologically important phenomena at the homogenized scale.