Variational asymptotic homogenization of elastoplastic composites

The objective of this paper is to develop a micromechanics approach to homogenizing elastoplastic composites. A rigorous second-order radial return algorithm, which can handle elastic and plastic anisotropy and nonlinear kinematic hardening, is developed. A variational statement for homogenization is formulated using the variational asymptotic method, discretized in a finite-dimensional space, and solved using a multilevel Newton-Raphson method. The versatility and accuracy of the present approach are demonstrated through homogenizing long fiber-, particle-, and short fiber-reinforced metal matrix composites (MMCs). Different types of reinforcement are found to differently affect the response of MMCs. The present approach is found to be capable of handling various microstructures, complex material models, complex loading conditions, and complex loading paths. More sophisticated material models can be implemented in it.