Computational homogenization of elastic–plastic composites

Abstract

This work describes a computational homogenization methodology to estimate the effective elastic–plastic response of random two-phase composite media. It is based on finite element simulations using three-dimensional cubic cells of different size but smaller than the deterministic representative volume element (DRVE) of the microstructure. We propose to extend the approach developed in the case of elastic heterogeneous media by Drugan and Willis (1996) and Kanit et al. (2003) to elastic–plastic composites. A specific polymer blend, made of two phases with highly contrasted properties, is selected to illustrate this approach; it consists of a random dispersion of elastic rubber spheres in an elastic–plastic glassy polymer matrix. It is found that the effective elastic–plastic response of this particulate composite can be accurately determined by computing a sufficient number of small subvolumes of fixed size extracted from the DRVE and containing different realizations of the random microstructure. In addition, the response of an individual subvolume is found anisotropic whereas the average of all subvolumes leads to recover the isotropic character of the DRVE. The necessary realization number to reach acceptable precision is given for two examples of particle volume fractions.