A novel method for investigating the isotropy of response for randomly generated unit cells of particulate composites

Abstract

This work investigates the isotropy of mechanical response of randomly generated unit cells of particulate composites. We propose a novel algorithm for assessing the isotropic behavior of such microstructures by applying different loading in random planes in space. The Random Plane Evaluation of Isotropy (RPEI) is based on calculating the averaged stress and strain under periodic boundary conditions and finding the maximum angle difference between the principal directions of them as a measure for deviation from coaxiality/isotropy. We show that an average of such data at a statistical level can be used for assessing closeness to isotropy. To put the RPEI in use, we have also proposed a new method for generating unit cells containing a random distribution of ellipsoidal particles. Then the isotropy of mechanical behavior for various unit cells enclosing random suspensions of spheres and ellipsoids was investigated. Our results show that (i) Merely random distribution of particles does not guarantee the isotropy of the response (ii) Checking the isotropy in limited directions can be misleading and data at a statistical level is needed (iii) RPEI proves a reliable tool for checking the isotropy of response of unit cells of heterogeneous materials for a variety of behaviors.