Transport properties of densely packed composites. Effect of shapes and spacings of inclusions

Abstract

Summary We analyze transport properties of ∞uid/solid and solid/solid composites containing flnite arrays of closely spaced rigid inclusions when a host medium is either an elastic matrix or an incompressible ∞uid. The appropriate choice of the number of inclusions and the symmetry of a periodicity cell allows us to introduce simple, yet physically relevant models so that efiective characteristics of homogenized media can be investigated analytically. For various applied loads and shapes of (polydisperse) inclusions we demonstrate the spatial non-uniformity of geometric conflgurations corresponding to either lowest dissipation rate (for ∞uid/solid composites) or to minimal stifiness (for solid/solid composites). In order to flnd the optimal conflgurations, we use a unifled framework based on asymptotic expansions in terms of inter-inclusion distances. Furthermore, we compare efiective transport properties of composite materials containing inclusions with either ∞at or curved boundaries.