© 2004 by Oxford University Press
Transport properties of densely packed composites. Effect of shapes and spacings of inclusions
( 1 Department of Mathematics & MRI, Penn State University, University Park, PA 16802, USA, 2 Department of Theoretical and Applied Mathematics, The University of Akron, Akron, OH 44325-4002, USA, 3 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, 4 Los Alamos National Laboratory, Engineering Sciences and Applications Division, P.O. Box 1663, MS C930, Los Alamos, NM 87545, USA )
We analyse transport properties of fluid/solid and solid/solid composites containing finite arrays of closely spaced rigid inclusions when a host medium is either an elastic matrix or an incompressible fluid. 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 effective 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 configurations corresponding to either lowest dissipation rate (for fluid/solid composites) or to minimal stiffness (for solid/solid composites). In order to find the optimal configurations, we use a unified framework based on asymptotic expansions in terms of inter-inclusion distances. Furthermore, we compare effective transport properties of composite materials containing inclusions with either flat or curved boundaries.
Received 30 June 2004. Revised 18 July 2004.
