GEOMETRICAL-PARAMETER BOUNDS ON THE EFFECTIVE MODULI OF COMPOSITES

We study bounds on the effective conductivity and elastic moduli of tw o-phase isotropic composites that depend on geometrical parameters tha t take into account up to three-point statistical information concerni ng the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These appr oaches allow us to get new and improved geometrical-parameter bounds o n the elastic moduli of two-dimensional composites. Applications of th e bounds for effective-medium geometries as well as random arrays of a ligned fibers in a matrix are discussed.