BOUNDS ON ELASTIC-MODULI OF COMPOSITES

General computable bounds are developed for the stored elastic energy of a finite-sized sample of heterogeneous material which consists of a matrix containing disconnected inclusions which may themselves be het erogeneous. These bounds also apply to the limiting cases of elastic s olids with disconnected cavities or rigid inclusions. The lower bounds for solids with cavities are nonzero, and the upper bounds for solids with rigid inclusions are finite. As an illustration, closed-form bou nds are obtained for the overall elastic parameters of fiber reinforce d composites. The fiber packing may be triangular, square, or hexagona l. Though the results are presented for fibers with hexagonal cross se ctions, the closed-form expressions also apply to arbitrarily shaped c ross sections. The general procedure also applies to nonlinear heterog eneous solids which possess convex strain and stress potentials.