Bounds on non-local effective relations for random composites loaded by configuration-dependent body force

An infinite domain occupied by composite material is considered. The compos ite is treated as random. The stress, strain and displacement fields within it are produced by body force with two types of components. One is determi nistic while the other depends on the particular realisation of the medium as would be the case, for instance, under gravity loading, so that the dist ribution of a density (physical or otherwise) enters the problem, as well a s the distribution of elastic constants. This feature introduces additional constitutive operators defining the mean response of the body. Besides the usual (non-local) effective modulus operator, there is another operator th at provides a contribution to the mean stress from the fluctuating part of the density, and one more that accounts for the non-zero contribution to th e mean energy from the interaction of the fluctuating part of the stress fi eld with itself. Bounds of flashin-Shtrikman type are developed which provi de restrictions on all these operators, in real space and in the transform domain. The formalism also provides direct Hashin-Shtrikman approximations for the non-local operators. (C) 2000 Elsevier Science Ltd. All rights rese rved.