EFFECTIVE STIFFNESS TENSOR OF COMPOSITE MEDIA .1. EXACT SERIES EXPANSIONS

The problem of determining exact expressions for the effective stiffne ss tensor macroscopically anisotropic, two-phase composite media of ar bitrary microstructure in arbitrary space dimension d is considered. W e depart from previous treatments by introducing an integral equation for the ''cavity'' strain field. This leads to new, exact series expan sions for the effective stiffness tensor of macroscopically anisotropi c, d-dimensional, two-phase composite media in powers of the ''elastic polarizabilities''. The nth-order tensor coefficients of these expans ions are explicitly expressed as absolutely convergent integrals over products of certain tensor fields and a determinant involving n-point correlation functions that characterize the microstructure. For the sp ecial case of macroscopically isotropic media, these series expression s may be regarded as expansions that perturb about the optimal structu res that realize the Hashin-Shtrikman bounds (e.g. coated-inclusion as semblages or finite-rank laminates). Similarly, for macroscopically an isotropic media, the series expressions may be regarded as expansions that perturb about optimal structures that realize Willis' bounds. For isotropic multiphase composites, we remark on the behavior of the eff ective moduli as the space dimension d tends to infinity. (C) 1997 Els evier Science Ltd.