Solids with non-spherical cavities: simplified representations of cavity compliance tensors and the overall anisotropy

Cavity compliances that determine the contribution of a cavity to the overa ll strain under given loads are analyzed. Generally, they are characterized by fourth rank tensors H. We identify the classes of pore shapes for which characterization by H-tensors can be reduced, with sufficient accuracy, to one in terms of second rank symmetric tensors and certain scalar shape fac tors. These tensors and shape factors are explicitly found in terms of cavi ty geometries. This simplification has far reaching implications: in the framework of the non-interaction approximation, a solid with pores of certain geometries is orthotropic for any orientational distribution of such pores. Moreover, the orthotropy is of a simplified type: the number of independent moduli is re duced from nine to five (or even four, in the case of cracks). It is also shown that randomly oriented ellipsoids (overall isotropy) can b e approximated, from the point of view of the effective moduli, by certain equivalent spheroids. However, further simplification-approximation by sphe res-cannot be made. (C) 1999 Elsevier Science Ltd. All rights reserved.