Solids with non-spherical cavities : simplifiedrepresentations of cavity compliance tensors and theoverall anisotropy

Abstract

Cavity compliances that determine the contribution of a cavity to the overall strainunder 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 bereduced, with sufficient accuracy, to one in terms of second rank symmetric tensors and certainscalar shape factors. These tensors and shape factors are explicitly found in terms of cavitygeometries. This simplification has far reaching implications : in the framework of thenon-interaction approximation, a solid with pores of certain geometries is orthotropic for anyorientational distribution of such pores. Moreover, the orthotropy is of a simplified type : thenumber of independent moduli is reduced from nine to five (or even four, in the case of cracks) .It is also shown that randomly oriented ellipsoids (overall isotropy) can be approximated, fromthe point of view of the effective moduli, by certain equivalent spheroids. However, furthersimplification—approximation by spheres—cannot be made.