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

摘要

Cavity compliances that determine the contribution of a cavity to the overall strain under given loads are analyzed. Generally, they are characterized by fourth and 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 and symmetric tensors and certain scalar shape factors. These tensors and shape factors are explicitly found in terms of cavity geometries. This simplification has far reaching implications: in the framework of the non-interaction approximation, a solid with pores of certain geometry's is orthotropic for any orientation distribution of such pores. Moreover, the orthotropy is of a simplified type: the number of independent moduli is reduced from nine to five (or even four, in the case of cracks).