Solids with cracks and non-spherical pores: proper parameters of defect density and effective elastic properties

The work is motivated by inadequacy of the conventional defect density para meters, such as porosity (relative volume of pores) or the usual crack dens ity in situations that are frequently encountered in applications: of non-s pherical pores of diverse shapes, fluid-filled cracks/pores, pores in an an isotropic matrix. We call a defect density parameter proper if it correctly reflects the individual defect contributions into the effective elastic pr operties. Only in terms of such parameters can these properties be uniquely expressed. Their identification is non-trivial even in the framework of th e non-interaction approximation; defect interactions further complicate the problem. We show that the proper parameters are identified by the structur e of the elastic potential. Besides being necessary, the proper parameters yield the following benefits: (1) anisotropy due to non-randomly oriented defects is established; (2) expressions for the effective moduli cover, in a unified way, all mixtu res of defects of diverse shapes and arbitrary orientational distributions; (3) they provide guidance for the proper interpretation of experimental dat a on elasticity of porous materials. For certain types of defects (field of pores of complex, but identical shap es, for example), the general results in terms of tensorial parameters redu ce, for each particular orientational distribution, to expressions in terms of the conventional parameters. However, in other situations (non-spherica l pores of diverse shapes, fluid-filled cracks/pores, pores in an anisotrop ic matrix) such a reduction cannot, generally, be done, even for a particul ar orientational distribution.