Elastic moduli for a class of porous materials

SummaryThe effective elastic moduli for a class of porous materials with various distributions of spheroidal voids are given explicitly. The distributions considered include the unidirectionally aligned voids, three-dimensionally and two-dimensionally, randomly oriented voids, and voids with two types of biased orientations. While the 3-d random orientation results in a macroscopically isotropic solid, the porous media associated with the other arrangements are transversely isotropic. The five independent elastic constants for each arrangement, as well as the two for the isotropic case, are derived by means of Mori-Tanaka's mean field theory in conjunction with Eshelby's solution. Specific results for long, cylindrical pores and for thin cracks with the above orientations are also obtained, the latter being expressed in terms of the crack-density parameter. Before we set out the analysis, it is further proven that, in the case of long, circular inclusions, the five effective moduli of a fiber composite derived from the Mori-Tanaka method coincide with Hill's and Hashin's lower bounds if the matrix is the softer phase, and coincide with their upper bounds if the matrix is the harder.

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