Representation of anisotropic phase morphology

A quantitative measure of anisotropic phase connectivity is investigated. The isotropic stereological parameter, contiguity, is extended to characterize the anisotropic phase connectivity. Two mathematical representations for characterizing the anisotropic contiguity are presented, one based on C-0 piecewise polynomials and the other on tensorial expansions. The anisotropic contiguities for several virtual specimens having different phase morphologies are investigated with the aid of a numerical probe that collects statistical data on phase connectivity. The mechanical responses of different specimens with the same phase volume fraction but different contiguity distributions are contrasted. Finally, contiguity changes due to the mechanical deformation are presented.