When modeling many porous fibrous materials and others, several porous material properties (as well as the elastic properties of the drained porous matrix) will be anisotropic. The effects of an anisotropic flow resistivity (or permeability), anisotropic tortuosity, and an anisotropic viscous characteristic length, are introduced through an anisotropic acoustics model that has an anisotropic (complex valued) density. This is much like the Anisotropic Acoustics model in The Pressure Acoustics, Frequency Domain Interface. Several formulations exist and can, for example, be found in Ref. 9, 12, 13, 14, 15, and 16.

In the formulation used in the Anisotropic Porous Material, the anisotropic effects of the porous properties are assumed to be oriented in the same direction. This assumption is true or a good assumption for most porous materials. In this way, the material data is always defined by a diagonal tensor. In the model, the (complex-valued) anisotropic density becomes: