“…Now, for porous materials with statistically isotropic microstructures relative sound velocities (additional index “ r ”) can be defined by normalizing with the sound velocities of the dense materials (additional index “0”), that is,
which is more convenient for comparison with theoretical predictions. Predictions for the porosity dependence of the sound velocity
22 can be derived from the well‐known predictive models for elastic properties, including the Maxwell–Mori–Tanaka (MMT) relation,
23,24 the differential relation
24,25 or Gibson–Ashby relation for open‐cell foams,
26,27 the (Pabst–Gregorová‐type) exponential relation
28,29 and the self‐consistent model relation,
24,29 as well as the numerical (Pabst–Uhlířová) benchmark relation for partially sintered materials with concave porosity (overlapping solid sphere model)
30 and the one‐parameter (Pabst–Gregorová) percolation relation,
31 the latter with critical porosity
0.36 (complement to the solid volume fraction of 0.64 for random close packing or maximally random jammed structure)
24 . In the following relations the porosity is denoted by ϕ and for simplicity all predictions are given here for Poisson's ratios sufficiently close to 0.2, if not noted otherwise (the generalization to other Poisson's ratios is straightforward, however, and may be invoked if needed)
22 …”