On wave phenomena in permeable foam

The linear Biot theory fur wave propagation in porous media is applied to waves in an open cell permeable foam. The relevant physical parameters are specified. In general two wave modes exist, with their own frequency dependent wave speeds and damping factors. The reflection of a weak shock wave from a semi-infinite elastic foam is considered. It is shown that the deformation of the foam and the related effective stress arc caused by friction. The total stress behaves as a damped wave, whereas the pressure and the effective stress show a mixed wave-like diffusion- like behaviour. Expressions are derived for the reflection coefficient and for the maximum effective stress in the foam. The non-linear permeabilities and stress strain relations for two types of flexible poly-urethane foams are specified. The reflection of a weak shock wave from a slab of foam material adjacent to a solid wall is simulated for both types of foams, making use of effective values of the permeability. It is shown that even for a weak shock of Mach number 1.07, a partial mechanical collapse of the foam is to be expected.