Spherically symmetric shock wave in a dilating medium

A theoretical study is presented of the expansion of a spherical region (a cavity) filled with gas with a high initial pressure in a continuous medium with the property of dilatancy, implying a kinematic relation between the rates of volumetric and maximum shear strains. Changes of density behind the shock front occur only due to this kinematic relation. Attention is given to the case when the dilation rate coefficient is a piecewise-constant function of the density of the medium. This type of model has been used to describe soil behavior in the case of underground explosions.