Dynamic expansion of a spherical cavity within a rate-dependent compressible porous material

The problem of shock expansion of cavities in geological or geologically derived media is of fundamental interest because it is closely related to the blast problem (propagation of waves from an explosion source) as well as to crater formation by hypervelocity projectile impact. Since rock and cementitious materials exhibit very strong high-rate and high-confinement sensitivities, those effects cannot be neglected in a realistic analysis of penetration events. In this paper a new model for the shock expansion of a spherical cavity in an infinite medium that displays very strong high-rate and high-confinement sensitivities is proposed. Waves are generated by an instantaneous rise of the pressure at the surface of the cavity. A complete description of the motion of the medium situated between the cavity and the shock wave as well as the distribution of stresses and deformation as functions of time and distance from the center of the cavity is obtained. Specifically, we provide a description of the dynamic compaction of the material, we determine the extent of the domain affected by the dynamic event and the moment at which the influence of the pulse on the medium ceases. A compressible zone develops as a continuation of the incompressible one. The solutions are proved to be compatible with the Rankine–Hugoniot shock conditions. We conclude with an application of the proposed model to concrete.