Approximate Universal Relations between Shock and Acceleration Wave Speeds for Oblique Plate Impact of Inelastic Solids

Abstract

We derive some approximate relations between shear wave speeds in inelastic solids subject to oblique plate impact. Attention is restricted to materials for which the fast wave is purely longitudinal. This includes isotropic solids as well as appropriately aligned orthotropic solids. For the case where the slower wave is a shear shock, we obtain approximate relations between this shock speed and the shear sound speeds (i.e., acceleration wave speeds) immediately ahead of and behind the shock. These relations are universally valid for isotropic or orthotropic elastic solids as well as inelastic solids with instantaneous elastic response.