A Discontinuity in Deformation Gradient Induced by Acceleration Waves in One-Dimensional Elastic Materials

Abstract

The discontinuity in the rate of the deformation gradient across an incident acceleration wave is partly reflected and partly transmitted at the boundary between two dissimilar one-dimensional elastic materials. The reflection and the transmission coefficients as-sociated with those discontinuities are expressed in terms of the ratios of the densities and the speeds of the acceleration waves on both sides of the boundary. The rest of the discontinuity in the incident wave stays at the boundary, which induces either a discontinuity in the deformation gradient, or influences the growth and decay of such a discontinuity if it already exists.