Weak Elastic Waves

Abstract

The linear theory of elasticity emerges when attention is restricted to the case in which deformations are small and stress is proportional to strain. The simplicity of this theory, combined with the applicability of many highly developed methods of linear analysis, makes it possible to solve complex multidimensional problems. It is not our purpose to address this entire body of work, however, but simply to consider the special case of linear plane waves of uniaxial strain. The theory of linear wave propagation is not usually regarded as a part of shock physics, but it does permit us to illustrate important aspects of wave propagation. The insight into the mechanics of wave propagation that follows from a study of this simple case is helpful as one seeks understanding of the more general problems.