Plane Wave Reflection in a Compressible Half Space with Initial Stress

Abstract

In this paper, the problem of wave propagation in a compressible half-space with an initial stress is considered. General discussion on the speed of wave in the presence of an initial stress is presented. Furthermore, reflection of a homogeneous plane P−wave is also studied. A special strain energy function dependent on this initial stress is used to understand the response of the materials. Explicit formulas for the reflection coefficients are also presented. General nonlinear theory and the theory of invariants are used to derive theoretical results. Graphical illustration of theoretical results for various numerical values of parameters show that initial stress has considerable bearing on the behavior of a plane wave.

Keywords

• compressible elastic material
• initial stress
• plane waves
• nonlinear elasticity
• 43.35.pt
• 52.35.mw
• 62.20.dc