Wave reflection in slightly compressible, finitely deformed elastic media

In this paper, the reflection of a plane wave at an incremeritally traction -free boundary of a half-space composed of nearly incompressible elastic ma terial is considered. It is shown that two distinct cases exist, these bein g dependent on the underlying primary deformation. In the first case, the a ppropriate slowness sections are each approximately elliptical, and the cor responding reflection phenomena closely mirrors that associated with the co rresponding linear isotropic theory. Specifically, an angular range of dire ction of incident wave exists, for which both a quasi-longitudinal and quas i-shear wave are reflected, the former being replaced by a surface wave out side this angular range. In the second case, the outer slowness section is re-enrant and, in addition to the scenarios previously mentioned, it is pos sible for two quasi-shear waves to be reflected. Numerical illustrations of reflection coefficients are presented in respect of a modified Varga mater ial and the case of increasing bulk modulus is investigated.