REFLECTION OF PLANE-WAVES FROM THE BOUNDARY OF A PRESTRESSED COMPRESSIBLE ELASTIC HALF-SPACE

The effect of pre-stress on the propagation and reflection of plane wa ves in an incompressible isotropic elastic half-space has been examine d recently by the authors (Ogden & Sotiropoulos, 1997). In the present paper the corresponding analysis for compressible materials is detail ed. In the two-dimensional context considered for incompressible mater ials the (homogeneous) plane waves were necessarily shear waves. By co ntrast, in the compressible context pure shear waves can propagate onl y in specific directions in the considered principal plane and, in a g eneral direction, a quasi-shear wave may be accompanied by a quasi-lon gitudinal wave, as is the case in the anisotropic linear theory. The d ependence of the (in-plane) slowness section on the pre-stress (and fi nite deformation) and on the choice of constitutive law is elucidated. This information is used to determine the reflection coefficients for reflection of either a (quasi-) shear wave or a (quasi-) longitudinal wave from the boundary of the half-space and to characterize the diff erent cases which arise depending on the geometry of the slowness sect ion. The theoretical results are illustrated by numerical calculations for the range of possible types of behaviour with reference to differ ent forms of strain-energy function and different states of finite def ormation and to the question of stability of the half-space.