Elastic waves in orthotropic incompressible materials and reflection from an interface

The propagation of elastic plane waves in orthotropic incompressible materials is examined under plane strain conditions in a plane of symmetry. The slowness surface is obtained by aligning a material axis of symmetry with the direction of minimum phase speed. The existence of incident homogeneous waves and reflected homogeneous and nonhomogeneous waves in the presence of a planar interface separating two half-spaces is subsequently examined. A surface which separates the range of existence of two homogeneous reflected waves from that of one homogeneous and one nonhomogeneous is obtained in terms of the angle of incidence, the orientation of the interface with respect to the material axis of symmetry, and one elastic parameter. The critical orientation beyond which there exist two homogeneous reflected waves is derived in explicit form in terms of the elastic parameter. Reflection coefficients are obtained and discussed when the interface is a free surface. Exclusion points are defined in the range of existence of the reflected waves as points for which only one reflected (homogeneous) wave exists. The analysis is complemented with numerical examples.