Reflection of plane waves from the boundary of an incompressible transversely isotropic elastic solid with initial stress

In this paper, the reflection of small-amplitude homogeneous plane waves from the boundary of an incompressible transversely isotropic elastic medium under initial stress is studied. We restrict our attention to the case where the initial stress direction is orthogonal to the preferred material direction. The explicit formulas for the wave speed, the reflection coefficients, and surface wave coefficients are derived in terms of the deformation and the angle of incidence. Based on a specific form of transversely isotropic strain-energy function, the numerical results are illustrated graphically to show the effects of initial stress and anisotropic parameters.