Reflection and Refraction for Three-Dimensional Plane Waves at the Interface between Distinct Anisotropic Half-Spaces under Initial Stresses

This paper deals with the reflection and refraction (transmission) phenomena that result from a three-dimensional plane-wave incident at the plane interface between two distinct triclinic media under the influence of initial stresses. Analytical expressions of all the phase velocities of reflected and transmitted quasi-compressional qP and quasi-shear waves qS1 and qS2 (or qSV and qSH) under initial stresses were obtained. Closed-form expressions for the amplitude ratios or reflection and refraction coefficients of the three quasi-waves were derived for suitable boundary conditions. It has been shown that reflection and transmission coefficients depend on the angle of incidence, the material constants, and the initial stresses present in the media. For numerical discussion, the variations of reflection and transmission coefficients with the initial stresses and angle of incidence are presented by means of graphs using mathematical software. Some particular remarkable cases are also considered.