3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Abstract

Elastic plane wave diffraction by a stress-free wedge is a canonical problem of interest to researchers in many different fields. To our knowledge, no fully analytical resolution has been found and semi-analytical evaluations of asymptotic approximations have therefore become a common approach. In this paper, a method called the spectral functions method is developed in a 3D configuration, meaning that the incident ray is not necessarily in the plane normal to the wedge edge. The diffracted displacement field is expressed as an integral in terms of two unknown functions called the spectral functions. These functions are decomposed into two parts: one which can be computed analytically and the other which is approached numerically using a collocation method. The details of the corresponding numerical scheme are given and first numerical validations are presented. The presented method is valid for incident skew angles which are below the critical angle in diffraction.