2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle

Abstract

2D 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 the aforementioned 2D configuration. This method has the advantage of being valid for wedge angles lower and higher than π. 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 the method is validated numerically for all wedge angles.