The spectral functions method for elastic plane wave diffraction by a wedge

Non destructive examination of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, back-wall, etc.) of inspected blocks. For that purpose, the study of plane elastic wave diffraction by a wedge is of great interest since surfaces of complex industrial specimen often include dihedral corners. These inspections often deal with high frequency (f = 2-5 MHz) ultrasonic waves. Simulation of realistic inspections by finite elements and finite differences can therefore be time consuming because such methods require a small mesh step for a better description of the scattered wave. Semi-analytical methods are therefore preferred for high frequency problems. There exist various approaches for semi-analytical modeling of plane elastic wave diffraction by a wedge but the theoretical and numerical aspects of these methods have so far only been developed for wedge angles lower than π. Croisille and Lebeau [1] have introduced a resolution method called the Spectral Functions method in the different case of an immersed elastic wedge of angle less than π. Kamotski and Lebeau [2] have then proven existence and uniqueness of the solution derived from this method to the diffraction problem of stress-free wedges embedded in an elastic medium. The advantages of this method are its validity for wedge angles greater than π and its adaptability to more complex cases. The methodology of Croisille and Lebeau [1] has been first extended by the authors to the simpler case of an immersed soft wedge [3] (submitted). It has then been developed here for the 2D scattering problem of an elastic longitudinal wave and a numerical validation of the method for all wedge angles is proposed.