On higher order terms and out-of-plane singular mode

It is well known that in a plate weakened by a through-the-thickness crack and subjected to remote anti-symmetric loading (mode II), the Poisson's effect leads to the generation of a coupled out-of-plane singular mode (mode O). Recent theoretical and numerical analyses have demonstrated that this effect also occurs in plates weakened by pointed V-notches, and it can play an important role in failure initiation especially in the case of large notch opening angles. Dealing with cracked plates the influence of higher order terms tied to mode II loading on the out-of-plane singular mode has not been investigated until now. The aim of this paper is to fill this gap with an accurate analysis of mode II higher order terms and their effects on mode O.