Second-order in-plane dynamic perturbation of a crack propagating under shear loading

Abstract

The title problem is solved, for a crack propagating in a slab which is composed of material which can be viscoelastic, “vertically stratified” and transversely isotropic with the axis in the “vertical” direction. The result is illustrated by specialising to the case of a stationary crack in the plane x3 = 0 of an infinite isotropic elastic medium, whose leading edge is at x1 =  a cos( kx2), with | k| a ≪ 1.