Ab. Movchan et Jr. Willis, DYNAMIC WEIGHT-FUNCTIONS FOR A MOVING CRACK .2. SHEAR LOADING, Journal of the mechanics and physics of solids, 43(9), 1995, pp. 1369-1383
Dynamic weight functions are constructed for general time-dependent sh
ear loading of a plane semi-infinite crack propagating with constant s
peed in an infinite isotropic elastic body. The use of Fourier transfo
rms reduces the problem to the analysis of a matrix Wiener-Hopf equati
on. The solution of the Wiener-Hopf problem is presented. An expressio
n is derived for the first-order perturbation to the stress intensity
factors induced by a small time-dependent deviation from straightness
of the crack front. The asymptotic procedure requires consideration of
two terms of the asymptotic expansions of the displacement and stress
tenser components in a neighbourhood of the crack front.