Asymptotic Analysis of a “Crack” in a Layer of Finite Thickness

Abstract

Rice et al. [1] studied a perturbation problem for the wave equation in a space containing a moving discontinuity surface. We analyse the solutions of the wave equation in a 3D layer, which contains a “crack” propagating dynamically, using the singular perturbation technique developed by Willis and Movchan [3]. The dynamic weight function is discussed for time-dependent Neumann boundary conditions on a semi-infinite “crack” extending at a constant speed V in a 3D layer. The Fourier transform of the weight function is constructed by solving a scalar Wiener-Hopf problem. In this case the weight function is no longer homogeneous (due to the geometry considered). Within the first order perturbation theory framework, a relationship between the intensity factor and a small time-dependent perturbation of the “crack” front is found; we also analyse the transfer function which relates the “crack” front position and the energy release rate.