3D CAUCHY PROBLEM FOR AN ELASTIC LAYER: INTERFACIAL CRACKS DETECTION

Abstract

This study presents a Cauchy-type problem of 3D elasticity for an elastic layer that can be bonded to an infinite base (half-space) made of dissimilar elastic material. The initial conditions are given on one side of the layer and both stress and displacement vectors are assumed to be known simultaneously. No conditions are specified on the other side. In the case of this side being fully bonded to the base, the stress and displacement vectors are continuous across the interface. This fact introduces certain relationships that have to be imposed on the initial conditions in order to obey continuity. We use these in order to detect a possible appearance of delamination of the interface. By using the double Fourier transform and the general solution of 3D elasticity in terms of harmonic functions, the initial value problem is reduced to a system of Fredholm integral equations of the first kind. Solutions of such systems are usually unstable; therefore, a numerical approach is suggested to overcome this difficulty by using the SVD regularisation. A possibility of delamination detection is discussed.