Transient two-dimensional Kirchhoff diffraction of a plane elastic SH wave by a generalized linear-slip fracture

Abstract

Closed-form analytic time-domain expressions are obtained for the particle displacement of the total wave motion arising from the 2-D diffraction of a plane elastic SH wave by an imperfection of finite width in the interfacial bonding of two semi-infinite media. The properties of the imperfection are characterized by a matrix of 'spring coefficients' through which the traction on each of its two faces is linearly related to the particle displacement on either of the two faces. A boundary condition of this kind generalizes that of a linear-slip fracture. For this reason, the imperfection can be denoted as a 'generalized linear-slip fracture'. The Kirchhoff approximation is used to solve the diffraction problem. The time-domain expressions are obtained with the aid of the modified Cagniard method.