2-D Elastodynamic Scattering from a Finite Closed Crack

Abstract

In the present paper the problem of 2-D elastodynamic scattering of horizontally polarized transverse waves from a finite planar or nonplanar closed crack is studied. The boundary conditions on the flaw are of a type which incorporate restoring forces (as well as energy dissipation), and this enables the modelling of a crack which is partly closed under a static background pressure. Given an incident plane wave and the crack geometry we calculate the backscattered far field in the time-harmonic case. In this study there are also a numerical comparison between two well known theoretical methods for 2-D scattering of ultrasonic sound by flaws in elastic solids. The methods are the GTD (Geometrical Theory of Diffraction) method that gives an asymptotic solution for high frequencies and the nullfield approach that yields an “exact” numerical solution. The boundary conditions for the partly closed crack are proposed by Boström and Wickham [1]. For a thorough description of the details of the GTD method as applied to scattering problems in elastodynamics, the reader is referred to the book by Achenbach, Gautesen, and McMaken [2]. The nullfield approach has previously been used for treating 3-D planar and nonplanar cracks with similar boundary conditions [3], the same ideas will here be used in the treatment of the 2-D case. The backscattered far field amplitude is numerically calculated and compared between the two methods.