An Asymptotic Method for Solving the Problem of Identifying a Curvilinear Crack in an Elastic Layer

Abstract

We solve an inverse geometric problem of identifying an internal curvilinear defect in an orthotropic elastic layer. Defect parameters (location, depth, size, orientation) are determined based on an acoustic analysis of displacement fields and their characteristics measured on part of layer’s upper boundary. We consider a steady-state oscillation mode and the two cases of antiplane and plane oscillations of the strip. An efficient asymptotic approach is proposed to studying the direct and inverse problems for cracks of a small relative size. The proposed scheme makes it possible to significantly simplify the solution of the direct problem and reduce the solution of the inverse one to characterizing the defect from transcendental equations. Numerical results of computational experiments are presented.