Exact inverse elastic scattering of a crack in the time domain

Abstract

This paper addresses the inverse elastic scattering problem of a planar crack in a bounded 3D solid and the time domain from measurements on its boundary. In a series of papers devoted to electrostatics, elasticity, heat diffusion, acoustics, and thermoelasticity, it has been shown that, using the reciprocity gap functional method combining current fields and adjoining ones, closed form solutions have been obtained for the identification of a planar crack in a bounded solid for different physics. This paper proposes the complete solution for the inverse elastic scattering by a crack, using new adjoint wave fields which provide each component of the slip jump so that the solution for the geometry is the union of the slip jump supports. The method of solution proposed takes into account the unilateral contact condition on the crack lips which has not been considered in the literature.