Enclosure method and reconstruction of a linear crack in an elastic body

Abstract

Abstract. In this paper we report a recent application of the idea of the enclosure method to an inverse problem related to a crack (inverse crack problem) in an elastic body. The problem is to extract information about the location and shape of an unknown crack from a single set of the surface displacement field and traction on the boundary of an arbitrary homogeneous elastic plate. Both anisotropic and isotropic bodies are considered. In states of both plane stress and plane strain, an extraction formula of an unknown crack is given provided: the crack is linear; one of two end points of the crack is known and located on the boundary of the body; a well-controlled surface traction is given on the boundary of the body.

The monotonicity method for inclusion detection and the time harmonic elastic wave equation

“…See e.g. [EH21,II08,Ik99]. The shape reconstruction problem has also been extensively studied for scalar equations, in particular for electrical impedance tomography, and acoustic and electromagnetic inverse problems.…”