Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data. (English) Zbl 1115.35149

Ikehata, Masaru; Itou, Hiromichi

Inverse Probl. 23, No. 2, 589-607 (2007).

Summary: An inverse problem related to a crack in elastostatics is considered. The problem is: 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 the elastic body. This is a typical problem from the nondestructive testing of materials. A version in a plane problem of elastostatics is considered. It is shown that, in a state of plane strain, the enclosure method which was introduced by Ikehata yields the extraction formula of an unknown crack provided: the crack is linear; one of the 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.

MSC:

35R30	Inverse problems for PDEs
74B05	Classical linear elasticity

Keywords:

inverse crack problem; Lamé equation; Dirichlet-to-Neumann map; elastostatics; surface displacement; nondestructive testing; enclosure method