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

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.