Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data

Abstract

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.

The interface crack with Coulomb friction between two bonded dissimilar elastic media

“…In the case of homogeneous material which means ε = 0 the formula in Proposition 4.1 coincides with the form in [15], [26] and, furthermore, the condition (4.17) implies nonnegativity of Re[â 0 ], which corresponds to the results in [3], [22].…”

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

“…For example, any uniform pressure force field is well controlled. See [6] for other examples of well-controlled tractions which are independent of the unknown crack. Now we state our main result.…”

“…In the following steps we consider only the case when µ 1 = µ 2 and see [6,7] for the case when µ 1 = µ 2 .…”

“…The aim of this expository paper is to report a recent application [6,7] of this method to an inverse problem for the crack in an elastic body in which the governing equation becomes an elliptic system. 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 the elastic plate which is in the both of anisotropic and isotropic.…”

“…Under the condition (2.2) one knows the existence and uniqueness of u in a suitable function space. In [6,7] we considered the following problem and gave an answer by using the enclosure method.…”