On extracting the positions of multiple unknown cracks that occur on the junction line of two elastic plates

This paper is concerned with the reconstruction issue of an inverse crack problem in a two-dimensional bounded domain, which may have a possible application to the nondestructive evaluation of materials. It is assumed that the domain consists of two elastic plates welded together and contains unknown cracks on the junction line. The governing equation for the in-plane displacement is the Navier equation. The problem is to extract information about the location of cracks from observation data consisting of a single set of applied surface traction and the resulting in-plane displacement field measured on the boundary of the domain. It is shown that the enclosure method combined with the Kelvin transform yields explicit formulae for extracting such information from the observation data.