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

TL;DR

This paper develops a method to identify the positions of multiple unknown cracks on the junction line of two elastic plates using boundary measurements, aiding nondestructive evaluation of materials.

Contribution

It introduces an explicit extraction formula based on the enclosure method and Kelvin transform for locating cracks from boundary data in elastic plates.

Findings

Successfully derives explicit formulas for crack location extraction.

Applicable to nondestructive testing of welded elastic plates.

Provides a mathematical framework for inverse crack problems.

Abstract

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 has some unknown cracks on the junction line and the governing equation of in-plane displacement is Navier's equation. The problem is to extract information about the location of cracks from the observation data which is a single set of a loading surface traction and the resulted in-plane displacement field on the boundary of the domain. It is shown that the enclosure method combined with the Kelvin transform yields explicit extraction formulae of such information from the observation data.