Crack Detection in Plane Semilinear Elasticity

Abstract

Let ­$\Omega$ be a two-dimensional semilinear elastic body limited by a known outer boundary $\Gamma$ represented by a Jordan curve and an unknown inner boundary $\gamma$ represented by a finite disjoint union of piecewise $C^1$ Jordan curves. Plane stress is considered. We assume that the Lamé coefficient depends on the spacial variables $x,y$ and the displacements $u,v$. Our main result asserts that $\gamma$ is uniquely determined by the displacements and stresses prescribed on an open portion ${\Gamma }_0$ of $\Gamma$.