An inverse problem method for crack detection in viscoelastic materials under anti-plane strain (Q1388299)

We study the problem of crack detection in viscoelastic materials under antiplane strain. The shape of the crack can be determined provided that the history of displacements along the boundary is known until the time \(t\), and the shear stress is known along the boundary at the time \(t\). The problem is ill-posed, and the ill-posedness is reflected in the difficulty of evaluating some of the integrals. A numerical example is shown where the integrals are calculated by using adaptive integration techniques.