Anti-plane inverse problem for inclined cracks in the elastic half-space

The present paper is concerned with the reconstruction of position, slope angle and size of a linear crack located in the elastic half-space, in the case of anti-plane (shear) deformation. It is assumed that the input data are given from the measurements of the boundary surface settlement. We first construct Green's function in the half-space with a free boundary line, then formulate respective direct problem as a certain hyper-singular integral equation. Then it becomes clear that the studied inverse problem can be reduced to an optimization problem for a certain non-linear functional. We propose a minimization method based on an advanced random search.