A Fictitious Domain Method for a Unilateral Contact Problem

The aim of this paper is to present a numerical method for solving the diffraction of elastic waves by cracks with unilateral contact (or Signorini’s) boundary conditions. From a mechanical point of view, the crack can partly close or open when such boundary conditions are assumed. Concerning theoretical aspects, there is no existence result to the dynamic unilateral contact problem for purely elastic media, to our knowledge. However, results are known in the scalar case (see [5, 4]) and for viscoelastic media (see [3]).