By introducing unknown Level-Sets fields on contact interface, the Signorini-Moreau dynamic contact conditions are written as equations. From this, a new continuous hybrid weakstrong formulation for dynamic contact between deformable solids is derived. In the global problem, the Level-Sets like fields are the intrinsic contact unknown ones. This problem is discretized by means of time, space and collocation schemes. Some numerical experimentations are carried out, showing the effectiveness of our approach. The paper is ended by showing a promising application of the multiscale Arlequin method to the multiscale impact problems.