Dynamics of an elastic punch on an elastic half-plane with crack formation

The dynamics of buildings and structures in an earthquake zone is studied relying on a model boundary value problem describing the dynamics of an elastic punch on an elastic half-plane under diffraction and refraction of waves generated by stress release on a crack. The problem is solved by applying an explicit difference scheme constructed using the method of bicharacteristics combined with dimensional splitting. The problems of wave diffraction and refraction by an elastic inclusion in the release of vertical and shear stresses on a horizontal crack in an elastic half-plane are considered, which model the dynamics of seismic processes in the formation of mode I and II cracks. Computer experiments are performed for media with various elastic parameters and various punch–crack distances. Their results are presented in the form of oscillograms on the ground surface and the punch, as well as diffraction displacement velocity fields and stress tensor invariants in the medium and the punch.