Energy dissipation due to frictional shake-down on a closed crack subjected to shear

The behaviour of a horizontal crack, subjected to cyclic shear and normal compressive stresses, is investigated with the aim of studying the shake-down and alternating plasticity phenomena. The analysis is carried out by means of the displacement discontinuity numerical method, conveniently modified so as to simulate the development of frictional stresses on the crack surfaces. The assumptions that the crack does not propagate and that the material behaves elastically are made. The critical values of the physical and geometrical parameters which determine the occurrence of frictional shake-down or alternating plasticity are identified. An evaluation of the amount of energy dissipated because of alternating plasticity is also provided.