A model of a breathing crack with relaxation damping

Relaxation damping is a phenomenon described recently for contact of two purely elastic bodies with infinite coefficient of friction. If a two-dimensional elastic body containing a mixed-mode crack with no sliding between the crack faces is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears that is independent of dissipation in the elastic material. It is shown that the rate of energy dissipation due to relaxation damping is proportional to the square of the crack length and depends on the ratio of the normal local prestress to the amplitude of the normal local stress oscillations as well as on the phase shift between both oscillations. In the case of low frequency tangential loading with superimposed high frequency normal oscillations, the system acts as a tunable linear damper. Generalization of the model for the three-dimensional case is discussed.