A model of damage mechanics for the deformation of the continental crust

We derive a continuum rheology for the deformation of the continental crust using continuum damage mechanics. It is hypothesized that when a constant strain rate (epsilon)over dot is applied to a solid material, the stress sigma and damage increase until failure occurs, which is analogous to an earthquake. We further assume that this process is repeated, in analogy to the reoccurrence of earthquakes on a fault. Our model assumes that the continental crust behaves elastically below a yield stress sigma(y). Above this stress the continuum deformations can be modeled as a non-Newtonian viscous flow with (epsilon)over dot proportional to (sigma - sigma(y))(n), where n is constant. We derive the modified Omori's law for aftershock decay using a viscoelastic version of our model and get good agreement with observations taking n = 6. Using parameter values appropriate for aftershocks, we obtain a continuum crustal rheology that can explain major orogenies such as the Indian-Asian collision.