The damage mechanics approach is based on the assumption that the density of microcracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the linear size of the volume considered. An intensive damage variable can be introduced for a representative volume, which includes lots of small cracks. The damage variable is related to the reduction of the rigidity of a spatial domain relative to the modulus of an ideal crack free solid. The present damage rheology model [Lyakhovsky et al., 1997] treats two aspects of the physics of damage:
(1) A mechanical aspect, namely the sensitivity of the macroscopic elastic shear modulus to distributed cracks and to the sense of loading, and
(2) a kinetic aspect, namely the evolution of damage(degradation/recovery of elasticity) in response to loading.
We study the coupled evolution of earthquakes and faults in a model consisting of a seismogenic upper crust governed by damage rheology, over a viscoelastic substrate.
Numerical simulations in a three dimensional realization of the model reproduce the main features of rock behavior including localization of damage to friction-like shear bands.
New 3-D results: Damage in cylinder under uniaxial loading