We consider a damage-based rheology for the ductile rheology of the upper brittle crust. We introduce a well-defined yield stress below which damage does not occur. A damage variable α is introduced, where α is a measure of the microcracking of brittle material. When α = 0 there is no cracking and when α = 1 failure occurs. Following standard damage mechanics, we take dα/dt to be proportional to powers of the excess stress and strain over the yield values. We first consider uniaxial stress. When a constant stress greater than the yield stress is applied, failure will occur after a finite time. This damage theory is in good agreement with the times to failure and acoustic emissions during laboratory studies of the failure of fiberboard. When a constant strain greater than the yield strain is applied, the stress relaxes to the yield stress. This stress relaxation due to damage explains the applicability of Omori's law to aftershock decay. We have also considered the damage behavior of a plate subjected to a constant bending moment. Three regimes of behavior are observed: 1) Elastic behavior if the maximum fiber stress is less than the yield stress; 2) Stress relaxation to a perfectly plastic solution if the applied moment is less than a critical value; and 3) Time dependent failure if the applied moment is greater than a critical value.

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