Avalanche behavior in creep failure of disordered materials

We present a mesoscale elastoplastic model of creep in disordered materials which considers temperature-dependent stochastic activation of localized deformation events which are mutually coupled by internal stresses, leading to collective avalanche dynamics. We generalize this stochastic plasticity model by introducing damage in terms of a local strength that decreases, on statistical average, with increasing local plastic strain. As a consequence the model captures failure in terms of strain localization in a catastrophic shear band concomitant with a finite-time singularity of the creep rate. The statistics of avalanches in the run-up to failure is characterized by a decreasing avalanche exponent $\tau$ that, at failure, approaches the value $\tau = 1.5$ typical of a critical branching process. The average avalanche rate exhibits an inverse Omori law as a function of the time-to-failure, whereas the distribution of inter-avalanche times turns out to be consistent with the ETAS model of earthquake statistics.