We present a mesoscale elastoplastic model of creep in disordered materials, which considers temperature-dependent stochastic activation of localized deformation events that are 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. 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 time to failure. The distribution of interavalanche times turns out to be consistent with the epidemic-type aftershock sequences (ETAS) model of earthquake statistics.

中文翻译：

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无序材料蠕变破坏中的雪崩行为

我们提出了一种无序材料中尺度蠕变的中尺度弹塑性模型，该模型考虑了温度依赖性的局部变形事件的随机激活，该变形事件与内部应力耦合，导致集体雪崩动力学。我们通过引入局部强度来破坏这种随机可塑性模型，该强度在统计平均值上随局部塑性应变的增加而降低。该模型捕获了在灾难性剪切带中的应变局部化以及蠕变速率的有限时间奇异性的故障。失败前雪崩的统计数据以雪崩指数下降为特征$\tau$ 在失败时接近价值 $\tau =1.5$典型的关键分支过程。平均雪崩率表现出大森逆定律，它是失效时间的函数。结果表明，雪崩时间的分布与地震统计的流行型余震序列（ETAS）模型一致。