Institute of Materials Simulation, Department of Materials Science, Friedrich-Alexander Universität Erlangen-Nürnberg, Dr.-Mack-Straße 77, 90762 Fürth, Germany.
Institute of Materials Simulation, Department of Materials Science, Friedrich-Alexander Universität Erlangen-Nürnberg, Dr.-Mack-Straße 77, 90762 Fürth, Germany and School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China.
Phys Rev Lett. 2018 Sep 21;121(12):125501. doi: 10.1103/PhysRevLett.121.125501.
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 τ that, at failure, approaches the value τ=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.
我们提出了一种用于无序材料蠕变的介观弹塑性模型，该模型考虑了由内应力耦合的局部变形事件的温度相关随机激活，从而导致集体雪崩动力学。我们通过引入局部强度的损伤来推广这个随机塑性模型，该局部强度会随着局部塑性应变的增加而按统计平均值减小。该模型可以根据与蠕变速率的有限时间奇点相伴的灾难性剪切带中的应变局部化来描述失效。失效前的雪崩统计特征在于下降的雪崩指数 τ，在失效时，τ趋近于典型的临界分支过程的 1.5 值 τ=1.5。平均雪崩速率作为失效时间的函数呈现出反向 Omori 定律。两次雪崩之间的时间分布与地震统计的流行病型余震序列 (ETAS) 模型一致。
