Protocol dependence for avalanches under constant stress in elastoplastic models

Tristan Jocteur, Eric Bertin, Romain Mari, Kirsten Martens
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引用次数: 0

Abstract

Close to the yielding transition, amorphous solids exhibit a jerky dynamics characterized by plastic avalanches. The statistics of these avalanches have been measured experimentally and numerically using a variety of different triggering protocols, assuming that all of them were equivalent for this purpose. In particular two main classes of protocols have been studied, deformation under controlled strain or under controlled stress. In this work, we investigate different protocols to generate plasticity avalanches and conduct twodimensional simulations of an elastoplastic model to examine the protocol dependence of avalanche statistics in yield-stress fluids. We demonstrate that when stress is controlled, the value and even the existence of the exponent governing the probability distribution function of avalanche sizes strongly depend on the protocol chosen to initiate avalanches. This confirms in finite dimensions a scenario presented in a previous mean-field analysis. We identify a consistent stress-controlled protocol whose associated avalanches differ from the quasi-static ones in their fractal dimension and dynamical exponent. Remarkably, this protocol also seems to verify the scaling relations among exponents previously proposed. Our results underscores the necessity for a cautious interpretation of avalanche universality within elastoplastic models, and more generally within systems where several control parameters exist.
弹塑性模型中恒定应力下雪崩的协议依赖性
在接近屈服转变时,无定形固体会表现出以塑性雪崩为特征的生涩动态。这些雪崩的统计数据已通过实验和数值方法,使用各种不同的触发协议进行了测量,并假定所有协议在此方面都是等效的。特别是对两大类协议进行了研究:受控应变下的变形和受控应力下的变形。在这项工作中,我们研究了产生塑性雪崩的不同协议,并对弹塑性模型进行了二维模拟,以检验屈服应力流体中雪崩统计的协议依赖性。我们证明,当应力受到控制时,雪崩大小概率分布函数的指数值甚至存在与否,在很大程度上取决于启动雪崩时所选择的协议。这证实了之前平均场分析中提出的无限大方案。我们确定了一种一致的应力控制协议,其相关雪崩的分形维数和动态指数与准静态雪崩不同。值得注意的是,该协议似乎还验证了之前提出的指数之间的比例关系。我们的研究结果强调了在弹塑性模型中谨慎解释雪崩普遍性的必要性,以及在存在多个控制参数的系统中谨慎解释雪崩普遍性的必要性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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