摩擦粘滑运动前兆的1D模型，允许与实验进行鲁棒比较
1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments
摘要：
我们研究的动态行为的1D弹簧块模型的摩擦时，施加外部载荷从一侧，而不是在所有的块一样，在经典的Burridge-Knopoff模型。从数值和物理的观点来看，这种载荷的变化会产生特殊的困难。为了解决其中的一些困难并澄清一系列模型参数的确切作用，我们从Maegawa等人的最小模型开始。Lett. 38，313，2010），其被提出来再现他们关于粘滑状态中摩擦滑动的前体的实验。通过连续添加（i）内粘度，（ii）界面刚度和（iii）在界面处的初始切向力分布，我们设法（i）避免模型的非物理应力波动，（ii）避免其对空间分辨率的非物理依赖性和（iii）分别提高其与实验结果的一致性。基于这种改进的一维模型的行为，我们开发了一个分析预测的前体的长度作为所施加的切向载荷的函数。并讨论了模型中微观摩擦系数与宏观摩擦系数之间的关系。
英文摘要：
We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.
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