Self-similar slip instability on interfaces with rate- and state-dependent friction
Self-similar slip instability on interfaces with rate- and state-dependent friction
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具有速率和状态相关摩擦的界面上的自相似滑移不稳定性
DOI：
10.1098/rspa.2016.0254
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Viesca
中科院分区：
文献类型：
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作者：
R. Viesca
我们研究了接触弹性体界面处具有不同滑动速率的摩擦不稳定性的发展。摩擦的演变由滑移率和状态依赖性决定。继 Viesca (2016 Phys. Rev. E 93, 060202(R). (doi:10.1103/PhysRevE.93.060202)) 之后，我们通过变量的适当变化证明了作为动力系统不动点的爆炸解的存在性。这些解决方案显示了简单品种的自相似性：时间和空间的可分离依赖性。对于具有均匀摩擦特性的界面，存在一个单一问题参数。我们检查这些固定点的线性稳定性，因为该问题参数是变化的。具体来说，我们考虑滑移面的两种典型弹性设置，其中表面上点之间的相互作用是局部的或非局部的。我们证明，与弹性相互作用的性质无关，当参数增加到极限值时，固定点在同一物质中失去稳定性：显然是无限的 Hopf 分岔序列。然而，对于任何参数值，由于稳定本征模态的存在，不稳定性的非线性发展即使不是渐近收敛，也会吸引到这些固定点。为了进行比较，我们对原始演化方程进行数值求解，并发现与分析结果精确一致。
We examine the development of a frictional instability, with diverging sliding rate, at the interface of elastic bodies in contact. Evolution of friction is determined by a slip rate and state dependence. Following Viesca (2016 Phys. Rev. E 93, 060202(R). (doi:10.1103/PhysRevE.93.060202)), we show through an appropriate change of variable, the existence of blow-up solutions that are fixed points of a dynamical system. The solutions show self-similarity of the simple variety: separable dependence of time and space. For an interface with uniform frictional properties, there is a single-problem parameter. We examine the linear stability of these fixed points, as this problem parameter is varied. Specifically, we consider two archetypical elastic settings of the slip surface, in which interactions between points on the surface are either local or non-local. We show that, independent of the nature of elastic interactions, the fixed-points lose stability in the same matter as the parameter is increased towards a limit value: an apparently infinite sequence of Hopf bifurcations. However, for any value of the parameter, the nonlinear development of the instability is attraction, if not asymptotic convergence, towards these fixed points, owing to the existence of stable eigenmodes. For comparison, we perform numerical solutions of the original evolution equations and find precise agreement with the results of the analysis.