标题： 摩擦性滑动在双材料界面处的动态不稳定性 显示英文标题

标题： Dynamic instabilities of frictional sliding at a bimaterial interface

摘要： 我们研究了在一般的速率-状态摩擦本构框架内，一个有限高度的可变形固体$H$，稳定地滑动在刚性固体之上时的二维线性稳定性分析，完全考虑了弹性动力学效应。 我们推导了线性稳定性谱，量化了与摩擦本构定律相关的稳定化作用与同时与法向应力变化和界面滑动之间的弹性动力学双材料耦合相关的不稳定化作用以及有限尺寸效应之间的相互作用。 与摩擦本构定律相关的稳定化作用包括速度增强摩擦（即摩擦阻力随滑动速度增加而增加，包括瞬时和稳态条件下的情况）以及对法向应力变化的正则化响应。 我们首先考虑小波数$k$的极限，并证明在这种情况下均匀滑动是普遍不稳定的，无论摩擦定律的具体细节如何。 这种普遍的不稳定性由传播波导样模式介导，其增长最快的模式由满足$k H\!\sim\!{\cal O}(1)$的波数特征，并且增长速率与$H^{-1}$成比例。 然后我们考虑极限$k H\!\to\!\infty$并在此情况下推导出稳定性相图。 我们表明，主要的不稳定性模式以接近膨胀波速的速度向与滑动方向相反的方向传播。 在某些物理参数范围内，以接近剪切波速向滑动方向传播的不稳定性模式也存在。 最后，我们表明在广义速率-状态摩擦模型框架内，对法向应力变化的有限时间正则化响应倾向于促进稳定性。 显示英文摘要

摘要： We study the 2D linear stability analysis of a deformable solid of a finite height $H$, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e.~an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number $k$ limit and demonstrate that homogeneous sliding in this case is universally unstable, independently of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying $k H\!\sim\!{\cal O}(1)$ and by a growth rate that scales with $H^{-1}$. We then consider the limit $k H\!\to\!\infty$ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability.