滑动摩擦从老化接触统计模型的弛豫
Relaxation of Sliding Friction from a Statistical Model of Aging Contacts
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中文总结 AI 辅助
本文提出一个结合对数老化与幂律接触尺寸分布的最小模型，解析推导出滑动摩擦弛豫函数，揭示中间时间响应随幂律指数呈现平台、对数或幂律衰减，并建立微观接触统计与宏观摩擦弛豫的实验可检验联系。
中文摘要 AI 辅助
突然速度变化后的摩擦弛豫是描述稳定滑动和地震断层稳定性的唯象定律的基础。为了将这种弛豫与微观接触的可测量统计联系起来，我们引入了一个最小模型，该模型结合了接触力的对数老化以及反映分形界面粗糙度的幂律接触尺寸分布，并解析地推导了弛豫函数。根据幂律指数$\alpha$的不同，中间时间响应表现出平台、对数衰减或幂律衰减，这与唯象定律中假设的指数衰减形成对比。该理论为微观接触统计与宏观摩擦弛豫之间提供了实验上可检验的联系。
英文摘要
Frictional relaxation after a sudden velocity change underlies the phenomenological laws that describe the stability of steady sliding and of seismic faults. To connect this relaxation with measurable statistics of microscopic contacts, we introduce a minimal model incorporating logarithmic aging of contact forces and a power-law contact-size distribution reflecting fractal interface roughness, and derive the relaxation function analytically. Depending on the power-law exponent $α$, the intermediate-time response exhibits a plateau, logarithmic decay, or power-law decay, in contrast to the exponential decay assumed in the phenomenological laws. The theory provides experimentally testable links between microscopic contact statistics and macroscopic frictional relaxation.
发表机构
- Kyoto University（京都大学）
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