基于速率状态方程的数值模拟实验研究

Numerical Simulation Experiment Research Based on Rate State Equation

摘要: 在过去的几十年中，我们看到了速率状态方程在理论应用和物理实验的持续进步。然而，尽管它们的效用和广泛使用，基于实验室的摩擦定律及其在自然界的应用有一些缺点。其中最主要的可能是定律的经验性质，以及与实验室条件范围之外的外推结果相关的尺度问题。因此，本文将重点研究经典速率状态方程的推导过程，探究其在正应力不变时静摩擦和动摩擦系数的表达式、正应力变化下摩擦系数的表达式，最后将通过数值模拟计算在速率状态方程下“滑动–保持–滑动”实验和速率分析步实验下摩擦系数的变化。最后得出发现静摩擦系数与摩擦面之间的静摩擦时长的对数呈现明显的线性关系。摩擦系数的确与滑动速率的对数呈负相关。

Abstract: In the past few decades, we have seen continuous progress in the theoretical application and physical experiments of the rate equation of state. However, despite their utility and widespread use, laboratory-based friction laws and their application in nature have a number of drawbacks. Chief among these is probably the empirical nature of the law, and the scaling problems associated with extrapolations beyond the scope of laboratory conditions. Therefore, this paper will focus on the derivation process of the classical rate equation of state, explore the expression of static and dynamic friction coefficients when the normal stress is constant, and the expression of friction coefficient under the change of normal stress. Finally, the change of friction coefficient under the “sliding-holding-sliding” experiment and rate analysis step experiment under the rate equation of state will be calculated by numerical simulation. Finally, it is found that there is an obvious linear relationship between the static friction coefficient and the logarithm of the static friction time. The friction coefficient is indeed negatively correlated with the logarithm of the sliding rate.