Finite-size scaling in the interfacial stiffness of rough elastic contacts
Finite-size scaling in the interfacial stiffness of rough elastic contacts
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DOI：
10.1103/physreve.87.062809
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发表时间：
2013-06-18
影响因子：
2.4
通讯作者：
Persson, Bo N. J.
中科院分区：
文献类型：
--
作者：
Pastewka, Lars;Prodanov, Nikolay;Persson, Bo N. J.
具有微观粗糙界面的两个接触体的总弹性刚度具有完全归因于表面粗糙度的界面贡献K。定量了解K是很重要的，因为它可以支配总的机械响应，因为它是成比例的连续介质理论中的电导率和热导率的界面贡献。数值模拟的依赖性K上施加的压缩压力p名义上平坦的弹性固体的表面粗糙度的范围。在很宽的p范围内，K随p线性上升。在小p处观察到次线性幂律缩放，但模拟显示这是有限尺寸效应。我们推导出准确的，分析表达式的指数和前置因子的这种低压缩放K通过扩展接触力学理论的Rewerson有限大小的系统。与我们的模拟结果一致，这些表达式表明，随着系统尺寸的增加，低压标度制度的开始向低压移动。
The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.