Using molecular dynamics we study the dependency of the contact mechanics on the sliding speed when an elastic block (cylinder) with a $cos\left(q_{0}x\right)$ surface height profile is sliding in adhesive contact on a rigid flat substrate. The atoms on the block interact with the substrate atoms by Lennard-Jones potentials, and we consider both commensurate and (nearly) incommensurate contacts. For the incommensurate system the friction force fluctuates between positive and negative values, with an amplitude proportional to the sliding speed, but with the average close to zero. For the commensurate system the (time-averaged) friction force is much larger and nearly velocity independent. For both types of systems the width of the contact region is velocity independent even when, for the commensurate case, the frictional shear stress increases from zero (before sliding) to $\approx 0.1\mathrm{MPa}$ during sliding. This frictional shear stress, and the elastic modulus used, are typical for polydimethylsiloxane rubber sliding on a glass surface, and we conclude that the reduction in the contact area observed in some experiments when increasing the tangential force must be due to effects not included in our model study, such as viscoelasticity or elastic nonlinearity.

中文翻译：

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滑动期间的圆柱-平面接触力学

使用分子动力学，我们研究了当弹性块（圆柱体）具有弹性时，接触力学对滑动速度的依赖性。 $cos（q_{0}X）$表面高度轮廓在刚性平面基板上以粘合剂接触的方式滑动。嵌段上的原子通过Lennard-Jones势能与底物原子相互作用，我们认为是相称的（几乎）是不相称的接触。对于不相称的系统，摩擦力在正负值之间波动，幅度与滑动速度成正比，但平均值接近零。对于相称的系统，（时间平均）摩擦力要大得多，并且几乎与速度无关。对于两种类型的系统，即使在相应的情况下，摩擦剪应力从零（在滑动之前）增加到零时，接触区域的宽度也不受速度影响。$\approx 0.1\mathrm{兆帕}$在滑动过程中。该摩擦剪切应力和所用的弹性模量是在玻璃表面上滑动的聚二甲基硅氧烷橡胶所特有的，并且我们得出结论，在某些实验中，当增加切向力时，接触面积的减小必须归因于我们未包括的效应模型研究，例如粘弹性或弹性非线性。