粗糙表面的粘着接触：数值计算与解析理论的比较
Adhesive contact of rough surfaces: comparison between numerical calculations and analytical theories
摘要：
我们采用数值方法分析了软弹性层与粗糙刚性基底之间的粘附接触。问题的解是通过计算格林函数得到的，格林函数将压力分布与界面处的法向位移联系起来。然后，该问题的形式制定的Fredholm积分方程的第一类与对数内核，和接触面积的边界计算，要求系统的能量是固定的。该方法已被用来研究弹性半无限固体和随机粗糙刚性轮廓之间的粘附接触与自仿射分形几何。我们表明，即使在存在的粘附，真正的接触面积仍然线性依赖于所施加的负载。然后，严格的数值计算结果进行比较，预测的扩展版本的Wellson的接触力学理论，能够处理各向异性表面，作为1D接口。结果表明，对于任何给定的负载，与我们的数值计算相比，Escherson的理论低估了约50%的接触面积。我们发现，这种差异大于在无粘附接触的情况下发现的2D粗糙表面。我们认为，这种增加的差异可能会解释，至少部分地，考虑到Rewerson的理论是一个平均场论的精神，所以它应该更好地为二维粗糙表面，而不是一维粗糙表面。我们还观察到，分离的预测值是非常好的协议与我们的数值计算结果，以及接触压力分布的功率谱密度和固体的弹性位移的指数。因此，我们可以得出结论，Rehlson的理论几乎准确地捕捉到了粗糙接触现象的主要定性行为。
英文摘要：
We have employed a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the prediction of an extended version of the Persson's contact mechanics theory, able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson's theory underestimates the contact area of about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than what is found for 2D rough surfaces in case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson's theory is a mean field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe, that the predicted value of separation is in very good agreement with our numerical results as well as the exponent of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson's theory captures almost exactly the main qualitative behavior of the rough contact phenomena.
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