再论弹性规则波浪面的接触
The contact of elastic regular wavy surfaces revisited
摘要：
我们重温经典问题的弹性固体与二维波浪表面挤压对弹性平坦的半空间从无穷小到完全接触。通过大量的数值计算和分析推导，我们发现以前被忽视的过渡制度。特别是在接触面积和周长、平均压力和接触压力概率密度随施加载荷的变化中可以看到这些变化。这些转变与接触区域形状相关，接触区域形状受长程弹性相互作用的影响。我们的分析一般随机粗糙表面的影响，类似的局部过渡连续发生在分离的区域或合并接触区。我们表明，零接触压力的概率密度是非零的完全接触。这可能意味着重新考虑在部分接触时应用Escherson模型的必要条件，并指导与数值模拟的比较。我们还解决了离散几何形状的接触周长的评价和Westergaard的三维几何形状的解决方案的适用性。
英文摘要：
We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is non-zero at full contact. This might suggest revisiting the conditions necessary for applying Persson's model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard's solution for three-dimensional geometries.
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