We study the problem of contact of two elastic half planes (plane deformation), one of which has a wavy surface under the conditions of partial filling of the interface gaps with compressible liquid. The formulated contact problem is reduced to a singular integral equation for the derivative of the height of the interface gaps and its analytic solution is obtained. We axnalyze the contact behavior of this system of bodies for two different levels of loading: on the first level the volume of the gap is larger than the volume of liquid, which does not exert pressure on the surfaces of the bodies, whereas on the second level the load exceeds the threshold value after which the liquid fills the entire space and resists crack closure.

中文翻译：

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用可压缩液体部分填充间隙对弹性体与波状表面接触的影响

我们研究了两个弹性半平面（平面变形）的接触问题，其中一个在界面间隙部分填充可压缩液体的条件下具有波浪形表面。将公式化的接触问题简化为界面间隙高度导数的奇异积分方程，并得到其解析解。我们分析了该物体系统在两个不同载荷水平下的接触行为：在第一水平上，间隙的体积大于液体体积，液体不会对物体表面施加压力，而在第二个水平上，间隙的体积大于液体的体积水平载荷超过阈值，之后液体充满整个空间并阻止裂缝闭合。