Abstract This paper investigates an axisymmetric and frictionless contact problem of a coated elastic substrate pressed onto a rigid foundation with a rigid disc by remoted uniform compressive stress. Such an incomplete contact problem is formulated as a three-parts mixed boundary values problem (MBVP). By means of Hankel transform technique and a new solution derived for a multilayered elastic solid subjected to surface displacement (dislocation), the MBVP is converted to a system of triple integral equations. A series expansion method characterized by expressing the unknown surface displacement as Bessel function series is adopted to solve the triple integral equations. Explicit analytical expressions for contact stress, resultant contact force and Mode-I stress intensity factor are obtained. The accuracy of the present solutions is verified by comparing to the results available in the literatures for the simple cases of a single layer and a homogeneous half space. Numerical studies are also performed to investigate the contact mechanics of coated material under incomplete contact. Results from this study are valuable for the design of coating to protect engineering machine components against third-body abrasive particles or solid contaminants induced contact damage.

中文翻译：

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带涂层的弹性基材和刚性基础之间的不完全接触受到刚性盘的干扰

摘要 本文研究了一个带涂层的弹性基体通过远程均匀压应力压在刚性圆盘刚性基础上的轴对称和无摩擦接触问题。这种不完全接触问题被表述为三部分混合边界值问题 (MBVP)。借助 Hankel 变换技术和针对受到表面位移（位错）的多层弹性固体推导出的新解，MBVP 被转换为三重积分方程组。采用以贝塞尔函数级数表示未知表面位移为特征的级数展开法求解三重积分方程。获得了接触应力、合成接触力和 I 型应力强度因子的显式解析表达式。通过与文献中关于单层和均匀半空间的简单情况的可用结果进行比较，验证了本解决方案的准确性。还进行了数值研究以研究涂层材料在不完全接触下的接触力学。这项研究的结果对于设计涂层以保护工程机械部件免受第三体磨粒或固体污染物引起的接触损坏很有价值。