Mechanics of an intimate contact between solid bodies is of key importance to a variety of scientific and engineering disciplines. However, currently, we can only quantify shallow elastic contacts between geometrically well-defined homogeneous materials. In this work we expand the classical formulations in Hertzian contact mechanics and derive an analytical description of a contact with an inhomogeneous material that emerges in numerous synthetic, geological and biological systems. The developed expression is successfully validated using static and dynamic nanoindentation-based measurements across a silicon/silicon dioxide interface. The presented experimental, numerical and theoretical framework is a stepping-stone towards establishing an analytical description of contact with complex structures.

固体之间紧密接触的力学对各种科学和工程学科至关重要。然而，目前，我们只能量化几何定义明确的均质材料之间的浅层弹性接触。在这项工作中，我们扩展了赫兹接触力学中的经典公式，并导出了与出现在众多合成、地质和生物系统中的非均质材料的接触的分析描述。使用静态和动态基于纳米压痕的测量在硅/二氧化硅界面上成功验证了开发的表达式。所提出的实验、数值和理论框架是建立与复杂结构接触的分析描述的垫脚石。