An AFM-based nanoindentation of a spherical particle absorbed on a corrugated surface of rigid substrate is considered in the framework of continuum mechanics. The corresponding problem of unilateral frictionless contact with multiple contact zones is formulated using isotropic infinitesimal elasticity. Both the AFM probe surface and the surfaces of rigid supports, which are exposed to contact with the elastic sphere, are assumed to be spherical. The method of matched asymptotic expansions is utilized for constructing the leading order asymptotic model of multiple contact. Explicit formulas are derived for the force-displacement relationship and the incremental indentation stiffness. It is shown that the difference between the one-point contact and the multi-point contact (e.g., with two and three local supports) is found to be significant. The case of tight hexagonal packing of the support spheres is considered in detail and illustrated by a comparison with the Hertzian theory of local contact.

在连续力学的框架内考虑了基于AFM的球形颗粒在刚性基材的波纹表面上吸收的纳米压痕。使用各向同性无穷小弹性来阐述与多个接触区域的单侧无摩擦接触的相应问题。假定AFM探针表面和暴露于与弹性球体接触的刚性支撑体表面均为球形。利用匹配渐近展开法构造多接触的前导渐近模型。推导出力-位移关系和压痕刚度增量的明确公式。结果表明，单点接触和多点接触（例如，具有两个和三个局部支撑）之间的差异是显着的。