Because of the huge specific surface area at the micro/nano scale, inter-surface adhesion and surface effects play a critical role in the behavior of solid-to-solid contact. The inter-surface adhesion originates from the intermolecular traction between two surfaces, while the surface effects, including residual surface stress and surface elasticity, result from the physical discrepancy between the surface atoms and their bulk counterparts. Despite the importance of both effects, theoretically modeling them together is still a challenging open issue because of the nonlinear coupling nature in between. This study is dedicated to the development of a unified theoretical framework with consideration of both inter-surface adhesion and surface effects based on the Gurtin–Murdoch surface elasticity theory. The two effects are integrated into a self-consistent equation concerning surface gaps and interactions, and a novel regularization method is proposed to address the oscillation and singularity of the equation. It is demonstrated that an adhesive contact problem with surface effects can be decomposed into two fundamental issues. One addresses the classical problem without considering residual surface stress or surface elasticity, and the other focuses solely on residual surface stress. Theoretical predictions show that the surface effects suppress or even eliminate the surface deformation and jumping instability during contact, effectively stiffening the solid surfaces. Three types of pull-off force transitions with surface effects are obtained, forming continuous bridges among the rigid (Bradley), soft (JKR), and liquid-like (Young–Dupre) limits. The adhesion transitions considering surface effects in this work are universal, and the existing limits or transitions can be regarded as special cases of this work. Our study provides a further understanding of the adhesive contact between micro/nano solids and may be instructive for practical applications where inter-surface adhesion and surface effects are dominant, such as nanoindentation, micro-electro-mechanical systems, and microelectronics.

中文翻译：

---

微/纳米尺度固体表面之间胶粘剂接触的统一模型


由于微米/纳米尺度上的巨大比表面积，表面间粘附和表面效应在固体与固体接触的行为中起着关键作用。表面间粘附源于两个表面之间的分子间牵引，而表面效应，包括残余表面应力和表面弹性，是由表面原子与其本体对应物之间的物理差异引起的。尽管这两种效应都很重要，但由于两者之间的非线性耦合性质，理论上将它们建模在一起仍然是一个具有挑战性的悬而未决的问题。本研究致力于在 Gurtin-Murdoch 表面弹性理论的基础上开发一个统一的理论框架，同时考虑表面间粘附和表面效应。将这两种效应整合到一个关于表面间隙和相互作用的自洽方程中，并提出了一种新的正则化方法来解决方程的振荡和奇异性。结果表明，具有表面效应的胶粘剂接触问题可以分解为两个基本问题。一个解决经典问题而不考虑残余表面应力或表面弹性，另一个只关注残余表面应力。理论预测表明，表面效应抑制甚至消除了接触过程中的表面变形和跳跃不稳定性，有效地使固体表面变硬。获得了三种具有表面效应的拉拔力过渡，在刚性 （Bradley）、软 （JKR） 和液体 （Young-Dupre） 极限之间形成连续的桥梁。 这项工作中考虑表面效应的粘附过渡是普遍的，现有的限制或过渡可以被视为这项工作的特例。我们的研究进一步了解了微/纳米固体之间的胶粘剂接触，并可能对表面间粘附和表面效应占主导地位的实际应用具有指导意义，例如纳米压痕、微机电系统和微电子学。