Finite Element Modeling of the Nano-scale Adhesive Contact and the Geometry-based Pull-off Force

Nano-scale adhesive contact mediated by intermolecular van der Waals forces has become a typical fundamental problem in many areas. Interpretation and control of the strength and efficiency of the nano-scale adhesive contacts require a proper modeling considering the actual interfacial forces, the varying contact area, and clearance. In this article, the finite-element (FE) method is developed to model the nano-scale adhesive contact of elastic bodies with an adhesive pressure derived from the interatomic interaction Lennard-Jones potential, which permits numerical solutions for a variety of interface geometries. Compared with the analytical results from conventional Hertz, JKR, and DMT models, the validity of the FE model is verified. For nano-scale contact, the assumption of equivalent radius adopted in the Hertz model is initially investigated and proved to be improper for nano-scale adhesive contact due to the distribution variations of interfacial force caused by local contact geometry. Then adhesive contact behaviors of four typical nano-scale contact geometries inspired by tip shapes of bio-adhesive pads are investigated in detail, which are flat punch tip, sphere tip, mushroom tip, and empty cup tip. The simulation results indicate that the nano-scale tip geometry plays a dominant role on the pull-off strength. Within the investigated geometries, cup tip results in a highest adhesion efficiency followed by flat punch tip, sphere tip, and mushroom tip, respectively, which are highly geometry dependent and verified by former experimental results. The dominant effect is found coming from the contact area ratio of the adhesive area to the sticking area or the whole contact area. The FE modeling can serve a useful purpose in revealing the nano-scale geometry-based adhesion contact for surface topography design in MEMS to avoid stiction failure and for the artificial sticky feet in bionics to increase adhesion strength.