Numerical Analyses on the Adhesive Contact between a Rigid Cylinder and an Elastic Half Space

The adhesive contact between a nano-scale two dimensional cylinder and a half-space is investigated. The three-dimension adhesive contact between a three-dimensional sphere and a half-space is fully understood. The JKR model and the DMT model were proposed in 1970’s. The Maugis-Dugdale model was proposed in 1992. Complete numerical analyses, were proposed by Greenwood and Feng in 1997 and in 2000, respectively. However, due to the intrinsic problem of the two-dimensional contact, the development for the adhesive contact between a cylinder and a half-space is much slower. The two-dimensional JKR model has not been proposed until 1996. The two-dimensional Maugis model appeared in 2000 firstly, and is well-developed in 2008. There is no numerical analysis appearing yet. Therefore, the proposed research will use the numerical analysis to investigate the adhesive contact between the two-dimensional cylinder and a half space. The two-dimensional line contact is used to describe the relation between the force and deformation. The Lennard-Jones potential and the Derjaguin’s approximation will be used to describe the force between the cylinder and half space. The governing equation can be obtained from the relation between the deformation and the force between the cylinder and the half space. The governing equation can be solved by the Newton-Raphson method. Since there will be bifurcation for the load-approach figure for large Tabor parameter, the path following method will be used near the turning point. The relation between the contact radius and total load will be found. The pull-off force will also be found. The result of the numerical analyses will be compared with those of the two dimensional JKR and the two dimensional Maugis model. The result is important for the micro/nano contact. It will make an important contribution to the MEMS and biomechanics.

Project ID:PB9807-2064
External Project ID:NSC98-2221-E182-019