基于Hamaker假设的黏着接触弹性模型

Elastic Model of Adhesive Contact Based on Hamaker Hypotheses

为研究微纳米系统中的黏着接触问题,基于Hamaker假设和Lennard-Jones的势能定律,通过积分方法得到了球体与平面间的黏着力,同时结合经典弹性理论建立了一种新型的球体与平面黏着接触的弹性模型．该模型可以同时得到平面轮廓随间距的变形过程及黏着力和平面变形量随间距的变化规律,当球体半径较大时,所建模型与基于Derjaguin近似的黏着模型给出的结果基本一致,随着球体半径的逐渐减小,2种模型的差异逐渐增大,这是由于Derjaguin近似的误差随球体半径的减小而增大引起的．因此,当球体的半径趋近纳米级时,基于Hamaker假设的黏着接触模型消除了Derjaguin近似所带来的误差,可以更加准确地给出黏着力和平面变形量随间距的变化规律．

Based on Hamaker hypotheses and Lennard-Jones potential, the adhesive force between a sphere and a plane is revealed with an integral method. Simultaneously, a novel model of adhesive contact between a rigid sphere and an elastic plane is established to investigate the adhesion problems in micro- and nano-systems, which is capable of obtaining the variations with the distance of the adhesive force, the deformation and the contour of the plane. For a large sphere, the results from the proposed model are coincident with that from the model based on the Derjaguin approximation. For a nano-scale sphere, the discrepancies appear between the two models due to the increased the error of the Derjaguin approximation with decreasing spheres. So for a nano- scale sphere, the proposed model enables to lead more accurate solutions.