Surface energy outside the contact zone, which is ignored in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft bodies. In this work, based on a simple elastic foundation model for a soft elastic half space with constant surface tension, an explicit expression for the change of surface energy outside the contact zone is proposed for a soft elastic substrate indented by a rigid sphere in terms of two JKR-type variables (δ, a), where a is the radius of the contact zone and δ is the indentation depth of the rigid sphere. The derived expression is added to the classical JKR model to achieve two explicit equations for the determination of the two JKR variables (δ, a). The results given by the present model are demonstrated with detailed comparison with known results reported in recent literature, which verified the validity and robust accuracy of the present method. In particular, the present model confirms that the change of surface energy of the substrate can play an essential role in micro/nanoscale contact of soft materials (defined by , where W is the adhesive energy, is the substrate elasticity, and R is the rigid sphere radius). The present model offers a simpler analytical method for adhesion mechanics of a rigid sphere on a soft elastic substrate when compared with several existing methods proposed in recent literature that request more substantial numerical calculations.
A Refined JKR Model for Adhesion of a Rigid Sphere on a Soft Elastic Substrate
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received December 23, 2018; final manuscript received January 13, 2019; published online March 5, 2019. Assoc. Editor: Yashashree Kulkarni.
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Zhang, L., and Ru, C. Q. (March 5, 2019). "A Refined JKR Model for Adhesion of a Rigid Sphere on a Soft Elastic Substrate." ASME. J. Appl. Mech. May 2019; 86(5): 051004. https://doi.org/10.1115/1.4042574
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