Adhesion of an Elastic Convex Shell onto a Rigid Plate

Abstract

Abstract An elastic spherical shell is compressed between two parallel rigid plates and undergoes large geometrical deformation. The convex surface conforms and adheres to the plates. The shell profile and contact stresses under large deformation are obtained numerically using a finite difference method. A thermodynamic energy balance following the classical Johnson-Kendall-Roberts (JKR) model is established to construct the adhesion mechanics, such that the sum of potential energy of the external load, elastic energy stored in the elastic shell, and surface energy to create new surface is minimized. Interrelationship between applied load, approach distance, contact radius, and deformed profile, as well as the "pull-off" phenomenon, are derived. A comparison is made between this model and existing models for a solid sphere in the literature. Keywords: AdhesionEnergy balanceLarge deformationShells ACKNOWLEDGMENTS This work is supported by the National Science Foundation Grant CMMI #0757140. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Notes †There is another related work due to Hencky [H. Hencky. "Uber den Spannungszustand in kreisrunden Platten mit verschwindender Biegungssteifigkeit," Zeitschrift fur Mathematik und Physik 63, 311–317 (1915)]. His classic paper, mentioned for historical reasons only, mentioned for historical reasons only, considers a planar (i.e., zero curvature) circular membrane clamped at the edge being deformed by a uniform pressure. The constitutive relation and membrane stress distribution are derived for large geometrical deformation. The calculation does not consider adhesion or delamination of the membrane. One of a Collection of papers honoring Chung-Yuen Hui, the recipient in February, 2011 of The Adhesion Society Award for Excellence in Adhesion Science, Sponsored by 3M.