Adhesion Mechanics of Cylindrical Shell


Adhesion between two solid spheres is extensively investigated in many branches of science and technology, especially in terms of the classical Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) theory. However, these models are quite invalid in biological cells, bacteria, or drug delivery microcapsules as these are membranous capsules encapsulating an incompressible liquid. Here we model a thin-wall cylindrical shell adhering to a substrate, rigid or deformable. The intersurface potentials are discussed in two situations: classic Lennard-Jones potential and DLVO potential with a secondary minimum. The shell is modeled as a thin 2-D circular ring with unit width, comprising extensible beam elements. The deformable membrane is modeled as 1-D extensible beam with unit width. Nonlinear deformation is considered. A Dugdale-Barenblatt-Maugis (DBM) cohesive zone approximation is employed to mimic the actual intersurface forces. A linear repulsion is applied to prevent interpenetration of contacting surfaces. The dynamic equations are solved iteratively by explicit Newmark