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From:
K Tamura, S Komura and T Kato (Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan),
"Adhesion induced buckling of spherical shells", J. Phys.: Condens. Matter 16 No 39 (6 October 2004) L421-L428 doi:10.1088/0953-8984/16/39/L01
ABSTRACT: Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters Cs/ε and Cb/ε, where Cs and Cb are respectively the stretching and the bending constants, and ε is the depth of the van der Waals potential. As a function of Cb/ε, we find both continuous and discontinuous buckling transitions for small and large Cs/ε, respectively, which is analogous to van der Waals fluids or gels. Some scaling arguments are employed to explain the adhesion induced buckling transition. This slide shows various typical final configurations of the adhering shell as the combination of Cs/ε and Cb/ε is varied.
There are four qualitatively distinct patterns of deformation as classified from (a) to (d) in this figure. For case (a) when both Cs/ε and Cb/ε are large enough, the shell hardly deforms in spite of the adhesion, and keeps its spherical shape. As both values are reduced, we observe case (b) where a flat contact disc develops at the bottom of the shell. Further decrease of Cb/ε results in the buckling of the shell as illustrated in case (c). In such a configuration, both the stretching and the bending energies are localized at a narrow `bending strip' of contact. For case (d) with still smaller Cb/ε, it becomes energetically favourable to create a polygonal structure composed of a number of ridges joined by the d-cones. The number of ridges (four in the case of (d)) depends on the strength of the vdW [van der Waals] attraction, which will be reported separately. In contrast to spherical shells, the buckling phenomenon has never been observed for elastic tubes.
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