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Buckling of spherical shells adhering onto a rigid substrate
1Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan. komura@comp.metro-u.ac.jp
The European Physical Journal. E, Soft Matter
|November 18, 2005
Summary
This study investigates spherical shell deformation on substrates, revealing adhesion-induced buckling transitions analogous to liquid-solid phase changes. A universal ratio predicts buckling independent of shell size.
Area of Science:
- Materials Science
- Physics
- Computational Mechanics
Background:
- Spherical shells adhering to substrates experience deformation due to van der Waals forces.
- Understanding shell conformation is crucial for predicting material behavior under adhesion.
Purpose of the Study:
- Investigate the deformation and buckling of spherical shells on rigid substrates under van der Waals attraction.
- Characterize deformation regimes and identify critical points for adhesion-induced buckling transitions.
Main Methods:
- Numerical minimization using the conjugate gradient method to minimize elastic and adhesion energies.
- Systematic variation of dimensionless parameters (Cs/epsilon, Cb/epsilon) to explore deformation regimes.
- Analysis of shell geometry and buckling transitions.
Main Results:
- Identified four deformation regimes: small deformation, disk formation, isotropic buckling, and anisotropic buckling.
- Observed both discontinuous and continuous buckling transitions, analogous to phase transitions in van der Waals liquids/gels.
- Determined a critical point for buckling and a universal ratio (2-3) of indentation length to shell thickness at transition, independent of shell size.
Conclusions:
- Adhesion-induced buckling transitions are governed by elastic and adhesion energies.
- The critical indentation length for buckling is predictable based on shell elastic constants.
- The universal ratio observed has implications for various experimental systems from nanoscale to macroscale.
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