Thin shells are found in nature at scales ranging from viruses to hens' eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus etal. [following paper, Phys. Rev. Lett. 109, 144301 (2012)PRLTAO0031-9007] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells. © 2012 American Physical Society.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported in part by Grant No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (D. V.). A. A. and A. V. are thankful for the support of NSF CMMI Grant No. 1149750. A. B. was supported by ANR-10BLAN-1516. During the completion of this work, we benefited from discussions with A. Lazarus and P. Reis about their experiments on a similar system .
This publication acknowledges KAUST support, but has no KAUST affiliated authors.