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FIG. 1.
(a) illustrations of the “ping-pong ball instability” in a spherical shell of radius b indented by a rigid plate (gray circle in left panel). Here, a polygonal deformation is observed in simulations (left) and experiments on a plastic spherical cap (right) with dimensionless indentation depth Z0 1⁄4 Z=t 1⁄4 13.2, t the thickness, and t=b 1⁄4 0.01. (Adapted from Ref. [1].)
(b) Axes of the ellipsoids considered here showing the rotational symmetry about the x axis.
(c) Indentation of a highly ellipsoidal shell by a rigid plate causes “anisotropic blistering” of the shell—the contact becomes nonconformal. As the dimensionless indentation Z0 1⁄4 Z=t increases, the pattern develops with additional “blisters” forming. The left panel shows the energy density (high energy density corresponds to regions of compression) as computed in simulations. The right panel shows images from experiments performed on a shell made of poly- vinylsiloxane using our mold and wetting technique.
FROM:
Hamid Ebrahimi (1), Amin Ajdari (2), Dominic Vella (3), Arezki Boudaoud (4), and Ashkan Vaziri (1)
(1) Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
(2) Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA
(3) Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG, United Kingdom
(4)Laboratoire Reproduction et Développement des Plantes & Laboratoire Joliot-Curie, INRA, CNRS, ENS, Université de Lyon, 46 Allée d’Italie, F-69364 Lyon Cedex 07, France
“Anisotropic Blistering Instability of Highly Ellipsoidal Shells”, Phys. Rev. Lett. 112, 094302 – Published 6 March 2014,
DOI: http://dx.doi.org/10.1103/PhysRevLett.112.094302
ABSTRACT: The formation of localized periodic structures in the deformation of elastic shells is well documented and is a familiar first stage in the crushing of a spherical shell such as a ping-pong ball. While spherical shells manifest such periodic structures as polygons, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined “blisters” along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations, and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell’s elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.
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