The Mathematical Institute, University of Oxford, Eprints Archive

Anticavitation and differential growth in elastic shells

Moulton, D. E. and Goriely, A. (2010) Anticavitation and differential growth in elastic shells. Anticavitation and differential growth in elastic shells . (Submitted)

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Abstract

Elastic anticavitation is the phenomenon of a void in an elastic solid collapsing on itself. Under the action of mechanical loading alone, very few materials admit anticavitation. We study the possibility of anticavitation as a consequence of an imposed differential growth.Working in the geometry of a spherical shell, we seek radial growth functions which cause the shell to deform to a solid sphere. It is shown, surprisingly, that most materials do not admit full anticavitation, even when infinite growth or resorption is imposed at the inner surface of the shell. However, void collapse can occur in a limiting sense when radial and circumferential growth are properly balanced. Growth functions which diverge or vanish at a point arise naturally in a cumulative growth process.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:967
Deposited By:Ruby Hawkins
Deposited On:02 Sep 2010 10:37
Last Modified:09 Feb 2012 16:02

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