The Mathematical Institute, University of Oxford, Eprints Archive

Mechanical growth and morphogenesis of seashells

Moulton, D. E. and Goriely, A. and Chirat, R. (2012) Mechanical growth and morphogenesis of seashells. Proceedings of the National Academy of Sciences . (Submitted)

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Abstract

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional
ornamentation in shells.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1476
Deposited By:Peter Hudston
Deposited On:02 Mar 2012 07:42
Last Modified:02 Mar 2012 07:42

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