Vol. 6, No. 9-10, 2011

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ISSN: 1559-3959
Turtle shell and mammal skull resistance to fracture due to predator bites and ground impact

David L. Hu, Kelly Sielert and Michael Gordon

Vol. 6 (2011), No. 9-10, 1197–1211
Abstract
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We investigate the relation between the thickness and diameter of naturally occurring shells, such as the carapaces of turtles and the skulls of mammals. We hypothesize that shells used for different protective functions (for example, protection against headbutting or falling on the ground) will exhibit different power-law trends for shell thickness and diameter. To test this hypothesis, we examine over 600 shells from museum collections with diameters between 1 and 100 cm. Our measurements indicate that eggs, turtle shells, and mammalian skulls exhibit clear and distinct allometric trends. We use a theoretical scaling analysis based on elastic thin shell theory to show that the trends observed are consistent with the corresponding protective functions hypothesized. We thus provide theoretical evidence that shells can be classified by their protective function.

Keywords
strength, function, protection, shells, allometry
Supplementary material

PDF file containing table of lengths and thicknesses of turtle shells and skulls

Milestones
Received: 8 November 2010
Accepted: 24 March 2011
Published: 15 January 2012
Authors
David L. Hu
Schools of Mechanical Engineering and Biology
Georgia Institute of Technology
801 Ferst Drive
Atlanta, GA 30332-0405
United States
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, NY 10012-1185
United States
Kelly Sielert
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, NY 10012-1185
United States
Michael Gordon
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, NY 10012-1185
United States