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Turtle shell and
mammal skull resistance to fracture due to predator bites and
ground impact
David L. Hu, Kelly Sielert and Michael Gordon |
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Vol. 6 (2011), No. 9-10, 1197–1211
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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
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Supplementary materialPDF 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
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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 |
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| Michael Gordon | |
| Courant Institute of Mathematical
Sciences New York University 251 Mercer Street New York, NY 10012-1185 United States |
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