Turtle shell and mammal skull resistance to fracture due to predator bites and ground impact

Abstract

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. © 2011 by Mathematical Sciences Publishers.