Fractal geometry and multi-scale mechanics of cephalopod shells
Final Report Abstract
Ammonoids are a group of highly diverse, common, and famous cephalopod fossils. The shells of these now extinct relatives of modern coleoids (e.g., squids and octopuses) and nautiloids (Nautilus and Allonautilus) form an important resource for paleontologists interested in evolutionary dynamics, ancient ecosystems, and biostratigraphy. Contrary to their modern counterparts, ammonoids explored atypical realms of shell morphology, nicely illustrated by Cretaceous heteromorphs such as Nipponites, Diplomoceras, and Turrilites. The other unusual feature of ammonoids is within their shell. A key evolutionary innovation of cephalopods was the transformation of the shell into a buoyancy device. To achieve this, the shell maintains in internal volume of gas that is kept around 1 atmosphere. In order to prevent the compression of this gas volume by the ambient water pressure, the gas is encased into a rigid “tank” formed by the shell wall, and internal walls formed by the posterior mantle tissue; these internal walls are called septa. These septa show a general evolutionary tendency towards increasing degrees of folding while also showing correlation to changing environmental patterns (e.g., transgression-regression cycles) that indicate they might not just be fabricational noise. Understanding the potential functions of these structures—and thereby use morphological changes to tell us something about environmental or ecological changes—has been an ongoing research topic for generations of biologists and paleontologists. Our contribution has been the examination of potential anti-predatory functioning of ammonitic septa through 3D-based methods. These methods include computational mechanics and compression tests of 3D printed geometries. In broad summary, we found that increasingly complex septa can mitigate the danger of localized (point) loads applied on the shell by focusing stress away from the vulnerable shell wall and redistributing stress and strain across the septum itself. While these results do not mean that the septa evolved as a response to increasing predation, they do mean that this is a possibility. This opens up a large number of additional avenues for future research: including searching for evolutionary correlations in the fossil record between predation and septal morphology, further exploration of the mechanical consequences of these unique biological shapes on ceramic strength and toughness, and the interplay between potentially competing evolutionary constraints of septal function, shell hydrodynamics, and energy expenditure in shell construction.
Publications
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Semi-empirical formulation of contact with an interphase boundary. Extreme Mechanics Letters, 50, 101541.
Tadayon, K.; Lemanis, R.; Bar-On, B. & Zlotnikov, I.
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Wet shells and dry tales: the evolutionary ‘Just-So’ stories behind the structure–function of biominerals. Journal of The Royal Society Interface, 19(191).
Lemanis, Robert; Tadayon, Kian; Reich, Elke; Joshi, Gargi; Johannes, Best Richard; Stevens, Kevin & Zlotnikov, Igor
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Fractal-like geometry as an evolutionary response to predation?. Science Advances, 9(30).
Lemanis, Robert & Zlotnikov, Igor
