I gave this talk at the British Applied Mathematics Colloquium which took place at Oxford 5th – 8th April 2016. Below you can find the abstract of my talk (see also the conference book of abstracts) as well as the slides.
Ammonites’ shells as mechanical oscillators
A. Erlich1, D.E. Moulton1, A. Goriely1 & R. Chirat2
1 Mathematical Institute, University of Oxford
2 Université Lyon 1
Compared to the intricate patterns observed in seashells, modern 3D printers seem almost primitive. To better understand the emergence of sophisticated patterns in the morphogenesis of seashells, we develop a morpho-elastic model for the growth of ammonites’s shells. Based on fundamental principles of growth and mechanics, we establish a mechanical basis for the relationships between the spiral-shaped coiling pattern, the oscillatory ribbing pattern and elliptic cross-section shape of the shells. Specifically, this is achieved by modeling the stretching, bending and active growth of the soft shell-generating organ. We demonstrate that our model is consistent with Buckman’s Law, which is a gold standard collection of rules about the relationship of geometry and ribbing in ammonite’s shells.