Geometry, Elasticity, Growth: The Connection Between Cowrie Growth Dynamics and Shell Form

Thin elastic sheets are currently a hot topic in soft matter physics. We propose a new model illustrating how the physics of bending and wrinkling sheets could underlie the geometry of Cowrie Seashells, offering both qualitative and quantitative insights. This work suggests generally new approaches to the mechanics underlying biological development. Despite both the cowry's import -- in monetary history and as a collector’s item -- and a rich history of seashell modeling, we are the first to mechanistically consider cowrie form at all, let alone couple growth, elasticity, and form to recapitulate the shape of the central spiral, the thickening of the shell base, and the ridge-like teeth which form at the shell opening. By conecting elasticity with the biological processes of shell repair and body growth, we suggest that most aspects of form are emergent from the developmental decision to extend the mantle and extrude it over the shell instead of standard volumetric growth. In addition to our theoretical results, we test our model against both published and reported data, suggest previously unreported scaling relations, and demonstrate methods for extracting geometrical information from both three-dimensional scans and two dimensional images.