Mechanics of Seashell Growth: Examining the relationship between incompatibility, shape, and internal stress

Abstract

Seashells are a fascinating example of surface growth in nature. As they develop, both their macroscopic form and their internal microstructure evolve, with the latter transitioning between different layer sizes and orientations during the shell's growth process. Several studies have examined the morphogenesis of seashells, with some considering the kinematics of growth that lead to different eventual shapes, and others investigating the biochemical pathways of these processes. However, the role of internal mechanical stresses that may develop due to incompatibility has yet to be investigated. In this thesis, we present a framework that models the shell growth continuously, with an aim to investigate the role of internal stresses on the structural changes that have been reported to occur within seashells. Considering an axisymmetric growing body and accounting for surface growth as an arbitrary sequence of addition of incompatible circular rings on its outer perimeter, we study the shape and mechanical forces that can develop throughout the shell's growth. Our findings show that incompatibility has a large impact on the shape of a shell during surface growth, especially during early stages of development. This influence may be crucial in explaining the recorded crystallographic reorientation that is typical to various seashells.