# A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth

## TL;DR

This paper introduces a comprehensive 3D computational model that simulates mollusk shell development by coupling surface accretion and volume growth, providing insights into the morpho-elastic mechanisms shaping shell morphology.

## Contribution

It presents a novel, general computational framework that integrates pre-existing shell shape, surface accretion, and volume growth to explain shell morphogenesis.

## Key findings

- The model captures stepwise shell growth and deformation patterns.
- Growth rates and initial geometries significantly influence shell morphology.
- Connections to complex shell ornamentations are demonstrated.

## Abstract

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell's morphology. Connections are made to a range of complex shells ornamentations.