Multiscale Mechanics and Optimization of Gastropod Shells

Abstract

A vast majority of mollusks grow a hard shell for protection. The structure of these shells comprises several levels of hierarchy that increase their strength and their resistance to natural threats. This article focuses on nacreous shells, which are composed of two distinct layers. The outer layer is made of calcite, which is a hard but brittle material, and the inner layer is made of nacre, a tough and ductile material. The inner and outer layers are therefore made of materials with distinct structures and properties. In this article, we demonstrate that this system is optimum to defeat attacks from predators. A two-scale modeling and optimization approach was used. At the macroscale, a two-layer finite element model of a seashell was developed to capture shell geometry. At the microscale, a representative volume element of the microstructure of nacre was used to model the elastic modulus of nacre as well as a multiaxial failure criterion, both expressed as function of microstructural parameters. Experiments were also performed on actual shells of red abalone to validate the results obtained from simulations and gain insight into the way the shell fails under sharp perforation. Both optimization and experimental results revealed that the shell displays optimum performance when two modes of failure coincide within the structure. Finally, guidelines for designing two-layer shells were proposed to improve the performance of engineered protective systems undergoing similar structural and loading conditions.