Decoding mathematical mystery of interlocking shells

A mathematical model explains how geometry and mechanical forces combine to generate the interlocking shells of oysters and other bivalves, according to a study. The 2 sides of oyster shells and those of other bivalves fit together seamlessly, protecting the animal inside and continuing to match up precisely even when environmental influences or injuries perturb the shell’s shape as it grows. Derek Moulton and colleagues investigated how the interlocking edges develop physically by creating a mathematical model of shell growth. The shell edges of bivalves and brachiopods grow throughout the animal’s life, each half secreted by a different part of the mantle. The authors considered the geometry and mechanics of each half of the mantle, which are constrained by the influence of one lobe on another and the rigid nature of the shell secreted. The model reveals that a toothed or wavy edge, as opposed to a flat edge, occurs when the mantle grows faster than the shell edge, causing it to buckle. The interlocking pattern is then created and maintained because the mechanical buckling instability is biaxially constrained. In addition, the intricate patterning on some brachiopods is due to a secondary mechanical instability, according to the authors.

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Article # 19-16520: “Mechanics unlocks the morphogenetic puzzle of interlocking bivalved shells,” by Derek E. Moulton, Alain Goriely, and Régis Chirat.

MEDIA CONTACT: Derek E. Moulton, University of Oxford, UNITED KINGDOM; e-mail:

[email protected]