Skip to main content Accessibility help


  • A. ERLICH (a1) (a2), R. HOWELL (a3) (a4) (a2), A. GORIELY (a5), R. CHIRAT (a6) and D. E. MOULTON (a5)...


Mollusc seashells grow through the local deposition and calcification of material at the shell opening by a soft and thin organ called the mantle. Through this process, a huge variety of shell structures are formed. Previous models have shown that these structural patterns can largely be understood by examining the mechanical interaction between the deformable mantle and the rigid shell aperture to which it adheres. In this paper we extend this modelling framework in two distinct directions. For one, we incorporate a mechanical feedback in the growth of the mollusc. Second, we develop an initial framework to couple the two primary and orthogonal modes of pattern formation in shells, which are termed antimarginal and commarginal ornamentation. In both cases we examine the change in shell morphology that occurs due to the different mechanical influences and evaluate the hypotheses in light of the fossil record.


Corresponding author


Hide All
[1] Checa, A., “A model for the morphogenesis of ribs in ammonites inferred from associated microsculptures”, Palaeontology 37 (1994) 863888;
[2] Chirat, R., Moulton, D. E. and Goriely, A., “Mechanical basis of morphogenesis and convergent evolution of spiny seashells”, Proc. Natl Acad. Sci. USA 110 (2013) 60156020;
[3] Dagys, A. S., Bucher, H. and Weitschat, W., “Intraspecific variation of parasibirites kolymensis bychkov (ammonoidea) from the lower triassic (spathian) of arctic asia”, Mitteilungen aus dem Geologisch-Paläontologischen der Institut Universität Hamburg 83 (1999) 163178.
[4] Erlich, A., “Growth laws in morphoelasticity”, Ph. D. Thesis, University of Oxford, 2017.
[5] Erlich, A., Moulton, D. E., Goriely, A. and Chirat, R., “Morphomechanics and developmental constraints in the evolution of ammonites shell form”, J. Exp. Zool. B 326 (2016) 437450; doi:10.1002/jez.b.22716.
[6] Howell, P., Kozyreff, G. and Ockendon, J., Applied solid mechanics, 43 (Cambridge University Press, Cambridge, UK, 2009); doi:10.1017/CBO9780511611605.
[7] Hutson, M. S. and Ma, X., “Mechanical aspects of developmental biology: perspectives on growth and form in the (post)-genomic age”, Phys. Biol. 5 (2008) 015001; doi:10.1088/1478-3975/5/1/015001.
[8] Mammoto, T., Mammoto, A. and Ingber, D. E., “Mechanobiology and developmental control”, Ann. Rev. Cell Dev. Biol. 29 (2013) 2761; doi:10.1146/annurev-cellbio-101512-122340.
[9] Moulton, D. E., Goriely, A. and Chirat, R., “Mechanical growth and morphogenesis of seashells”, J. Theoret. Biol. 311 (2012) 6979; doi:10.1016/j.jtbi.2012.07.009.
[10] Moulton, D. E., Goriely, A. and Chirat, R., “The morpho-mechanical basis of ammonite form”, J. Theoret. Biol. 364 (2015) 220230; doi:10.1016/j.jtbi.2014.09.021.
[11] Moulton, D. E., Lessinnes, T. and Goriely, A., “Morphoelastic rods. Part 1: a single growing elastic rod”, J. Mech. Phys. Solids 61 (2012) 398427; doi:10.1016/j.jmps.2012.09.017.
[12] Nelson, C. M., Jean, R. P., Tan, J. L., Liu, W. F., Sniadecki, N. J., Spector, A. A. and Chen, C. S., “Emergent patterns of growth controlled by multicellular form and mechanics”, Proc. Natl Acad. Sci. USA 102 (2005) 1159411599; doi:10.1073/pnas.0502575102.
[13] O’Keeffe, S. G., Moulton, D. E., Waters, S. L. and Goriely, A., “Growth-induced axial buckling of a slender elastic filament embedded in an isotropic elastic matrix”, Intl J. Non-Linear Mech. 56 (2013) 94104; doi:10.1016/j.ijnonlinmec.2013.04.017.
[14] Raup, D. M., “Geometric analysis of shell coiling: coiling in ammonoids”, J. Paleontol. 41 (1967) 4365;
[15] Rodriguez, E. K., Hoger, A. and McCulloch, A. D., “Stress-dependent finite growth in soft elastic tissues”, J. Biomech. 27 (1994) 455467; doi:10.1016/0021-9290(94)90021-3.
[16] Simkiss, K. and Wilbur, K. M., Biomineralization (Academic Press, New York, 1989);
MathJax is a JavaScript display engine for mathematics. For more information see


MSC classification

Related content

Powered by UNSILO


  • A. ERLICH (a1) (a2), R. HOWELL (a3) (a4) (a2), A. GORIELY (a5), R. CHIRAT (a6) and D. E. MOULTON (a5)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.