Morphoelasticity of large bending deformations of cell sheets during development

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination.

Automated summary

The study derives a shell theory for large intrinsic bending deformations by asymptotically expanding three-dimensional incompressible morphoelasticity in the limit of a thin shell, highlighting geometric material anisotropy and the elastic role of cell constriction. Using the invagination of the green alga Volvox as a model developmental event, the results of this theory are shown to differ from those of classical shell theory and reveal how geometric effects stabilize invagination.