We investigate the elasticity of unsupported epithelial monolayers and discover a novel wrinkling mechanism, which relies on finite-thickness effects and surface tension
of the cells. The mechanism results in the same shapes as those seen in thin supported elastic sheets as a consequence of geometric mismatch with the substrate. By using both continuum–mechanics arguments and finite-element simulations, we show that unsupported monolayers can autonomously transition from the expected buckling deformation mode to the wrinkling mode. By introducing an effective stiffness of a phantom substrate, we formally reconcile our theory with the wrinkling of thin sheets, which shows that the combined effects of the finite epithelial thickness and the cells’ surface tension can replace the interaction with a supporting bulk material.
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