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Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another.


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Authors

Tallinen, Tuomas 
Biggins, John S 

Abstract

We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer-to-substrate modulus ratio is varied from above unity toward zero, we find a first transition from supercritical smooth folding followed by cusping of the valleys to direct subcritical cusped folding, then another to supercritical cusped folding. Beyond threshold, the high-amplitude fold spacing converges to about four layer thicknesses for many modulus ratios. In three dimensions, the instability gives rise to a wide variety of morphologies, including almost degenerate zigzag and triple-junction patterns that can coexist when the layer and substrate are of comparable softness. Our study unifies these results providing understanding for the complex and diverse fold morphologies found in biology, including the zigzag precursors to intestinal villi, and disordered zigzags and triple junctions in mammalian cortex.

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Keywords

Animals, Cerebral Cortex, Chick Embryo, Computer Simulation, Ferrets, Intestinal Mucosa, Models, Biological, Nonlinear Dynamics

Journal Title

Phys Rev E Stat Nonlin Soft Matter Phys

Conference Name

Journal ISSN

1539-3755
1550-2376

Volume Title

92

Publisher

American Physical Society (APS)
Sponsorship
T. T. acknowledges the Academy of Finland for funding. The computational resources were provided by CSC – IT Center for Science. J.B. acknowledges the 1851 Royal Commission and Trinity Hall Cambridge for funding.