Mechanics of invagination and folding: hybridized instabilities when one soft tissue grows on another
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
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Tallinen, T., & Biggins, J. (2015). Mechanics of invagination and folding: hybridized instabilities when one soft tissue grows on another. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 92 (022720)https://doi.org/10.1103/PhysRevE.92.022720
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/substrate modulus ratio is varied from above unity towards 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 triplejunction 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 triplejunctions in mammalian cortex.
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.
External DOI: https://doi.org/10.1103/PhysRevE.92.022720
This record's URL: https://www.repository.cam.ac.uk/handle/1810/250383
Attribution-NonCommercial 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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