Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another
Tallinen, T., & Biggins, J. S. (2015). Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another. Physical Review E, 92 (2), 022720. doi:10.1103/PhysRevE.92.022720
Published inPhysical Review E
©2015 American Physical Society
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. ...