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Wrinkling (shown next) of an inner hydrogel layer because it swells when the bilayer is immersed in water

The authors write:
“We designed experiments on tubular bilayer structures made of a hydrogel tube inside a rubber tube, and placed in water where the hydrogel swells. One bilayer tube is initially stress-free, the other is subject to an initial stress achieved by shrink-fit.”

This and the next 2 images are from:

Yangkun Du (1,2), Chaofeng Lue (3,4,5), Congshan Liu (3), Zilong Han (1), Jian Li (1), Weiqiu Chen (1,4,5), Shaoxing Qu (1,4,5) and Michel Destrade (1,2)
(1) Department of Engineering Mechanics, Zhejiang University, Hangzhou, P. R. China
(2) School of Mathematics, Statistics and Applied Mathematics, NUI Galway, Galway, Ireland
(3) Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P. R. China.
(4) Key Lab of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, P. R. China
(5) Soft Matter Research Center, Zhejiang University, Hangzhou 310027, P. R. China

“Prescribing patterns in growing tubular soft matter by initial residual stress”, Soft Matter, Vol. 15, pp 8468-8474, 2019, DOI: 10.1039/c9sm01563a

ABSTRACT: Initial residual stress is omnipresent in biological tissues and soft matter, and can affect growth-induced pattern selection significantly. Here we demonstrate this effect experimentally by letting soft tubes grow in the presence or absence of initial residual stress and by observing different growth pattern evolutions. These experiments motivate us to model the mechanisms at play when a growing bilayer tubular organ spontaneously displays buckling patterns on its inner surface. We demonstrate that not only differential growth, geometry and elasticity, but also initial residual stress distribution, exert a notable influence on these pattern phenomena. Prescribing an initial residual stress distribution offers an alternative or a more effective way to implement pattern selection for growable bio-tissues or soft matter. The results also show promise for the design of 4D bio-mimic printing protocols or for controlling hydrogel actuators.

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