Abstract
We report a phenomenon of phase separation that relates in many aspects to Yves Couder's work: an inflatable architectured elastomer plate, expected to expand homogeneously in its plane, buckles instead widely out-of-plane into very complex shape when internal pressure is applied. We show that this morphogenetic pattern formation is due to a two-dimensional elastic phase separation, which induces incompatible patchy non-Euclidean reference metric.
Highlights
Morphogenesis has been one of the subjects of interest of Yves Couder, with a strong contribution on how geometry and mechanics play a role in plant spatial organisation of organs [1, 2], and shape regulation [3]
We have reported in this article a surprising shape morphogenesis from an uniform object, expected to expand uniformly
In contrast with the shape-morphing triggered by programmed inhomogeneous in-plane expansion, here the internal structure of the plate is identical everywhere, but phase separation induces area with very large expansion to co-exist with regions with very little expansion
Summary
Morphogenesis has been one of the subjects of interest of Yves Couder, with a strong contribution on how geometry and mechanics play a role in plant spatial organisation of organs [1, 2], and shape regulation [3]. When a pressure p is imposed in this internal chamber, which has a internal structure everywhere identical, we can expect a uniform response of the material, so that the plate should expand everywhere by the same factor. We show that several states may be attained for the same imposed internal pressure and a phase separation instability is expected; the coexistence of the two phases (in strongly different stretch state and geometrically incompatible) explains the complex shapes observed
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