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This is a schematic of the interaction model.
Both the circular filament and the confining spherical sheet are characterized by a Young’s modulus E, Poisson’s ratio ν and mass density ρ. We assume stick–slip Coulomb friction between any contacting surfaces.
This and the next slide are from:
R. Vetter, F.K. Wittel and H.J. Herrmann (Computational Physics for Engineering Materials, IfB, ETH Zurich, Stefano-Franscini-Platz 3, CH-8093 Zurich, Switzerland), “Morphogenesis of filaments growing in flexible confinements”, Nature Communications, Vol. 5, Article number 4437, July 2014, DOI: 10.1038/ncomms5437
ABSTRACT: Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside deformable vesicles or soft tissue-like cell walls, chorions and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements—perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.
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