Wrinkling-banding transition in lipid monolayers through Structured Deformations
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Experiments on compressed lipid monolayers show switching between out-of-plane folding and in-plane shear banding of lipid domains; without banding, domains retain a powder-like structure associated with folding. A prior phenomenological study modeled the monolayer as a hyperelastic material with macroscopic softening \cite{Paper-1}. That model reproduced localized shear bands that break domain symmetry and enable in-plane relaxation, but did not explain the physical origin of the softening. Despite this, it provided a first experimentally validated framework linking folding and in-plane relaxation in lipid monolayers and other thin films. % Fluorescence microscopy reveals that lipid domains consist of coexisting liquid-condensed and liquid-expanded phases, which experience not only different out-of-plane conformation but also in-plane rearrangements. These combined sub-microscopic geometric features likely influence the monolayer’s effective macroscopic behavior. Here, we investigate this connection using the framework of Structured Deformations (see e.g. \cite{Paper-2}), a two-scale approach that captures both sub-microscopic rearrangements and macroscopic response.
