Abstract
We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes are faster than viscoelastic relaxation, wrinkles that are formed due to remodelling are unable to relax to a configuration that minimises the elastic energy and the sheet is inherently out of equilibrium. We argue that this non-equilibrium regime is of particular interest in biology as it allows the system to access morphologies that are unavailable if restricted to the adiabatic evolution between configurations that minimise the elastic energy alone. Here, we introduce activity using the formalism of evolving target metric and showcase the diversity of wrinkling morphologies arising from out of equilibrium dynamics.
Highlights
Thompson set the mathematical foundation for describing and classifying the astonishing diversity of shapes and form in the living world [1]
We argue that this nonequilibrium regime is of particular interest in biology as it allows the system to access morphologies that are unavailable if restricted to the adiabatic evolution between configurations that minimize the elastic energy alone
By applying an active solid model to viscoelastic thin sheets subject to active structural remodeling, we showed that the interplay between activity and viscous relaxation leads to a diverse morphology of out-of-equilibrium wrinkling patterns
Summary
Thompson set the mathematical foundation for describing and classifying the astonishing diversity of shapes and form in the living world [1]. Example, showed that part of the energy intake is diverted into local elastic deformations leading to prominent spatial and temporal heterogeneities in observed velocity fields [8] Such dynamical heterogeneity is a hallmark of an active glassy state [9], with epithelial cell monolayers being prime examples of such behavior [10,11,12,13]. Bending out of plane can fully or partly remove the residual stresses due to remodeling, depending on whether or not the particular reference state is embeddable in R3 It has been recently argued [22] that viscoelastic relaxation can stabilize cell shapes during morphogenesis. We focus on the regime where active remodeling is faster than both elastic and viscoelastic relaxation, leading to the system being inherently out of equilibrium This regime is expected to be of particular importance to early embryonic development.
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