Curvature-controlled beading in stretched hydrogel cylinders #

Matteo Taffetani, Matthew Hennessy

12:50 Monday in 2Q48.

Part of the Mechanics of hydrogels and poroelastic media session.

Abstract #

Matsuo and Tanaka [1] revealed how a thin, cylindrical hydrogel can accommodate a variety of patterns in response to external stimuli, such as a change in solvent composition or an applied stretch. One of these patterns, corresponding to a beaded or undulating axisymmetric morphology, has caught the attention of researchers due to its similarity to the Rayleigh-Plateau instability in thin jets of fluid. Current modelling of this instability has focused on the competition between bulk elasticity and surface tension. However, this competition only admits the emergence of a long-wavelength instability, which is inconsistent with experimental observations.

In this work we consider a soft elastic cylinder coated by a thin membrane that responds to stretching, bending, and a mismatch against an imposed natural curvature. We minimise the potential energy to obtain the bulk equilibrium equations and the effective boundary conditions generated by the superficial contributions. We then perform a linear stability analysis to derive the relation between the critical stretch at which the critical wavemode of the instability emerges and the material properties of the effective coating. Interestingly, by introducing a competition between the bulk elasticity and an incompatible natural curvature, a beaded pattern can emerge with a finite wavelength. Finally, we carry out a weakly nonlinear analysis to investigate how the localized envelope of the beaded pattern depends on the properties of the coating.

[1] Matsuo, E., Tanaka, T. Patterns in shrinking gels. Nature 358, 482–485 (1992).