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Research Papers

The Buckling of a Swollen Thin Gel Layer Bound to a Compliant Substrate

[+] Author and Article Information
Eric Sultan

 Institüt-Lorentz, P.O. Box 9506, 2300 RA Leiden, The Netherlands

Arezki Boudaoud

 Laboratoire de Physique Statistique, UMR8550 du CNRS/ENS/Paris VI/Paris VII, 24 Rue Lhomond, 75231 Paris Cedex 05, France

J. Appl. Mech 75(5), 051002 (Jul 02, 2008) (5 pages) doi:10.1115/1.2936922 History: Received January 25, 2007; Revised June 12, 2007; Published July 02, 2008

Gels are used to design bilayered structures with high residual stresses. The swelling of a thin layer on a compliant substrate leads to compressive stresses. The postbuckling of this layer is investigated experimentally; the wavelengths and amplitudes of the resulting modes are measured. A simplified model with a self-avoiding rod on a Winkler foundation is in semiquantitative agreement with experiments and reproduces the observed cusplike folds.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Top view after swelling of the top layer (thickness h=1mm above a 3cm thick substrate) in a dish of 10cm diameter. The valleys are lighter than the crests. The lighting is not uniform as a dark strip was placed below to increase the contrast.

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Figure 2

Typical geometry and dimensions of the main experimental setup. Plane displacements are constrained by enclosing the whole between two glass plates with a gap of 1mm.

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Figure 3

The swelling process. Partial side views of the gel top layer (intial thickness 4mm) taken at intervals of 3h. A screen with horizontal dark lines was placed at the back to increase the contrast.

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Figure 4

Side view of the gel top layer (colored with ink) after swelling. Thickness h=3mm (after swelling), wavelength λ=8.9mm, and amplitude A=5.1mm.

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Figure 5

View of the gel after taking out one glass plate showing that the cusps did not damage the gel. The swollen layer is oscillating out of plane due to the strong compressive residual stress.

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Figure 6

Geometry of the model

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Figure 7

Numerical equilibrium configurations for three values of the thickness h (a) 1.7mm, (b) 2mm, and (c) 4mm. The swelling ratio of the top layer is 1.8. Its Young’s modulus is Etop=4.6104Pa and Young’s modulus of the substrate Esubs is (a) 292Pa, (b) 375Pa, and (c) 585Pas, respectively.

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Figure 8

Experiments: Wavelength (a) and amplitude (b) of the gel oscillations as a function of the top layer thickness. The wavelength λ was rescaled by the dimensionless coefficient (Esubs∕Etop)1∕3≃0.67. Horizontal errorbars correspond to the (≃1mm) measure error on the thickness h; vertical bars correspond to (typically 10%) fluctuations on the distance between two adjacent folds and their amplitudes.

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Figure 9

Numerics: Wavelength (a) and amplitude (b) of the gel oscillations as a function of the top layer thickness. The wavelength λ was rescaled by the dimensionless coefficient (Etop∕Esubs)1∕3.

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