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.
Issue Section:
Research Papers
1.
Allen
, H. G.
, 1969, Analysis and Design of Structural Sandwich Panels
, Pergamon
, New York
.2.
Genzer
, J.
, and Groenewold
, J.
, 2006, “Soft Matter With Hard Skin: From Skin Wrinkles to Templating and Material Characterization
,” Soft Mater.
1539-445X, 2
, pp. 310
–323
.3.
Bowden
, N.
, Brittain
, S.
, Evans
, A. G.
, Hutchinson
, J. W.
, and Whitesides
, G. M.
, 1998, “Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer
,” Nature (London)
0028-0836, 393
, pp. 146
–149
.4.
Efimenko
, K.
, Rackaitis
, M.
, Manias
, E.
, Mahadevan
, L.
, and Vaziri
, A.
, 2005, “Nested Self-Similar Wrinkling Patterns in Skins
,” Nat. Mater.
1476-1122, 4
(4
), pp. 293
–297
.5.
Chen
, X.
, and Hutchinson
, J. W.
, 2004, “Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates
,” ASME J. Appl. Mech.
0021-8936, 71
, pp. 597
–603
.6.
Mahadevan
, L.
, and Rica
, S.
, 2005, “Self-Organized Origami
,” Science
0036-8075, 307
, pp. 1740
.7.
Huang
, Z. Y.
, Hong
, W.
, and Suo
, Z.
, 2005, “Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 2101
–2118
.8.
Skalak
, R.
, Zargaryan
, S.
, Jain
, R. K.
, Netti
, P. A.
, and Hoger
, A.
, 1996, “Compatibility and the Genesis of Residual Stress by Volumetric Growth
,” J. Math. Biol.
0303-6812, 34
, pp. 889
–914
.9.
Ben Amar
, M.
, and Goriely
, A.
, 2005, “Growth and Instability in Elastic Tissues
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 2284
–2319
.10.
Richman
, D. P.
, Stewart
, R. M.
, Hutchinson
, J. W.
, and Caviness
, V. S.
, Jr., 1975, “Mechanical Model of Brain Convolutional Development
,” Science
0036-8075, 189
, pp. 18
–21
.11.
Toro
, R.
, and Burnod
, Y.
, 2005, “A Morphogenetic Model for the Development of Cortical Convolutions
,” Cereb. Cortex
1047-3211, 15
, pp. 1900
–1913
.12.
Steele
, C. R.
, 2000, “Shell Stability Related to Pattern Formation in Plants
,” ASME J. Appl. Mech.
0021-8936, 67
, pp. 237
–247
.13.
Kücken
, M.
, and Newell
, A. C.
, 2004, “A Model for Fingerprint Formation
,” Europhys. Lett.
0295-5075, 68
(1
), pp. 141
–146
.14.
Tanaka
, T.
, Fillmore
, D.
, Sun
, S.-T.
, Nishio
, I.
, Swislow
, G.
, and Shah
, A.
, 1980, “Phase Transitions in Ionic Gels
,” Phys. Rev. Lett.
0031-9007, 45
, pp. 1636
–1639
.15.
Boudaoud
, A.
, and Chaïeb
, S.
, 2003, “Mechanical Phase Diagram of Shrinking Cylindrical Gels
,” Phys. Rev. E
1063-651X, 68
, p. 021801
.16.
Tanaka
, T.
, Sun
, S.-T.
, Hirokawa
, Y.
, Katayama
, S.
, Kucera
, J.
, Hirose
, Y.
, and Amiya
, T.
, 1987, “Mechanical Instability of Gels at the Phase Transition
,” Nature (London)
0028-0836, 325
, pp. 796
–798
.17.
Tanaka
, H.
, and Sigehuzi
, T.
, 1994, “Surface-Pattern Evolution in a Swelling Gel Under a Geometrical Constraint: Direct Observation of Fold Structure and its Coarsening Dynamics
,” Phys. Rev. E
1063-651X, 49
, pp. R39
–R42
.18.
Mora
, T.
, and Boudaoud
, A.
, 2006, “Buckling of Swelling Gels
,” Eur. Phys. J. E
1292-8941, 20
, pp. 119
–124
.19.
Sharon
, E.
, Roman
, B.
, Marder
, M.
, Shin
, G.-S.
, and Swinney
, H. L.
, 2002, “Buckling Cascades in Free Sheets
,” Nature (London)
0028-0836, 419
, p. 579
.20.
Audoly
, B.
, and Boudaoud
, A.
, 2003, “Self-Similar Structures Near Boundaries in Strained Systems
,” Phys. Rev. Lett.
0031-9007, 91
, p. 086105
.21.
Klein
, Y.
, Efrati
, E.
, and Sharon
, E.
, 2007, “Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
,” Science
0036-8075, 315
, pp. 1116
–1120
.22.
Basu
, S. K.
, McCormick
, A. V.
, and Scriven
, L. E.
, 2006, “Stress Generation by Solvent Absorption and Wrinkling of a Cross-Linked Coating Atop a Viscous or Elastic Base
,” Langmuir
0743-7463, 22
, pp. 5916
–5924
.23.
Landau
, L.
, and Lifchitz
, E.
, 1990, “Théorie de l’élasticité
,” Physique théorique (Tome 7)
. (Éditions Mir), Mir
, Moscow
.24.
Press
, W. H.
, Teukolsky
, S. A.
, Vetterling
, W. T.
, and Flannery
, B. P.
, 2002, Numerical Recipes in C
, Cambridge University Press
, Cambridge, England
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
