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The plots were obtained with the following parameters for Eq. 17: (a) A = 1, b = c = d = 0, (b) A = 1, b = .5, c = d = 0, (c) A = 1, c = .5, b = d = 0, (d) A = d = .7, b = c = 0.
This and the next two slides are from:
Basile Audoly (1) and Arezki Boudaoud (2)
(1) Institut Jean le Rond d’Alembert, UMR 7190 du CNRS, CNRS/UPMC Univ Paris 06, 4 place Jussieu, F-75252 Paris Cedex 05, France
(2) Laboratoire de Physique Statistique, UMR 8550 du CNRS/Paris 6/Paris 7 École normale supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France
“Buckling of a stiff film bound to a compliant substrate—Part I: Formulation, linear stability of cylindrical patterns, secondary bifurcations”, Journal of the Mechanics and Physics of Solids, Vol. 56, No. 7, July 2008, pp.2401-2421, doi:10.1016/j.jmps.2008.03.003
ABSTRACT: The buckling of a thin elastic film bound to a compliant substrate is studied: we analyze the different patterns that arise as a function of the biaxial residual compressive stress in the film. We first clarify the boundary conditions to be used at the interface between film and substrate. We carry out the linear stability analysis of the classical pattern made of straight stripes, and point out secondary instabilities leading to the formation of undulating stripes, varicose, checkerboard or hexagonal patterns. Straight stripes are found to be stable in a narrow window of load parameters only. We present a weakly nonlinear post-buckling analysis of these patterns: for equi-biaxial residual compression, straight wrinkles are never stable and square checkerboard patterns are found to be optimal just above threshold; for anisotropic residual compression, straight wrinkles are present above a primary threshold and soon become unstable with respect to undulating stripes. These results account for many of the previously published experimental or numerical results on this geometry.
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