Buckling instability

Nolle AJ, Rubner MF, Cohen RE (2005) Determining the Young s modulus of polyelectrolyte multilayer films via stress-induced mechanical buckling instabilities. Macromolecules 38 5367-5370... 

Keywords wrinkling Thin-film Elastomeric polymer Polydimethylsiloxane Patterns Deformation Surfaces Self-assembly Polyelectrolyte multilayer films Thin-films Polymer brushes Colloidal crystallization Mechanical-properties Assembled monolayers Buckling instability Elastomeric polymer Tobacco-mosaic-virus Soft lithography Arrays... 

Fig. 3 A typical situation in which wrinkles occur in the presence of a macroscopic stress is schematically depicted A thin sheet is exposed to a uniaxial macroscopic deformation (1). As a consequence, the sheet is compressed in the direction perpendicular to the elongation axis and the reacts by a buckling instability. Wrinkles are formed, which however relax as the macroscopic strain is released (2), unless plastic deformations occur in the macroscopically stressed state...

A possibility for the formation of more complex patterns is the use of prepatterned substrates as presented by several authors by either masking the surface partially to avoid the formation of a hard layer in the masked regions [19] or topographical prepatterning, where a relief structure is modified in order to wrinkle [15-17, 34], Periodic porous structures have been reported to undergo pattern transformation due to buckling instabilities when external forces are applied. This results in more complex hierarchical structures [35-37],... 

Volynskii AL, Bazhenov S, Lebedeva OV, Bakeev NF (2000) Mechanical buckling instability of thin coatings deposited on soft polymer substrates. J Mater Sci 35 547-554... 

Jiang C, Singamaneni S, Merrick E, Tsukruk VV (2006) Complex buckling instability patterns of nanomembranes with encapsulated gold nanoparticle arrays. Nano Lett 6 2254-2259... 

Another type of instability arises from the coupling between and or u. This may be described as a buckling instability. The analysis is very similar except that a compressive stress is applied parallel to the columns. At a critical value of the stress given by... 

Evans, E.A. 1983. Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests. Biophys. J. 43 27-30. 

The out-of-plane equilibrium of a plate subject to in-plane forces Nx, Ny and Nxy which give rise to buckling instability is defined by... 

Bending and Buckling Instabilities of Free Liquid Jets... 

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