Periodic patterns and energy states of buckled films on compliant substrates
By Shengqiang Cai, D. Breid, A. Crosby, Zhigang Suo, J. W. Hutchinson. 2011
329 citations recorded by the source corpus.
Thin stiff films on compliant elastic substrates subject to equi-biaxial compressive stress states are observed to buckle into various periodic mode patterns including checkerboard, hexagonal and herringbone. An experimental setting in which these modes are observed and evolve is described. The modes are characterized and ranked by the extent to which they reduce the elastic energy of the film–substrate system relative to that of the unbuckled state over a wide range of overstress. A new mode is identified and analyzed having nodal lines coincident with an equilateral triangular pattern. Two methods are employed to ascertain the energy in the buckled state: an analytical upper-bound method and a full numerical analysis. The upper-bound is shown to be reasonably accurate to large levels of overstress. For flat films, except at small states of overstress where the checkerboard is preferred, the herringbone mode has the lowest energy, followed by the checkerboard, with the hexagonal, triangular, and one-dimensional modes lowering the energy the least. At low overstress, the hexagonal mode is observed in the experiments not the square mode. It is proposed that a slight initial curvature of the film may play role in selecting the hexagonal pattern accompanied by a detailed analysis. An intriguing finding is that the hexagonal and triangular modes have the same energy in the buckled state and, moreover, a continuous transition between these modes exists involving a linear combination of the two modes with no change in energy. Experimental observations of various periodic modes are discussed with reference to the energy landscape. Discrepancies between observations and theory are identified and open issues are highlighted.
Subfields: Control and Systems Engineering, Mechanical Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/d5da3cf57154a7b9c5169e76d537ef650a0c4d70
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In Control and Systems Engineering
In Mechanical Engineering
In Mechanics of Materials
Citations in the corpus
- Advances in Mechanics of Soft Materials: A Review of Large Deformation Behavior of Hydrogels (2015, background): “The buckling of bilayer structures present many interesting buckling patterns, such as the herringbone, labyrinth patterns, peanut, lamellar and hexagonal structures [Cai et al., 2011; Guvendiren et al., 2009].”
- Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates (2011, unknown): “Meanwhile, mechanics of surface wrinkling has been studied extensively over the last decade (e.g., Shield et al., 1994; Groenewold, 2001; Huang and Suo, 2002; Chen and Hutchinson, 2004; Huang and Im, 2006; Jiang et al., 2007; Lee et al., 2008; Audoly and Boudaoud, 2008; Im and Huang, 2008; Sun et al”
- Elasticity and stability of shape-shifting structures (2018, background): “the commonly observed herringbone pattern [29, 30, 33].”