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Published November 2015 | Submitted
Journal Article Open

Effective Behavior of Nematic Elastomer Membranes


We derive the effective energy density of thin membranes of liquid crystal elastomers as the Γ -limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and due to oscillations in the nematic director that one expects in liquid crystal elastomers. We provide an explicit characterization of the effective energy density of membranes and the effective state of stress as a function of the planar deformation gradient. We also provide a characterization of the fine-scale features. We show the existence of four regimes: one where wrinkling and microstructure reduces the effective membrane energy and stress to zero, a second where wrinkling leads to uniaxial tension, a third where nematic oscillations lead to equi-biaxial tension and a fourth with no fine scale features and biaxial tension. Importantly, we find a region where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling.

Additional Information

© 2015 Springer. (Received November 18, 2014 / Accepted April 23, 2015) / Published online May 19, 2015. Dedicated to Jerald L. Ericksen on the occasion of his 90th birthday. This work was partially conducted when PC held a position at the California Institute of Technology. We acknowledge support from the US Department of Energy National Nuclear Security Administration (Award Number DE-FC52-08NA28613, all authors), the US National Science Foundation (Award Number OISE-0967140, PPP and KB) and the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013, ERC Grant Agreement No. 291053, PC). The authors thank Jan Kristensen for his advice on a draft version of the paper.

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