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Nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on compliant substrates

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Abstract

A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates. In this way, the problem is reduced to finding the steady state of an overdamped evolution system according to a kinetic law, rather than directly solving the coupled nonlinear equations. This enables one to account for the complicated director distribution and obtain the precise wrinkling morphology of the film. Though the approach proposed here is for a twist nematic film, it can be extended to study glassy nematic films with other director distributions.

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Acknowledgments

This project was supported by the National Natural Science Foundation of China (Grant 11072231) and Collaborative Innovation Center of Suzhou Nano Science and Technology.

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Authors and Affiliations

  1. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230026, China

    Dong Yang & Ling-Hui He

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  1. Dong Yang
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  2. Ling-Hui He
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Correspondence to Ling-Hui He.

Appendix

Appendix

Expressions of the parameters \(c_{ij}\) in Eq. (4) are given as follows:

$$\begin{aligned} c_{11}= & {} {c}^{\prime }_{11} \sin ^{4}\phi +2\left( {c}^{\prime }_{13} +{c}^{\prime }_{44} \right) \sin ^{2}\phi \cos ^{2}\phi +{c}^{\prime }_{33} \cos ^{4}\phi , \nonumber \\ c_{12}= & {} {c}^{\prime }_{13} \sin ^{4}\phi +\left( {c}^{\prime }_{11} +{c}^{\prime }_{33} -2{c}^{\prime }_{44} \right) \sin ^{2}\phi \cos ^{2}\phi \nonumber \\&+\,\,{c}^{\prime }_{13} \cos ^{4}\phi , \nonumber \\ c_{13}= & {} {c}^{\prime }_{12} \sin ^{2}\phi +{c}^{\prime }_{13} \cos ^{2}\phi , \nonumber \\ c_{16}= & {} 2\left( {c}^{\prime }_{33} -{c}^{\prime }_{13} -{c}^{\prime }_{44} \right) \sin \phi \cos ^{3}\phi \nonumber \\&-2\left( {c}^{\prime }_{11} -{c}^{\prime }_{13} -{c}^{\prime }_{44} \right) \sin ^{3}\phi \cos \phi , \nonumber \\ c_{22}= & {} {c}^{\prime }_{33} \sin ^{4}\phi +2\left( {c}^{\prime }_{13} +{c}^{\prime }_{44} \right) \sin ^{2}\phi \cos ^{2}\phi +{c}^{\prime }_{11} \cos ^{4}\phi , \nonumber \\ c_{23}= & {} {c}^{\prime }_{13} \sin ^{2}\phi +{c}^{\prime }_{12} \cos ^{2}\phi , \nonumber \\ c_{26}= & {} -2\left( {c}^{\prime }_{11} -{c}^{\prime }_{13} -{c}^{\prime }_{44} \right) \sin \phi \cos ^{3}\phi \nonumber \\&+\,\,2\left( {c}^{\prime }_{33} -{c}^{\prime }_{13} -{c}^{\prime }_{44} \right) \sin ^{3}\phi \cos \phi , \nonumber \\ c_{33}= & {} {c}^{\prime }_{11}, \nonumber \\ c_{36}= & {} 2\left( {c}^{\prime }_{13} -{c}^{\prime }_{12} \right) \sin \phi \cos \phi , \nonumber \\ c_{44}= & {} {c}^{\prime }_{44} \sin ^{2}\phi +\left( {c}^{\prime }_{11} -{c}^{\prime }_{12} \right) \cos ^{2}\phi , \nonumber \\ c_{45}= & {} \left( {c}^{\prime }_{12} +{c}^{\prime }_{44} -{c}^{\prime }_{11} \right) \sin \phi \cos \phi , \nonumber \\ c_{55}= & {} \left( {c}^{\prime }_{11} -{c}^{\prime }_{12} \right) \sin ^{2}\phi +{c}^{\prime }_{44} \cos ^{2}\phi , \nonumber \\ c_{66}= & {} {c}^{\prime }_{44} \sin ^{4}\phi +2\left( {c}^{\prime }_{11} -2{c}^{\prime }_{13} +{c}^{\prime }_{33} -{c}^{\prime }_{44} \right) \sin ^{2}\phi \cos ^{2}\phi \nonumber \\&+\,\,{c}^{\prime }_{44} \cos ^{4}\phi . \end{aligned}$$
(26)

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Yang, D., He, LH. Nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on compliant substrates. Acta Mech. Sin. 31, 672–678 (2015). https://doi.org/10.1007/s10409-015-0463-0

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