Abstract
Programming desired shapes of stimuli-responsive nematic sheets is a challenging yet crucial problem for morphing applications. Here, we propose a strategy for inverse design of axisymmetric shapes via circular bilayers composed of two glassy nematic layers with radially symmetric and orthogonal director fields. In this situation, an explicit link can be established between the director orientation and the bilayer deflection. The result provides a recipe for how to construct a director pattern which, upon stimulation, leads to a prescribed shape of revolution. For illustration, two examples concerning simply supported and loosely clamped bilayer discs are given.
Issue Section:
Research Papers
References
1.
Finkelmann
, H.
, Nishikawa
, E.
, Pereira
, G. G.
, and Warner
, M.
, 2001
, “New Photomechanical Effect in Solids
,” Phys. Rev. Lett.
, 87
(1
), p. 015501
. 2.
Hogan
, P. M.
, Tajbakhsh
, A. R.
, and Terentjev
, E. M.
, 2002
, “UV Manipulation of Order and Macroscopic Shape in Nematic Elastomers
,” Phys. Rev. E
, 65
(4
), p. 041720
. 3.
Harris
, K. D.
, Cuypers
, R.
, Scheibe
, P.
, van Oosten
, C. L.
, Bastiaansen
, C. W. M.
, Lub
, J.
, and Broer
, D. J.
, 2005
, “Large Amplitude Light-Induced Motion in High Elastic Modulus Polymer Actuators
,” J. Mater. Chem.
, 15
(47
), pp. 5043
–5048
. 4.
Tajbakhsh
, A.
, and Terentjev
, E.
, 2001
, “Spontaneous Thermal Expansion of Nematic Elastomers
,” Eur. Phys. J. E
, 6
(2
), pp. 181
–188
. 5.
Mol
, G. N.
, Harris
, K. D.
, Bastiaansen
, C. W. M.
, and Broer
, D. J.
, 2005
, “Thermo-Mechanical Responses of Liquid-Crystal Networks With a Splayed Molecular Organization
,” Adv. Funct. Mater.
, 15
(7
), pp. 1155
–1159
. 6.
de Haan
, L. T.
, Sánchez-Somolinos
, C.
, Bastiaansen
, C. M. W.
, Schenning
, A. P. H. J.
, and Broer
, D. J.
, 2012
, “Engineering of Complex Order and the Macroscopic Deformation of Liquid Crystal Polymer Networks
,” Angew. Chem. Int. Ed.
, 51
(50
), pp. 12469
–12472
. 7.
Ware
, T. H.
, McConney
, M. E.
, Wie
, J. J.
, Tondiglia
, V. P.
, and White
, T. J.
, 2015
, “Voxelated Liquid Crystal Elastomers
,” Science
, 347
(6225
), pp. 982
–984
. 8.
Kowalski
, B.
, Tondiglia
, V.
, Guin
, T.
, and White
, T. J.
, “Voxel Resolution in the Directed Self-Assembly of Liquid Crystal Polymer Networks and Elastomers
,” Soft Matter
, 13
(24
), pp. 4335
–4340
. 9.
White
, T. J.
, and Broer
, D. J.
, 2015
, “Programmable and Adaptive Mechanics With Liquid Crystal Polymer Networks and Elastomers
,” Nat. Mater.
, 14
(11
), pp. 1087
–1098
. 10.
Modes
, C. D.
, and Warner
, M.
, 2016
, “Shape-Programmable Materials
,” Phys. Today
, 69
(1
), pp. 32
–38
. 11.
Warner
, M.
, 2020
, “Topographic Mechanics and Applications of Liquid Crystalline Solids
,” Annu. Rev. Condens. Matter Phys.
, 11
, pp. 125
–145
.12.
Warner
, M.
, and Mahadevan
, L.
, 2004
, “Photoinduced Deformations of Beams, Plates, and Films
,” Phys. Rev. Lett.
, 92
(13
), p. 134302
. 13.
Warner
, M.
, Modes
, C. D.
, and Corbett
, D.
, 2010
, “Curvature in Nematic Elastica Responding to Light and Heat
,” Proc. R. Soc. A
, 466
(2122
), pp. 2975
–2989
. 14.
Modes
, C. D.
, Bhattacharya
, K.
, and Warner
, M.
, 2010
, “Disclination-Mediated Thermo-Optical Response in Nematic Glass Sheets
,” Phys. Rev. E
, 81
(6
), p. 060701
. 15.
Sawa
, Y.
, Ye
, F.
, Urayama
, K.
, Takigawa
, T.
, Gimenez-Pinto
, V.
, Selinger
, R. L. B.
, and Selinger
, J. V.
, 2011
, “Shape Selection of Twist-Nematic-Elastomer Ribbons
,” Proc. Natl. Acad. Sci.
, 108
(16
), pp. 6364
–6368
. 16.
Modes
, C. D.
, and Warner
, M.
, 2011
, “Blueprinting Nematic Glass: Systematically Constructing and Combining Active Points of Curvature for Emergent Morphology
,” Phys. Rev. E
, 84
(2
), p. 021711
. 17.
Mostajeran
, C.
, 2015
, “Curvature Generation in Nematic Surfaces
,” Phys. Rev. E
, 91
(6
), p. 062405
. 18.
He
, L. H.
, Zheng
, Y.
, and Ni
, Y.
, 2018
, “Programmed Shape of Glassy Nematic Sheets With Varying in-Plane Director Fields: A Kinetics Approach
,” Int. J. Solids Struct.
, 130–131
, pp. 183
–189
.19.
Aharoni
, H.
, Sharon
, E.
, and Kupferman
, R.
, 2014
, “Geometry of Thin Nematic Elastomer Sheets
,” Phys. Rev. Lett.
, 113
(25
), p. 257801
. 20.
Mostajeran
, C.
, Warner
, M.
, Ware
, T. H.
, and White
, T. J.
, 2016
, “Encoding Gaussian Curvature in Glassy and Elastomeric Liquid Crystal Solids
,” Proc. R. Soc. A
, 472
(2189
), p. 20160112
. 21.
Kowalski
, B. A.
, Mostajeran
, C.
, Godman
, N. P.
, Warner
, M.
, and White
, T. J.
, 2018
, “Curvature by Design and on Demand in Liquid Crystal Elastomers
,” Phys. Rev. E
, 97
(1
), p. 012504
. 22.
Aharoni
, H.
, Xia
, Y.
, Zhang
, X.
, Kamien
, R. D.
, and Yang
, S.
, 2018
, “Universal Inverse Design of Surfaces With Thin Nematic Elastomer Sheets
,” Proc. Natl. Acad. Sci.
, 115
(28
), pp. 7206
–7211
. 23.
Plucinsky
, P.
, Lemm
, M.
, and Bhattacharya
, K.
, 2016
, “Programming Complex Shapes in Thin Nematic Elastomer and Glass Sheets
,” Phys. Rev. E
, 94
(1
), p. 010701(R)
. 24.
Griniasty
, I.
, Aharoni
, H.
, and Efrati
, E.
, 2019
, “Curved Geometries From Planar Director Fields: Solving the Two-Dimensional Inverse Problem
,” Phys. Rev. Lett.
, 123
(12
), p. 127801
. 25.
Landau
, L.
, and Lifshitz
, E.
, 1959
, Theory of Elasticity
, Pergamon Press
, New York
.26.
Modes
, C. D.
, Warner
, M.
, van Oosten
, C. L.
, and Corbett
, D.
, 2010
, “Anisotropic Response of Glassy Splay-Bend and Twist Nematic Cantilevers to Light and Heat
,” Phys. Rev. E
, 82
(4
), p. 041111
. 27.
van Oosten
, C. L.
, Harris
, K. D.
, Bastiaansen
, C. W. M.
, and Broer
, D. J.
, 2007
, “Glassy Photomechanical Liquid-Crystal Network Actuators for Microscale Devices
,” Eur. Phys. J. E
, 23
(3
), pp. 329
–336
. Copyright © 2021 by ASME
You do not currently have access to this content.