Bending deformation of nematic liquid crystal elastomers (abbreviated as NLCEs) serves not only as a benchmark but also as a basic action of soft robots. It is, therefore, of fundamental importance to carry out a thorough analysis of finite bending of NLCEs. This paper studies such a problem by coating an NLCE to a hyperelastic substrate. The aim is to derive the analytical solution and investigate whether or not different constitutive models of NLCEs can drastically affect the theoretical predictions. For that purpose, four NLCE models are considered. The governing system of each case is established, and solving it leads to two different bending solutions. In order to determine which is the preferred one, we compare the total potential energy for both solutions and find that the two energy curves may have an intersection point at , a critical value of the bending angle, for some material parameters. In particular, the director abruptly rotates from one solution to another at , which indicates a director reorientation. By applying the solution procedure to different material models, we find that the theoretically predicted behavior is dependent on the material models applied. Besides unraveling a possible director reorientation in a bent NLCE, the current work also suggests that an experimental investigation on bending may be a good way for selecting a suitable constitutive relation for practical applications.
REFERENCES
1.
M.
Warner
and E. M.
Terentjev
, Liquid Crystal Elastomers
(Clarendon Press
, Oxford
, 2007
).2.
N.
Torras
, K. E.
Zinoviev
, J. E.
Marshall
, E. M.
Terentjev
, and J.
Esteve
, “Bending kinetics of a photo-actuating nematic elastomer cantilever
,” Appl. Phys. Lett.
99
, 254102
(2011
). 3.
J.
Wei
and Y.
Yu
, “Photodeformable polymer gels and crosslinked liquid-crystalline polymers
,” Soft Matter
8
, 8050
(2012
). 4.
K.
Urayama
, S.
Honda
, and T.
Takigawa
, “Electrically driven deformations of nematic gels
,” Phys. Rev. E
71
, 051713
(2005
). 5.
K.
Urayama
, S.
Honda
, and T.
Takigawa
, “Deformation coupled to director rotation in swollen nematic elastomers under electric fields
,” Macromolecules
39
, 1943
–1949
(2006
). 6.
A.
Kaiser
, M.
Winkler
, S.
Krause
, H.
Finkelmann
, and A. M.
Schmidt
, “Magnetoactive liquid crystal elastomer nanocomposites
,” J. Mater. Chem.
19
, 538
–543
(2009
). 7.
M.
Winkler
, A.
Kaiser
, S.
Krause
, H.
Finkelmann
, and A. M.
Schmidt
, “Liquid crystal elastomers with magnetic actuation
,” Macromol. Symp.
291–292
, 186
–192
(2010
). 8.
A.
Agrawal
, T. H.
Yun
, S. L.
Pesek
, W. G.
Chapman
, and R.
Verduzco
, “Shape-responsive liquid crystal elastomer bilayers
,” Soft Matter
10
, 1411
–1415
(2014
). 9.
Z.
Wang
, H.
Tian
, Q.
He
, and S.
Cai
, “Reprogrammable, reprocessible, and self-healable liquid crystal elastomer with exchangeable disulfide bonds
,” ACS Appl. Mater. Interfaces
9
, 33119
–33128
(2017
). 10.
P. G.
de Gennes
, M.
Hebert
, and R.
Kant
, “Artificial muscles based on nematic gels
,” Macromol. Symp.
113
, 39
–49
(1997
). 11.
H.
Tian
, Z.
Wang
, Y.
Chen
, J.
Shao
, T.
Gao
, and S.
Cai
, “Polydopamine-coated main-chain liquid crystal elastomer as optically driven artificial muscle
,” ACS Appl. Mater. Interfaces
10
, 8307
–8316
(2018
). 12.
A.
DeSimone
, P.
Gidoni
, and G.
Noselli
, “Liquid crystal elastomer stripes as soft crawlers
,” J. Mech. Phys. Solids
84
, 154
–272
(2015
). 13.
Z.
Wang
, K.
Li
, Q.
He
, and S.
Cai
, “A light-powered ultralight tensegrity robot with high deformability and load capacity
,” Adv. Mater.
31
, 1806849
(2019
). 14.
J. A.
Lv
, Y.
Liu
, J.
Wei
, E.
Chen
, L.
Qin
, and Y.
Yu
, “Photocontrol of fluid slugs in liquid crystal polymer microactuators
,” Nature
537
, 179
–184
(2016
). 15.
Z.
Wang
, Q.
He
, Y.
Wang
, and S.
Cai
, “Programmable actuation of liquid crystal elastomers via living exchange reaction
,” Soft Matter
15
, 2811
(2019
). 16.
P.
Bladon
, E.
Terentjev
, and M.
Warner
, “Transitions and instabilities in liquid crystal elastomers
,” Phys. Rev. E
47
(6
), R3838
–R3840
(1993
). 17.
A.
DeSimone
and G.
Dolzmann
, “Macroscopic response of nematic elastomers via relaxation of a class of so (3)-invariant energies
,” Arch. Ration. Mech. Anal.
161
(3
), 181
–204
(2002
). 18.
D. R.
Anderson
, D. E.
Carlson
, and E.
Fried
, “A continuum-mechanical theory for nematic elastomers
,” J. Elast.
56
(1
), 33
–58
(1999
). 19.
G. C.
Verwey
and M.
Warner
, “Compositional fluctuations and semisoftness in nematic elastomers
,” Macromolecules
30
, 4189
–4195
(1997
). 20.
D. E.
Carlson
, E.
Fried
, and S.
Sellers
, “Force-free states, relative strain, and soft elasticity in nematic elastomers
,” J. Elast.
69
, 161
–180
(2002
). 21.
E.
Fried
and S.
Sellers
, “Free-energy density functions for nematic elastomers
,” J. Mech. Phys. Solids
52
, 1671
–1689
(2004
). 22.
A.
DeSimone
and L.
Teresi
, “Elastic energies for nematic elastomers
,” Eur. Phys. J. E
29
, 191
–204
(2009
). 23.
Y. C.
Chen
and E.
Fried
, “Uniaxial nematic elastomers: Constitutive framework and a simple application
,” Proc. R. Soc. A
462
, 1295
–1314
(2006
).24.
V.
Agostiniani
and A.
DeSimone
, “Ogden-type energies for nematic elastomers
,” Int. J. Nonlinear Mech.
47
, 402
–417
(2012
). 25.
Y.
Zhang
, C.
Xuan
, Y.
Jiang
, and Y.
Huo
, “Continuum mechanical modeling of liquid crystal elastomers as dissipative ordered solids
,” J. Mech. Phys. Solids
126
, 285
–303
(2019
). 26.
I.
Kundler
and H.
Finkelmann
, “Strain-induced director reorientation in nematic liquid single crystal elastomers
,” Macromol. Rapid Commun.
16
, 679
–686
(1995
). 27.
G. C.
Verwey
, M.
Warner
, and E. M.
Terentjev
, “Elastic instability and stripe domains in liquid crystalline elastomers
,” J. Phys. II
6
, 1273
–1290
(1996
).28.
S. V.
Fridrikh
and E. M.
Terentjev
, “Polydomain-monodomain transition in nematic elastomers
,” Phys. Rev. E
60
, 1847
–1857
(1999
). 29.
S.
Conti
, A.
DeSimone
, and G.
Dolzmann
, “Semisoft elasticity and director reorientation in stretched sheets of nematic elastomers
,” Phys. Rev. E
66
(6
), 061710
(2002
). 30.
S.
Conti
, A.
DeSimone
, and G.
Dolzmann
, “Soft elastic response of stretched sheets of nematic elastomers: A numerical study
,” J. Mech. Phys. Solids
50
(7
), 1431
–1451
(2002
). 31.
E.
Fried
and V.
Korchagin
, “Striping of nematic elastomer
,” Int. J. Solids Struct.
39
, 3451
–3467
(2002
). 32.
E.
Fried
and S.
Sellers
, “Soft elasticity is not necessary for striping in nematic elastomers
,” J. Appl. Phys.
100
, 043521
(2006
). 33.
A.
Petelin
and M.
Čopič
, “Observation of a soft mode of elastic instability in liquid crystal elastomers
,” Phys. Rev. Lett.
103
, 077801
(2009
). 34.
Z.
Wu
and Z.
Zhong
, “A nonlinear theory accounting for stress-induced orientational transitions in nematic gels
,” Acta Mech.
224
, 1243
–1250
(2013
). 35.
Y.
Zhang
, Z.
Zhang
, and Y.
Huo
, “Nucleation and critical conditions for stripe domains in monodomain nematic elastomer sheets under uniaxial loading
,” J. Mech. Phys. Solids
144
, 104110
(2020
). 36.
Q.
He
, Y.
Zheng
, Z.
Wang
, X.
He
, and S.
Cai
, “Anomalous inflation of a nematic balloon
,” J. Mech. Phys. Solids
142
, 104013
(2020
). 37.
L. A.
Mihai
and A.
Goriely
, “Likely striping in stochastic nematic elastomers
,” Math. Mech. Solids
25
, 1
–22
(2020
). 38.
E.
Fried
and B. C.
Roy
, “Disclinations in a homogenously deformed nematic elastomer
,” Contin. Mech. Thermodyn.
18
, 259
–280
(2006
). 39.
T. J.
Pence
, “Soft elastic bending response of a nematic elastomer described by a microstructurally relaxed free energy
,” Contin. Mech. Thermodyn.
18
, 281
–304
(2006
). 40.
Y.
Liu
, W.
Ma
, and H.-H.
Dai
, “On a consistent finite-strain plate model of nematic liquid crystal elastomers
,” J. Mech. Phys. Solids
145
, 104169
(2020
). 41.
R. S.
Rivlin
, “Large elastic deformations of isotropic materials. V. The problem of flexure
,” Proc. R. Soc. A
195
(1043
), 463
–473
(1949
).42.
43.
Wolfram Research Inc., Mathematica: Version 12, Wolfram Research Inc., Champaign, 2019.
44.
M.
Warner
and E. M.
Terentjev
, “Nematic elastomers–a new state of matter?
,” Prog. Polym. Sci.
21
, 853
–891
(1996
). 45.
H.
Finkelmann
, I.
Kundler
, E. M.
Terentjev
, and M.
Warner
, “Critical stripe domain instability of nematic elastomers
,” J. Phys. II
7
, 1059
–1069
(1997
).46.
E.
Fried
and R. E.
Todres
, “Disclinated states in nematic elastomers
,” J. Mech. Phys. Solids
50
, 2691
–2716
(2002
). 47.
G. R.
Mitchell
, F.
Davis
, and W.
Guo
, “Strain-induced transitions in liquid-crystal elastomers
,” Phys. Rev. Lett.
71
, 2947
–2950
(1993
). © 2021 Author(s).
2021
Author(s)
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