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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2016, Vol. 17 Issue (1): 22-36    DOI: 10.1631/jzus.A1500207
    
Constitutive models of artificial muscles: a review
Hui-ming Wang1,2,†(),Shao-xing Qu1,2,†()
1 Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Hangzhou 310027, China
2 Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China
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Abstract  

Artificial muscles are materials which possess muscle-like characteristics; they have many promising applications and many materials have been exploited as artificial muscles. In this review, the artificial muscles discussed are confined to dielectric elastomers and responsive gels. We focus on their constitutive models based on free energy function theory. For dielectric elastomers, both hyperelastic and visco-hyperelastic models are involved. For responsive gels, we consider different kinds of gels, such as hydrogel, pH-sensitive gel, temperature-sensitive gel, polyelectrolyte gel, reactive gel, etc. With an accurate, reliable, and powerful constitutive model, exact theoretical analysis can be achieved and the important intrinsic characteristics of artificial muscle based systems can be revealed.

Key words： Constitutive model      Artificial muscle      Dielectric elastomer      Responsive gel      Free energy function     
Received: 13 July 2015      Published: 06 January 2016
Fund:  the National Natural Science Foundation of China(No. 11222218, 11372273, 11321202);the Zhejiang Provincial Natural Science Foundation of China(No. LY13A020001,LZ14A020001);the Fundamental Research Funds for the Central Universities, China
Corresponding Authors: Hui-ming Wang,Shao-xing Qu     E-mail: wanghuiming@zju.edu.cn;squ@zju.edu.cn
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Hui-ming Wang,Shao-xing Qu. Constitutive models of artificial muscles: a review. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2016, 17(1): 22-36.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A1500207     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2016/V17/I1/22

Fig. 1 Schematics of a dielectric elastomer in different states In the reference state (a), an elastomeric membrane of sides L1 and L2 and thickness H is sandwiched between two compliant electrodes. In the deformed state (b), the dielectric elastomer deforms to sides l1 and l2 and thickness h when subjected to the mechanical loadings P1 and P2 and a high voltage Φ
Model Expression of Ws WLCE NMP Parameter Type
neo-Hookean (Treloar, 1943) ${W_s} = \frac{\mu }{2}({I_1} - 3)$ No 1 μ A
Mooney-Rivlin (Mooney, 1940; Rivlin, 1948) ${W_s} = {C_1}({I_1} - 3) + {C_2}({I_2} - 3)$ No 2 C1, C2 B
Ogden (Ogden, 1972) ${W_s} = \sum\limits_{i = 1}^N {\frac{{{\mu _i}}}{{{\alpha _i}}}\left( {\lambda _1^{{\alpha _i}} + \lambda _2^{{\alpha _i}} + \lambda _3^{{\alpha _i}} - 3} \right)} $ Yes 2N μi , αi (i=1, 2, …, N) B
Yeoh (Yeoh, 1990) ${W_s} = \sum\limits_{i = 1}^3 {{C_i}{{\left( {{I_1} - 3} \right)}^i}} $ No 3 C1, C2, C3 B
Arruda-Boyce (Arruda and Boyce, 1993) ${W_s} = \mu n\left[ {\frac{{{\beta _{ch}}{\lambda _{ch}}}}{{\sqrt n }} + \ln \left( {\frac{{{\beta _{ch}}}}{{\sinh {\beta _{ch}}}}} \right)} \right],{\lambda _{ch}} = \sqrt {\frac{{{I_1}}}{3}} = \sqrt n \left( {\frac{1}{{\tanh {\beta _{ch}}}} - \frac{1}{{{\beta _{ch}}}}} \right)$ Yes 2 μ, n A
Gent (Gent, 1996) ${W_s} = - \frac{\mu }{2}{J_{\lim }}\ln \left( {1 - \frac{{{I_1} - 3}}{{{J_{\lim }}}}} \right)$ Yes 2 μ, Jlim B
Table 1 Some frequently-used stretching energy functions for incompressible dielectric elastomers
Fig. 2 Comparison of the nominal stress-stretch behavior of four frequently-used models, i.e., the neo-Hookean model, the Gent model, the Arruda-Boyce model, and the Ogden model with N=3 (a) Uniaxial tension; (b) Equibiaxial tension
Factor Key contribution or description
Compressibility Another strain energy term Wb (J) is appended to the existing strain energy form: $W(F,\tilde D) = {W_s}(F) + {W_E}(\tilde D) + {W_b}(J),{W_b} = - p(J - 1 + 0.5p/K)$ (Vertechy et al., 2012) or ${W_b} = 0.5K{(J - 1)^2}$ (Tagarielli et al., 2012), where K is the bulk modulus and p is the hydrostatic pressure
Conditional polarization ${W_E}(\tilde D) = \frac{{\lambda _1^{ - 2}\lambda _2^{ - 2}}}{{2\varepsilon ({\lambda _1},{\lambda _2})}}{\tilde D^2},\varepsilon = {\varepsilon _0} + \frac{N}{{3kT}}\left[ {\phi (1 + {\Lambda ^{ - 1}})\mu _B^2 + (1 - \phi )\mu _S^2} \right]$ where ε0 is the permittivity of the vacuum and N is the number of molecules per unit volume. ϕ is the volumetric fraction of the backbone dipoles over the total monomer dipoles in a single chain. λ is a negative value representing the number of states that the dipoles may locate before polarization. μB and μS are the dipolar moments of monomers in the backbone and in the side chains (Li B. et al., 2012)
Variation of permittivity ${W_E}(\tilde D) = \frac{{\lambda _1^{ - 1}\lambda _2^{ - 1}{\lambda _3}}}{{2\varepsilon ({\lambda _1},{\lambda _2},{\lambda _3})}}{\tilde D^2},\varepsilon = {\varepsilon _0}[1 + a({\lambda _3} - 1) + b({\lambda _1} + {\lambda _2} + {\lambda _3} - 3)]$ where ε0 is the permittivity of the dielectric in the absence of deformation, and a and b are the coefficients of electrostriction (Zhao and Suo, 2008a)
Thermally coupled $W(F,\tilde D,T) = {W_s}(F,T) + {W_E}(\tilde D),{W_s}(F,T) = \frac{T}{{2{T_0}}}\left[ {{C_1}({I_1} - 3) + {C_2}({I_2} - 3)} \right] + {c_0}\left[ {(T - {T_0}) - T\ln \left( {\frac{T}{{{T_0}}}} \right)} \right]$ where T is the current temperature and T0 is the reference temperature. c0 is the specific heat of dielectric elastomers (Liu et al., 2011)
Unidirectional constraint The dielectric elastomeric membrane contracts in the directions normal to the fibers, but keeps its dimension in the direction along the fibers (Huang et al., 2012b; Lu et al., 2012)
Hydrostatically coupled The fluid sealed between the active and passive membranes remains constant at a prescribed volume 2V0. That is, the confined fluid is taken to be incompressible. Vact+Vpas=2V0 (Wang et al., 2012b)
Air coupled The air enclosed in the chamber and bubble obeys the ideal-gas law: (p+patm)(V+Vc)=(p0+patm)(V0+Vc). Here p+patm and V+Vc are the pressure and volume in the current state; p0+patm and V0+Vc are those quantities in the reference state. patm is the atmosphere pressure and Vc is the volume of the chamber (Keplinger et al., 2012; Li et al., 2013)
Table 2 Some special effects in modeling dielectric elastomers
Fig. 3 Schematics (a) and photos (b) of a responsive gel
[1]   Afroze F, Nies E, Berghmans H . Phase transitions in the system poly(N-isopropylacrylamide)/water and swelling behavior of the corresponding networks. Journal of Molecular Structure. 2000, 554(1): 55-68 doi: 10.1016/S0022-2860(00)00559-7
doi: 10.1016/S0022-2860(00)00559-7
[2]   Agoras M, Lopez-Pamies O, Castañeda PP . A general hyperelastic model for incompressible fiber-reinforced elastomers. Journal of the Mechanics and Physics of Solids. 2009, 57(2): 268-286 doi: 10.1016/j.jmps.2008.10.014
doi: 10.1016/j.jmps.2008.10.014
[3]   Ahnert K, Abel M, Kollosche M et al. Soft capacitors for wave energy harvesting. Journal of Materials Chemistry. 2011, 21(38): 14492-14497 doi: 10.1039/c1jm12454d
doi: 10.1039/c1jm12454d
[4]   Akbari S, Shea HR . Microfabrication and characterization of an array of dielectric elastomer actuators generating uniaxial strain to stretch individual cells. Journal of Micromechanics and Microengineering. 2012, 22(4): 045020 doi: 10.1088/0960-1317/22/4/045020
doi: 10.1088/0960-1317/22/4/045020
[5]   Arruda EM, Boyce MC . A three-dimensional constitutive model for the large strech behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids. 1993, 41(2): 389-412 doi: 10.1016/0022-5096(93)90013-6
doi: 10.1016/0022-5096(93)90013-6
[6]   Aschwanden M, Stemmer A . Polymeric, electrically tunable diffraction grating based on artificial muscles. Optics Letters. 2006, 31(17): 2610-2612 doi: 10.1364/OL.31.002610
doi: 10.1364/OL.31.002610
[7]   Aw KC, McDaid AJ . Bio-applications of ionic polymer metal composite transducers. Smart Materials and Structures. 2014, 23(7): 074005
[8]   Bai YY, Jiang YH, Chen BH et al. Cyclic performance of viscoelastic dielectric elastomers with solid hydrogel electrodes. Applied Physics Letters. 2014, 104(6): 062902 doi: 10.1063/1.4865200
doi: 10.1063/1.4865200
[9]   Balasubramanian R, Santos VJ . The Human Hand as an Inspiration for Robot Hand Development. 2014 Springer, Heidelberg
[10]   Bassil M, Davenas J, Tahchi ME . Electrochemical properties and actuation mechanisms of polyacrylamide hydrogel for artificial muscle application. Sensors and Actuators B: Chemical. 2008, 134(2): 496-501 doi: 10.1016/j.snb.2008.05.025
doi: 10.1016/j.snb.2008.05.025
[11]   Beda T . An approach for hyperelastic model-building and parameters estimation: a review of constitutive models. European Polymer Journal. 2014, 50: 97-108 doi: 10.1016/j.eurpolymj.2013.10.006
doi: 10.1016/j.eurpolymj.2013.10.006
[12]   Biddiss E, Chau T . Dielectric elastomers as actuators for upper limb prosthetics: challenges and opportunities. Medical Engineering & Physics. 2008, 30(4): 403-418 doi: 10.1016/j.medengphy.2007.05.011
doi: 10.1016/j.medengphy.2007.05.011
[13]   Boissonade J . Simple chemomechanical process for self-generation of rhythms and forms. Physical Review Letters. 2003, 90(18): 188302 doi: 10.1103/PhysRevLett.90.188302
doi: 10.1103/PhysRevLett.90.188302
[14]   Boissonade J . Oscillatory dynamics induced in polyelectrolyte gels by a non-oscillatory reaction: a model. European Physical Journal E. 2009, 28(3): 337-346 doi: 10.1140/epje/i2008-10425-1
doi: 10.1140/epje/i2008-10425-1
[15]   Boyce MC, Arruda EM . Constitutive models of rubber elasticity: a review. Rubber Chemistry and Technology. 2000, 73(3): 504-523 doi: 10.5254/1.3547602
doi: 10.5254/1.3547602
[16]   Cai SQ, Suo ZG . Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels. Journal of the Mechanics and Physics of Solids. 2011, 59(11): 2259-2278 doi: 10.1016/j.jmps.2011.08.008
doi: 10.1016/j.jmps.2011.08.008
[17]   Cai SQ, Suo ZG . Equations of state for ideal elastomeric gels. Europhysics Letters. 2012, 97(3): 34009 doi: 10.1209/0295-5075/97/34009
doi: 10.1209/0295-5075/97/34009
[18]   Cai SQ, Lou YC, Ganguly P et al. Force generated by a swelling elastomer subject to constraint. Journal of Applied Physics. 2010, 107(10): 103535 doi: 10.1063/1.3428461
doi: 10.1063/1.3428461
[19]   Carpi F, Rossi DD . Dielectric elastomer cylindrical actuators: electromechanical modelling and experimental evaluation. Materials Science and Engineering: C. 2004, 24(4): 555-562 doi: 10.1016/j.msec.2004.02.005
doi: 10.1016/j.msec.2004.02.005
[20]   Carpi F, Migliore A, Serra G et al. Helical dielectric elastomer actuators. Smart Materials and Structures. 2005, 14(6): 1210-1216
[21]   Carpi F, Salaris C, Rossi DD . Folded dielectric elastomer actuators. Smart Materials and Structures. 2007, 16(2): S300-S305
[22]   Carpi F, Frediani G, Rossi DD . Hydrostatically coupled dielectric elastomer actuators. IEEE/ASME Transactions on Mechatronics. 2010, 15(2): 308-315 doi: 10.1109/TMECH.2009.2021651
doi: 10.1109/TMECH.2009.2021651
[23]   Carpi F, Kornbluh R, Sommer-Larsen P et al. Electroactive polymer actuators as artificial muscles: are they ready for bioinspired applications. Bioinspiration & Biomimetics. 2011, 6(4): 045006
[24]   Carpi F, Frediani G, Turco S et al. Bioinspired tunable lens with muscle-like electroactive elastomers. Advanced Functional Materials. 2011, 21(21): 4152-4158 doi: 10.1002/adfm.201101253
doi: 10.1002/adfm.201101253
[25]   Chen XY, Dai HH . Asymptotic solutions and new insights for cylinder and core–shell polymer gels in a solvent. Soft Matter. 2013, 9(36): 8664-8677 doi: 10.1039/c3sm50674f
doi: 10.1039/c3sm50674f
[26]   Chiba S, Waki M, Wada T et al. Consistent ocean wave energy harvesting using electroactive polymer (dielectric elastomer) artificial muscle generators. Applied Energy. 2013, 104: 497-502 doi: 10.1016/j.apenergy.2012.10.052
doi: 10.1016/j.apenergy.2012.10.052
[27]   Chu LY, Xie R, Ju XJ et al. Smart Hydrogel Functional Material. 2013, Springer, Heidelberg
[28]   Dai HH, Song ZL . Some analytical formulas for the equilibrium states of a swollen hydrogel shell. Soft Matter. 2011, 7(18): 8473-8483 doi: 10.1039/c1sm05425b
doi: 10.1039/c1sm05425b
[29]   Danielsson M, Parks DM, Boyce MC . Constitutive modeling of porous hyperelastic materials. Mechanics of Materials. 2004, 36(4): 347-358 doi: 10.1016/S0167-6636(03)00064-4
doi: 10.1016/S0167-6636(03)00064-4
[30]   Fang ZH, Punckt C, Leung EY et al. Tuning of structural color using a dielectric actuator and multifunctional compliant electrodes. Applied Optics. 2010, 49(35): 6689-6696 doi: 10.1364/AO.49.006689
doi: 10.1364/AO.49.006689
[31]   Fereidoonnezhad B, Naghdabadi R, Arghavani J . A hyperelastic constitutive model for fiber-reinforced rubber-like materials. International Journal of Engineering Science. 2013, 71: 36-44 doi: 10.1016/j.ijengsci.2013.06.001
doi: 10.1016/j.ijengsci.2013.06.001
[32]   Flory PJ, Rehner J . Statistical mechanics of cross-linked polymer networks. II. Swelling. Journal of Chemical Physics. 1943, 11(11): 521-526 doi: 10.1063/1.1723792
doi: 10.1063/1.1723792
[33]   Foo CC, Cai SQ, Koh SJA et al. Model of dissipative dielectric elastomers. Journal of Applied Physics. 2012, 111(3): 034102 doi: 10.1063/1.3680878
doi: 10.1063/1.3680878
[34]   Foo CC, Koh SJA, Keplinger C et al. Performance of dissipative dielectric elastomer generators. Journal of Applied Physics. 2012, 111(9): 094107 doi: 10.1063/1.4714557
doi: 10.1063/1.4714557
[35]   Gent AN . A new constitutive relation for rubber. Rubber Chemistry and Technology. 1996, 69(1): 59-61 doi: 10.5254/1.3538357
doi: 10.5254/1.3538357
[36]   Gerlach G, Guenther M, Sorber J et al. Chemical and pH sensors based on the swelling behavior of hydrogels. Sensors and Actuators B: Chemical. 2005, 111-112: 555-561 doi: 10.1016/j.snb.2005.03.040
doi: 10.1016/j.snb.2005.03.040
[37]   Giousouf M, Kovacs G . Dielectric elastomer actuators used for pneumatic valve technology. Smart Materials and Structures. 2013, 22(10): 104010
[38]   Gisby TA, O’Brien BM, Anderson IA . Self sensing feedback for dielectric elastomer actuators. Applied Physics Letters. 2013, 102(19): 193703 doi: 10.1063/1.4805352
doi: 10.1063/1.4805352
[39]   Graf C, Hitzbleck J, Feller T et al. Dielectric elastomer-based energy harvesting: material, generator design, and optimization. Journal of Intelligent Material Systems and Structures. 2014, 25(8): 951-966 doi: 10.1177/1045389X13502857
doi: 10.1177/1045389X13502857
[40]   Guo ZY, Peng XQ, Moran B . A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. Journal of the Mechanics and Physics of Solids. 2006, 54(9): 1952-1971 doi: 10.1016/j.jmps.2006.02.006
doi: 10.1016/j.jmps.2006.02.006
[41]   Haus H, Matysek M, Moßinger H et al. Modelling and characterization of dielectric elastomer stack actuators. Smart Materials and Structures. 2013, 22(10): 104009
[42]   Hong W . Modeling viscoelastic dielectrics. Journal of the Mechanics and Physics of Solids. 2011, 59(3): 637-650 doi: 10.1016/j.jmps.2010.12.003
doi: 10.1016/j.jmps.2010.12.003
[43]   Hong W, Zhao XH, Zhou JX et al. A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids. 2008, 56(5): 1779-1793 doi: 10.1016/j.jmps.2007.11.010
doi: 10.1016/j.jmps.2007.11.010
[44]   Hong W, Liu ZS, Suo ZG . Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures. 2009, 46(17): 3282-3289 doi: 10.1016/j.ijsolstr.2009.04.022
doi: 10.1016/j.ijsolstr.2009.04.022
[45]   Hong W, Zhao XH, Suo ZG . Large deformation and electrochemistry of polyelectrolyte gels. Journal of the Mechanics and Physics of Solids. 2010, 58(4): 558-577 doi: 10.1016/j.jmps.2010.01.005
doi: 10.1016/j.jmps.2010.01.005
[46]   Horgan CO, Saccomandi G . Constitutive modelling of rubber-like and biological materials with limiting chain extensibility. Mathematics and Mechanics of Solids. 2002, 7(4): 353-371 doi: 10.1177/108128028477
doi: 10.1177/108128028477
[47]   Horgan CO, Saccomandi G . A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. Journal of the Mechanics and Physics of Solids. 2005, 53(9): 1985-2015 doi: 10.1016/j.jmps.2005.04.004
doi: 10.1016/j.jmps.2005.04.004
[48]   Horgan CO, Saccomandi G . Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chemistry and Technology. 2006, 79(1): 152-169 doi: 10.5254/1.3547924
doi: 10.5254/1.3547924
[49]   Hu YH, Suo ZG . Viscoelasticity and poroelasticity in elastomeric gels. Acta Mechanica Solida Sinica. 2012, 25(5): 441-458 doi: 10.1016/S0894-9166(12)60039-1
doi: 10.1016/S0894-9166(12)60039-1
[50]   Huang JS, Li TF, Foo CC et al. Giant, voltage-actuated deformation of a dielectric elastomer under dead load. Applied Physics Letters. 2012, 100(4): 041911 doi: 10.1063/1.3680591
doi: 10.1063/1.3680591
[51]   Huang JS, Lu TQ, Zhu J et al. Large, uni-directional actuation in dielectric elastomers achieved by fiber stiffening. Applied Physics Letters. 2012, 100(21): 211901 doi: 10.1063/1.4720181
doi: 10.1063/1.4720181
[52]   Huang JS, Shian S, Suo ZG et al. Maximizing the energy density of dielectric elastomer generators using equi-biaxial loading. Advanced Functional Materials. 2013, 23(40): 5056-5061 doi: 10.1002/adfm.201300402
doi: 10.1002/adfm.201300402
[53]   Huang ZP . A novel constitutive formulation for rubberlike materials in thermoelasticity. Journal of Applied Mechanics. 2014, 81(4): 041013 doi: 10.1115/1.4025272
doi: 10.1115/1.4025272
[54]   Hunt S, McKay TG, Anderson IA . A self-healing dielectric elastomer actuator. Applied Physics Letters. 2014, 104(11): 113701 doi: 10.1063/1.4869294
doi: 10.1063/1.4869294
[55]   Joglekar MM . An energy-based approach to extract the dynamic instability parameters of dielectric elastomer actuators. Journal of Applied Mechanics. 2014, 81(9): 091010 doi: 10.1115/1.4027925
doi: 10.1115/1.4027925
[56]   Jung K, Kim KJ, Choi HR . A self-sensing dielectric elastomer actuator. Sensors and Actuators A: Physical. 2008, 143(2): 343-351 doi: 10.1016/j.sna.2007.10.076
doi: 10.1016/j.sna.2007.10.076
[57]   Kaltseis R, Keplinger C, Baumgartner R et al. Method for measuring energy generation and efficiency of dielectric elastomer generators. Applied Physics Letters. 2011, 99(16): 162904 doi: 10.1063/1.3653239
doi: 10.1063/1.3653239
[58]   Keplinger C, Li TF, Baumgartner R et al. Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation. Soft Matter. 2012, 8(2): 285-288 doi: 10.1039/C1SM06736B
doi: 10.1039/C1SM06736B
[59]   Kim S, Laschi C, Trimmer B . Soft robotics: a bioinspired evolution in robotics. Trends in Biotechnology. 2013, 31(5): 287-294 doi: 10.1016/j.tibtech.2013.03.002
doi: 10.1016/j.tibtech.2013.03.002
[60]   Klinkel S, Zwecker S, Muller R . A solid shell finite element formulation for dielectric elastomers. ASME Journal of Applied Mechanics. 2013, 80(2): 021026 doi: 10.1115/1.4007435
doi: 10.1115/1.4007435
[61]   Knudson D . Fundamentals of Biomechanics, 2nd Edition. 2007, New York: Springer
[62]   Koh SJA, Zhao XH, Suo ZG . Maximal energy that can be converted by a dielectric elastomer generator. Applied Physics Letters. 2009, 94(26): 262902 doi: 10.1063/1.3167773
doi: 10.1063/1.3167773
[63]   Koh SJA, Keplinger C, Li TF et al. Dielectric elastomer generators: how much energy can be converted. IEEE/ASME Transactions on Mechatronics. 2011, 16(1): 33-41 doi: 10.1109/TMECH.2010.2089635
doi: 10.1109/TMECH.2010.2089635
[64]   Kovacs G, Duering L, Michel S et al. Stacked dielectric elastomer actuator for tensile force transmission. Sensors and Actuators A: Physical. 2009, 155(2): 299-307 doi: 10.1016/j.sna.2009.08.027
doi: 10.1016/j.sna.2009.08.027
[65]   Kuksenok O, Yashin VV, Balazs AC . Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. Physical Review E. 2008, 78(4): 041406 doi: 10.1103/PhysRevE.78.041406
doi: 10.1103/PhysRevE.78.041406
[66]   Kwon HJ, Yasuda K, Gong JP et al. Polyelectrolyte hydrogels for replacement and regeneration of biological tissues. Macromolecular Research. 2014, 22(3): 227-235 doi: 10.1007/s13233-014-2045-6
doi: 10.1007/s13233-014-2045-6
[67]   La TG, Lau GK . Very high dielectric strength for dielectric elastomer actuators in liquid dielectric immersion. Applied Physics Letters. 2013, 102(19): 192905 doi: 10.1063/1.4806976
doi: 10.1063/1.4806976
[68]   Lawrence DB, Cai T, Hu ZB et al. Temperature-responsive semipermeable capsules composed of colloidal microgel spheres. Langmuir. 2007, 23(2): 395-398 doi: 10.1021/la062676z
doi: 10.1021/la062676z
[69]   Leng JS, Liu LW, Liu YJ et al. Electromechanical stability of dielectric elastomer. Applied Physics Letters. 2009, 94(21): 211901 doi: 10.1063/1.3138153
doi: 10.1063/1.3138153
[70]   Li B, Chen HL, Qiang JH et al. A model for conditional polarization of the actuation enhancement of a dielectric elastomer. Soft Matter. 2012, 8(2): 311-317 doi: 10.1039/C1SM05847A
doi: 10.1039/C1SM05847A
[71]   Li TF, Qu SX, Yang W . Energy harvesting of dielectric elastomer generators concerning inhomogeneous fields and viscoelastic deformation. Journal of Applied Physics. 2012, 112(3): 034119 doi: 10.1063/1.4745049
doi: 10.1063/1.4745049
[72]   Li TF, Keplinger C, Baumgartner R et al. Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. Journal of the Mechanics and Physics of Solids. 2013, 61(2): 611-628 doi: 10.1016/j.jmps.2012.09.006
doi: 10.1016/j.jmps.2012.09.006
[73]   Li TF, Zou ZA, Mao GY et al. Electromechanical bi-stable behavior of a novel dielectric elastomer actuator. Journal of Applied Mechanics. 2014, 81(4): 041019 doi: 10.1115/1.4025530
doi: 10.1115/1.4025530
[74]   Liang X, Cai SQ . Shape bifurcation of a spherical dielectric elastomer balloon under the actions of internal pressure and electric voltage. Journal of Applied Mechanics. 2015, 82(10): 101002 doi: 10.1115/1.4030881
doi: 10.1115/1.4030881
[75]   Lim HL, Hwang Y, Kar M et al. Smart hydrogels as functional biomimetic systems. Biomaterials Science. 2014, 2(5): 603-618 doi: 10.1039/c3bm60288e
doi: 10.1039/c3bm60288e
[76]   Liu JJ, Mao GY, Huang XQ et al. Enhanced compressive sensing of dielectric elastomer sensor using a novel structure. Journal of Applied Mechanics. 2015, 81(4): 041019 doi: 10.1115/1.4030889
doi: 10.1115/1.4030889
[77]   Liu L, Chen HL, Sheng JJ et al. Experimental study on the dynamic response of inplane deformation of dielectric elastomer under alternating electric load. Smart Materials and Structures. 2014, 23(2): 025037
[78]   Liu LW, Liu YJ, Li B et al. Thermo-electro-mechanical instability of dielectric elastomers. Smart Materials and Structures. 2011, 20(7): 075004
[79]   Liu LW, Liu YJ, Luo XJ et al. Electromechanical instability and snap-through instability of dielectric elastomers undergoing polarization saturation. Mechanics of Materials. 2012, 55: 60-72 doi: 10.1016/j.mechmat.2012.07.009
doi: 10.1016/j.mechmat.2012.07.009
[80]   Liu LW, Zhang Z, Liu YJ et al. Failure modeling of folded dielectric elastomer actuator. Science China: Physics, Mechanics & Astronomy. 2014, 57(2): 263-272 doi: 10.1007/s11433-013-5047-z
doi: 10.1007/s11433-013-5047-z
[81]   Liu LW, Yu K, Liu YJ et al. Polar elastic dielectric of large electrocaloric effect and deformation. Mechanics of Materials. 2014, 69(1): 71-92 doi: 10.1016/j.mechmat.2013.09.006
doi: 10.1016/j.mechmat.2013.09.006
[82]   Liu LW, Liu YJ, Yu K et al. Thermoelectromechanical stability of dielectric elastomers undergoing temperature variation. Mechanics of Materials. 2014, 72: 33-45 doi: 10.1016/j.mechmat.2013.05.013
doi: 10.1016/j.mechmat.2013.05.013
[83]   Liu LW, Zhang Z, Li JR et al. Stability of dielectric elastomer/carbon nanotube composites coupling electrostriction and polarization. Composites Part B: Engineering. 2015, 78(1): 35-41 doi: 10.1016/j.compositesb.2015.03.069
doi: 10.1016/j.compositesb.2015.03.069
[84]   Liu YJ, Liu LW, Zhang Z et al. Comment on method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters. 2008, 93(10): 106101 doi: 10.1063/1.2979236
doi: 10.1063/1.2979236
[85]   Liu YJ, Liu LW, Sun SH et al. An investigation on electromechanical stability of dielectric elastomers undergoing large deformation. Smart Materials and Structures. 2009, 18(9): 095040
[86]   Liu YJ, Liu LW, Zhang Z et al. Dielectric elastomer film actuators: characterization, experiment and analysis. Smart Materials and Structures. 2009, 18(9): 095024
[87]   Liu YJ, Liu LW, Zhang Z et al. Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer. Europhysics Letters. 2010, 90(3): 36004 doi: 10.1209/0295-5075/90/36004
doi: 10.1209/0295-5075/90/36004
[88]   Lochmatter P, Kovacs G, Wissler M . Characterization of dielectric elastomer actuators based on a visco-hyperelastic film model. Smart Materials and Structures. 2007, 16(2): 477-486
[89]   Lu TQ, Huang JS, Jordi C et al. Dielectric elastomer actuators under equal-biaxial forces, uniaxial forces, and uniaxial constraint of stiff fibers. Soft Matter. 2012, 8(22): 6167-6173 doi: 10.1039/c2sm25692d
doi: 10.1039/c2sm25692d
[90]   Lu TQ, Foo CC, Huang JS et al. Highly deformable actuators made of dielectric elastomers clamped by rigid rings. Journal of Applied Physics. 2014, 115(18): 184105 doi: 10.1063/1.4876722
doi: 10.1063/1.4876722
[91]   Lucantonio A, Nardinocchi P . Reduced models of swelling-induced bending of gel bars. International Journal of Solids and Structures. 2012, 49(11-12): 1399-1405 doi: 10.1016/j.ijsolstr.2012.02.025
doi: 10.1016/j.ijsolstr.2012.02.025
[92]   Mao GY, Li TF, Zou ZA et al. Prestretch effect on snap-through instability of inflated tubular elastomeric balloons. International Journal of Solids and Structures. 2014, 51(11-12): 2109-2115 doi: 10.1016/j.ijsolstr.2014.02.013
doi: 10.1016/j.ijsolstr.2014.02.013
[93]   Mao GY, Huang XQ, Liu JJ et al. Dielectric elastomer peristaltic pump module with finite deformation. Smart Materials and Structures. 2015, 24(7): 075026
[94]   Marckmann G, Verron E . Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry and Technology. 2006, 79(5): 835-858 doi: 10.5254/1.3547969
doi: 10.5254/1.3547969
[95]   Marcombe R, Cai SQ, Hong W et al. A theory of constrained swelling of a pH-sensitive hydrogel. Soft Matter. 2010, 6(4): 784-793 doi: 10.1039/b917211d
doi: 10.1039/b917211d
[96]   McKay T, O’Brien B, Calius E et al. An integrated, self priming dielectric elastomer generator. Applied Physics Letters. 2010, 97(6): 062911 doi: 10.1063/1.3478468
doi: 10.1063/1.3478468
[97]   McKay TG, O’Brien BM, Calius EP et al. Soft generators using dielectric elastomers. Applied Physics Letters. 2011, 98(14): 142903 doi: 10.1063/1.3572338
doi: 10.1063/1.3572338
[98]   Mooney M . A theory of large elastic deformation. Journal of Applied Physics. 1940, 11(9): 582-592 doi: 10.1063/1.1712836
doi: 10.1063/1.1712836
[99]   Moscardo M, Zhao XH, Suo ZG et al. On designing dielectric elastomer actuators. Journal of Applied Physics. 2008, 104(9): 093503 doi: 10.1063/1.3000440
doi: 10.1063/1.3000440
[100]   Mutlu R, Alici G, Xiang X et al. Electro-mechanical modelling and identification of electroactive polymer actuators as smart robotic manipulators. Mechatronics. 2014, 24(3): 241-251 doi: 10.1016/j.mechatronics.2014.02.002
doi: 10.1016/j.mechatronics.2014.02.002
[101]   Nguyen CH, Alici G, Mutlu R . A compliant translational mechanism based on dielectric elastomer actuators. Journal of Mechanical Design. 2014, 136(6): 061009 doi: 10.1115/1.4027167
doi: 10.1115/1.4027167
[102]   Nguyen CT, Phung H, Nguyen TD et al. A small biomimetic quadruped robot driven by multistacked dielectric elastomer actuators. Smart Materials and Structures. 2014, 23(6): 065005
[103]   Ogden RW . Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubber-like solids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 1972, 326(1567): 565-584 doi: 10.1098/rspa.1972.0026
doi: 10.1098/rspa.1972.0026
[104]   O’Halloran A, O’Malley F, McHugh P . A review on dielectric elastomer actuators, technology, applications, and challenges. Journal of Applied Physics. 2008, 104(7): 071101 doi: 10.1063/1.2981642
doi: 10.1063/1.2981642
[105]   Otake M . Electroactive Polymer Gel Robots: Modelling and Control of Artificial Muscles. 2010 Berlin Springer
[106]   Park HS, Nguyen TD . Viscoelastic effects on electromechanical instabilities in dielectric elastomers. Soft Matter. 2013, 9(4): 1031-1042 doi: 10.1039/C2SM27375F
doi: 10.1039/C2SM27375F
[107]   Pelrine R, Kornbluh R, Pei QB et al. High-speed electrically actuated elastomers with strain greater than 100%. Science. 2000, 287(5454): 836-839 doi: 10.1126/science.287.5454.836
doi: 10.1126/science.287.5454.836
[108]   Plante JS, Dubowsky S . Large-scale failure modes of dielectric elastomer actuators. International Journal of Solids and Structures. 2006, 43(25-26): 7727-7751 doi: 10.1016/j.ijsolstr.2006.03.026
doi: 10.1016/j.ijsolstr.2006.03.026
[109]   Plante JS, Dubowsky S . On the performance mechanisms of dielectric elastomer actuators. Sensors and Actuators A: Physical. 2007, 137(1): 96-109 doi: 10.1016/j.sna.2007.01.017
doi: 10.1016/j.sna.2007.01.017
[110]   Qu SX, Suo ZG . A finite element method for dielectric elastomer. Acta Mechanica Solida Sinica. 2012, 25(5): 459-466 doi: 10.1016/S0894-9166(12)60040-8
doi: 10.1016/S0894-9166(12)60040-8
[111]   Qu SX, Li K, Li TF et al. Rate dependent stress-stretch relation of dielectric elastomers subjected to pure shear like loading and electric field. Acta Mechanica Solida Sinica. 2012, 25(5): 542-549 doi: 10.1016/S0894-9166(12)60048-2
doi: 10.1016/S0894-9166(12)60048-2
[112]   Rivlin RS . Large elastic deformations of isotropic materials. IV. further developments of the general theory. Philosophical Transactions of the Royal Society of London Series A: Mathematical and Physical Sciences. 1948, 241(835): 379-397 doi: 10.1098/rsta.1948.0024
doi: 10.1098/rsta.1948.0024
[113]   Rotzetter ACC, Schumacher CM, Bubenhofer SB et al. Thermoresponsive polymer induced sweating surfaces as an efficient way to passively cool buildings. Advanced Materials. 2012, 24(39): 5352-5356 doi: 10.1002/adma.201202574
doi: 10.1002/adma.201202574
[114]   Shahinpoor M . Ionic polymer-conductor composites as biomimetic sensors, robotic actuators and artificial muscles-a review. Electrochimica Acta. 2003, 48(14-16): 2343-2353 doi: 10.1016/S0013-4686(03)00224-X
doi: 10.1016/S0013-4686(03)00224-X
[115]   Shahinpoor M, Bar-Cohen Y, Simpson JO et al. Ionic polymer–metal composites (IPMCs) as biomimetic sensors, actuators and artificial muscles-a review. Smart Materials and Structures. 1998, 7(6): R15-R30
[116]   Shahinpoor M, Kim KJ, Mojarrad M . Artificial Muscles: Applications of Advanced Polymeric Nanocomposites. 2007 London Taylor & Francis
[117]   Shankar R, Ghosh TK, Spontak RJ . Dielectric elastomers as next-generation polymeric actuators. Soft Matter. 2007, 3(9): 1116-1129 doi: 10.1039/b705737g
doi: 10.1039/b705737g
[118]   Shian S, Diebold RM, Clarke DR . Tunable lenses using transparent dielectric elastomer actuators. Optics Express. 2013, 21(7): 8669-8676 doi: 10.1364/OE.21.008669
doi: 10.1364/OE.21.008669
[119]   Siboni MH, Castañeda PP . Fiber-constrained, dielectric-elastomer composites: finite-strain response and stability analysis. Journal of the Mechanics and Physics of Solids. 2014, 68: 211-238 doi: 10.1016/j.jmps.2014.03.008
doi: 10.1016/j.jmps.2014.03.008
[120]   Son S, Goulbourne NC . Finite deformations of tubular dielectric elastomer sensors. Journal of Intelligent Material Systems and Structures. 2009, 20(18): 2187-2199 doi: 10.1177/1045389X09350718
doi: 10.1177/1045389X09350718
[121]   Son SI, Pugal D, Hwang T et al. Electromechanically driven variable-focus lens based on transparent dielectric elastomer. Applied Optics. 2012, 51(15): 2987-2996 doi: 10.1364/AO.51.002987
doi: 10.1364/AO.51.002987
[122]   Suo ZG . Theory of dielectric elastomers. Acta Mechanica Solida Sinica. 2010, 23(6): 549-578 doi: 10.1016/S0894-9166(11)60004-9
doi: 10.1016/S0894-9166(11)60004-9
[123]   Suo ZG, Zhao XH, Greene WH . A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids. 2008, 56(2): 467-486 doi: 10.1016/j.jmps.2007.05.021
doi: 10.1016/j.jmps.2007.05.021
[124]   Tagarielli VL, Hildick-Smith R, Huber JE . Electro-mechanical properties and electrostriction response of a rubbery polymer for EAP applications. International Journal of Solids and Structures. 2012, 49(23-24): 3409-3415 doi: 10.1016/j.ijsolstr.2012.07.018
doi: 10.1016/j.ijsolstr.2012.07.018
[125]   Toh W, Liu ZS, Ng TY et al. Inhomogeneous large deformation kinetics of polymeric gels. International Journal of Applied Mechanics. 2013, 5(1): 1350001 doi: 10.1142/S1758825113500014
doi: 10.1142/S1758825113500014
[126]   Toh W, Ng TY, Liu ZS et al. Deformation kinetics of pH-sensitive hydrogels. Polymer International. 2014, 63(9): 1578-1583 doi: 10.1002/pi.4652
doi: 10.1002/pi.4652
[127]   Treloar LRG . The elasticity of a network of long-chain molecules-II. Transactions of the Faraday Society. 1943, 39(36): 241-246 doi: 10.1039/tf9433900241
doi: 10.1039/tf9433900241
[128]   Treloar LRG . The Physics of Rubber Elasticity, 3rd Edition. 1975, Oxford, UK: Oxford University Press
[129]   Vertechy R, Frisoli A, Bergamasco M et al. Modeling and experimental validation of buckling dielectric elastomer actuators. Smart Materials and Structures. 2012, 21(9): 094005
[130]   Wallace GG, Spinks GM, Kane-Maguire LAP et al. Conductive Electroactive Polymers: Intelligent Polymer Systems. 2009, London: Taylor & Francis
[131]   Wang E, Desai MS, Lee S . Light-controlled graphene-elastin composite hydrogel actuators. Nano Letters. 2013, 13(6): 2826-2830 doi: 10.1021/nl401088b
doi: 10.1021/nl401088b
[132]   Wang HM, Zhu YL, Wang L et al. Experimental investigation on energy conversion for dielectric electroactive polymer generator. Journal of Intelligent Material Systems and Structures. 2012, 23(8): 885-895 doi: 10.1177/1045389X12442011
doi: 10.1177/1045389X12442011
[133]   Wang HM, Cai SQ, Carpi F et al. Computational model of hydrostatically coupled dielectric elastomer actuators. Journal of Applied Mechanics. 2012, 79(3): 031008 doi: 10.1115/1.4005885
doi: 10.1115/1.4005885
[134]   Wang HM, Lei M, Cai SQ . Viscoelastic deformation of a dielectric elastomer membrane subject to electromechanical loads. Journal of Applied Physics. 2013, 113(21): 213508 doi: 10.1063/1.4807911
doi: 10.1063/1.4807911
[135]   Wang J, Nguyen TD, Park HS . Electrostatically driven creep in viscoelastic dielectric elastomers. Journal of Applied Mechanics. 2014, 81(5): 051006 doi: 10.1115/1.4025999
doi: 10.1115/1.4025999
[136]   Wang M, Guth E . Statistical theory of networks of non-Gaussian flexible chains. Journal of Chemical Physics. 1952, 20(7): 1144-1157 doi: 10.1063/1.1700682
doi: 10.1063/1.1700682
[137]   Wissler M, Mazza E . Modeling of a pre-strained circular actuator made of dielectric elastomers. Sensors and Actuators A: Physical. 2005, 120(1): 184-192 doi: 10.1016/j.sna.2004.11.015
doi: 10.1016/j.sna.2004.11.015
[138]   Wissler M, Mazza E . Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators. Sensors and Actuators A: Physical. 2007, 134(2): 494-504 doi: 10.1016/j.sna.2006.05.024
doi: 10.1016/j.sna.2006.05.024
[139]   Wu PD, van der Giessen E . On improved network models for rubber elasticity and their applications to orientation hardening in glassy-polymers. Journal of the Mechanics and Physics of Solids. 1993, 41(3): 427-456 doi: 10.1016/0022-5096(93)90043-F
doi: 10.1016/0022-5096(93)90043-F
[140]   Wu Z, Zhong Z . Inhomogeneous equilibrium swelling of core-shell-coating gels. Soft Materials. 2013, 11(2): 215-220 doi: 10.1080/1539445X.2012.617644
doi: 10.1080/1539445X.2012.617644
[141]   Yamaue T, Doi M . Theory of one-dimensional swelling dynamics of polymer gels under mechanical constraint. Physical Review E. 2004, 69(4): 041402 doi: 10.1103/PhysRevE.69.041402
doi: 10.1103/PhysRevE.69.041402
[142]   Yamaue T, Doi M . The stress diffusion coupling in the swelling dynamics of cylindrical gels. Journal of Chemical Physics. 2005, 122(8): 084703 doi: 10.1063/1.1849153
doi: 10.1063/1.1849153
[143]   Yashin VV, Balazs AC . Modeling polymer gels exhibiting self-oscillations due to the Belousov-Zhabotinsky reaction. Macromolecules. 2006, 39(6): 2024-2026 doi: 10.1021/ma052622g
doi: 10.1021/ma052622g
[144]   Yashin VV, Kuksenok O, Dayal P et al. Mechano-chemical oscillations and waves in reactive gels. Reports on Progress in Physics. 2012, 75(6): 066601 doi: 10.1088/0034-4885/75/6/066601
doi: 10.1088/0034-4885/75/6/066601
[145]   Yeoh OH . Characterization of elastic properties of carbon black filled rubber vulcanizates. Rubber Chemistry and Technology. 1990, 63(5): 792-805 doi: 10.5254/1.3538289
doi: 10.5254/1.3538289
[146]   Yong HD, He XZ, Zhou YH . Electromechanical instability in anisotropic dielectric elastomers. International Journal of Engineering Science. 2012, 50(1): 144-150 doi: 10.1016/j.ijengsci.2011.08.007
doi: 10.1016/j.ijengsci.2011.08.007
[147]   Zarzar LD, Liu QH, He XM et al. Multifunctional actuation systems responding to chemical gradients. Soft Matter. 2012, 8(32): 8289-8293 doi: 10.1039/c2sm26064f
doi: 10.1039/c2sm26064f
[148]   Zhao XH, Suo ZG . Method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters. 2007, 91(6): 061921 doi: 10.1063/1.2768641
doi: 10.1063/1.2768641
[149]   Zhao XH, Suo ZG . Electrostriction in elastic dielectrics undergoing large deformation. Journal of Applied Physics. 2008, 104(12): 123530 doi: 10.1063/1.3031483
doi: 10.1063/1.3031483
[150]   Zhao XH, Suo ZG . Method to analyze programmable deformation of dielectric elastomer layers. Applied Physics Letters. 2008, 93(25): 251902 doi: 10.1063/1.3054159
doi: 10.1063/1.3054159
[151]   Zhao XH, Wang QM . Harnessing large deformation and instabilities of soft dielectrics: theory, experiment, and application. Applied Physics Reviews. 2014, 1(2): 021304 doi: 10.1063/1.4871696
doi: 10.1063/1.4871696
[152]   Zhao XH, Hong W, Suo ZG . Electromechanical hysteresis and coexistent states in dielectric elastomers. Physical Review B. 2007, 76(13): 134113 doi: 10.1103/PhysRevB.76.134113
doi: 10.1103/PhysRevB.76.134113
[153]   Zhao XH, Hong W, Suo ZG . Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core. Applied Physics Letters. 2008, 92(5): 051904 doi: 10.1063/1.2840158
doi: 10.1063/1.2840158
[154]   Zhao XH, Koh SJA, Suo ZG . Nonequilibrium thermodynamics of dielectric elastomers. International Journal of Applied Mechanics. 2011, 3(2): 203-217 doi: 10.1142/S1758825111000944
doi: 10.1142/S1758825111000944
[155]   Zhou J, Jiang L, Khayat RE . Failure analysis of a dielectric elastomer plate actuator considering boundary constraints. Journal of Intelligent Material Systems and Structures. 2013, 24(14): 1667-1674 doi: 10.1177/1045389X13483025
doi: 10.1177/1045389X13483025
[156]   Zhu J . Instability in nonlinear oscillation of dielectric elastomers. Journal of Applied Mechanics. 2015, 82(6): 061001 doi: 10.1115/1.4030075
doi: 10.1115/1.4030075
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