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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.

Soft active materials have emerged as novel materials for diverse applications that can not be addressed by classical hard passive materials. The field of soft active materials is wide and open, where mechanics meets physics, chemistry and machinery. To understand the unique behavior of soft active materials, as well as to aid the design of soft materials based machines, mechanics modeling and analysis plays an important role to tackle these problems, where constitutive law of soft materials is the focus and core of the problem. Focusing on two currently popular soft materials, i.e., dielectric elastomer and hydrogel, the authors present an excellent overview of the constitutive laws developed in the past decades. They formulate and review the constitutive laws of artificial muscles from the pointview of free energy function.The authors give detailed and comprehensive review of the various forms of free energy used in the literature. They also provide their perspectives on the features and limitations of the models.The review is an excellent review and is very helpful for the researcher in this field, particularly those who just start up their research.

人工肌肉本构模型的综述

[1]Afroze, F., Nies, E., Berghmans, H., 2000. Phase transitions in the system poly(N-isopropylacrylamide)/water and swelling behavior of the corresponding networks. Journal of Molecular Structure, 554(1):55-68.

[2]Agoras, M., Lopez-Pamies, O., Castañeda, P.P., 2009. A general hyperelastic model for incompressible fiber-reinforced elastomers. Journal of the Mechanics and Physics of Solids, 57(2):268-286.

[3]Ahnert, K., Abel, M., Kollosche, M., et al., 2011. Soft capacitors for wave energy harvesting. Journal of Materials Chemistry, 21(38):14492-14497.

[4]Akbari, S., Shea, H.R., 2012. Microfabrication and characterization of an array of dielectric elastomer actuators generating uniaxial strain to stretch individual cells. Journal of Micromechanics and Microengineering, 22(4):045020.

[5]Arruda, E.M., Boyce, M.C., 1993. A three-dimensional constitutive model for the large strech behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids, 41(2):389-412.

[6]Aschwanden, M., Stemmer, A., 2006. Polymeric, electrically tunable diffraction grating based on artificial muscles. Optics Letters, 31(17):2610-2612.

[7]Aw, K.C., McDaid, A.J., 2014. Bio-applications of ionic polymer metal composite transducers. Smart Materials and Structures, 23(7):074005.

[8]Bai, Y.Y., Jiang, Y.H., Chen, B.H., et al., 2014. Cyclic performance of viscoelastic dielectric elastomers with solid hydrogel electrodes. Applied Physics Letters, 104(6):062902.

[9]Balasubramanian, R., Santos, V.J., 2014. The Human Hand as an Inspiration for Robot Hand Development. Springer, Heidelberg.

[10]Bassil, M., Davenas, J., Tahchi, M.E., 2008. Electrochemical properties and actuation mechanisms of polyacrylamide hydrogel for artificial muscle application. Sensors and Actuators B: Chemical, 134(2):496-501.

[11]Beda, T., 2014. An approach for hyperelastic model-building and parameters estimation: a review of constitutive models. European Polymer Journal, 50:97-108.

[12]Biddiss, E., Chau, T., 2008. Dielectric elastomers as actuators for upper limb prosthetics: challenges and opportunities. Medical Engineering & Physics, 30(4):403-418.

[13]Boissonade, J., 2003. Simple chemomechanical process for self-generation of rhythms and forms. Physical Review Letters, 90(18):188302.

[14]Boissonade, J., 2009. Oscillatory dynamics induced in polyelectrolyte gels by a non-oscillatory reaction: a model. European Physical Journal E, 28(3):337-346.

[15]Boyce, M.C., Arruda, E.M., 2000. Constitutive models of rubber elasticity: a review. Rubber Chemistry and Technology, 73(3):504-523.

[16]Cai, S.Q., Suo, Z.G., 2011. Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels. Journal of the Mechanics and Physics of Solids, 59(11):2259-2278.

[17]Cai, S.Q., Suo, Z.G., 2012. Equations of state for ideal elastomeric gels. Europhysics Letters, 97(3):34009.

[18]Cai, S.Q., Lou, Y.C., Ganguly, P., et al., 2010. Force generated by a swelling elastomer subject to constraint. Journal of Applied Physics, 107(10):103535.

[19]Carpi, F., Rossi, D.D., 2004. Dielectric elastomer cylindrical actuators: electromechanical modelling and experimental evaluation. Materials Science and Engineering: C, 24(4):555-562.

[20]Carpi, F., Migliore, A., Serra, G., et al., 2005. Helical dielectric elastomer actuators. Smart Materials and Structures, 14(6):1210-1216.

[21]Carpi, F., Salaris, C., Rossi, D.D., 2007. Folded dielectric elastomer actuators. Smart Materials and Structures, 16(2):S300-S305.

[22]Carpi, F., Frediani, G., Rossi, D.D., 2010. Hydrostatically coupled dielectric elastomer actuators. IEEE/ASME Transactions on Mechatronics, 15(2):308-315.

[23]Carpi, F., Kornbluh, R., Sommer-Larsen, P., et al., 2011a. Electroactive polymer actuators as artificial muscles: are they ready for bioinspired applications? Bioinspiration & Biomimetics, 6(4):045006.

[24]Carpi, F., Frediani, G., Turco, S., et al., 2011b. Bioinspired tunable lens with muscle-like electroactive elastomers. Advanced Functional Materials, 21(21):4152-4158.

[25]Chen, X.Y., Dai, H.H., 2013. Asymptotic solutions and new insights for cylinder and core–shell polymer gels in a solvent. Soft Matter, 9(36):8664-8677.

[26]Chiba, S., Waki, M., Wada, T., et al., 2013. Consistent ocean wave energy harvesting using electroactive polymer (dielectric elastomer) artificial muscle generators. Applied Energy, 104:497-502.

[27]Chu, L.Y., Xie, R., Ju, X.J., et al., 2013. Smart Hydrogel Functional Material. Springer, Heidelberg.

[28]Dai, H.H., Song, Z.L., 2011. Some analytical formulas for the equilibrium states of a swollen hydrogel shell. Soft Matter, 7(18):8473-8483.

[29]Danielsson, M., Parks, D.M., Boyce, M.C., 2004. Constitutive modeling of porous hyperelastic materials. Mechanics of Materials, 36(4):347-358.

[30]Fang, Z.H., Punckt, C., Leung, E.Y., et al., 2010. Tuning of structural color using a dielectric actuator and multifunctional compliant electrodes. Applied Optics, 49(35):6689-6696.

[31]Fereidoonnezhad, B., Naghdabadi, R., Arghavani, J., 2013. A hyperelastic constitutive model for fiber-reinforced rubber-like materials. International Journal of Engineering Science, 71:36-44.

[32]Flory, P.J., Rehner, J., 1943. Statistical mechanics of cross-linked polymer networks. II. Swelling. Journal of Chemical Physics, 11(11):521-526.

[33]Foo, C.C., Cai, S.Q., Koh, S.J.A., et al., 2012a. Model of dissipative dielectric elastomers. Journal of Applied Physics, 111(3):034102.

[34]Foo, C.C., Koh, S.J.A., Keplinger, C., et al., 2012b. Performance of dissipative dielectric elastomer generators. Journal of Applied Physics, 111(9):094107.

[35]Gent, A.N., 1996. A new constitutive relation for rubber. Rubber Chemistry and Technology, 69(1):59-61.

[36]Gerlach, G., Guenther, M., Sorber, J., et al., 2005. Chemical and pH sensors based on the swelling behavior of hydrogels. Sensors and Actuators B: Chemical, 111-112:555-561.

[37]Giousouf, M., Kovacs, G., 2013. Dielectric elastomer actuators used for pneumatic valve technology. Smart Materials and Structures, 22(10):104010.

[38]Gisby, T.A., O’Brien, B.M., Anderson, I.A., 2013. Self sensing feedback for dielectric elastomer actuators. Applied Physics Letters, 102(19):193703.

[39]Graf, C., Hitzbleck, J., Feller, T., et al., 2014. Dielectric elastomer-based energy harvesting: material, generator design, and optimization. Journal of Intelligent Material Systems and Structures, 25(8):951-966.

[40]Guo, Z.Y., Peng, X.Q., Moran, B., 2006. A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. Journal of the Mechanics and Physics of Solids, 54(9):1952-1971.

[41]Haus, H., Matysek, M., Moßinger, H., et al., 2013. Modelling and characterization of dielectric elastomer stack actuators. Smart Materials and Structures, 22(10):104009.

[42]Hong, W., 2011. Modeling viscoelastic dielectrics. Journal of the Mechanics and Physics of Solids, 59(3):637-650.

[43]Hong, W., Zhao, X.H., Zhou, J.X., et al., 2008. A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 56(5):1779-1793.

[44]Hong, W., Liu, Z.S., Suo, Z.G., 2009. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures, 46(17):3282-3289.

[45]Hong, W., Zhao, X.H., Suo, Z.G., 2010. Large deformation and electrochemistry of polyelectrolyte gels. Journal of the Mechanics and Physics of Solids, 58(4):558-577.

[46]Horgan, C.O., Saccomandi, G., 2002. Constitutive modelling of rubber-like and biological materials with limiting chain extensibility. Mathematics and Mechanics of Solids, 7(4):353-371.

[47]Horgan, C.O., Saccomandi, G., 2005. A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. Journal of the Mechanics and Physics of Solids, 53(9):1985-2015.

[48]Horgan, C.O., Saccomandi, G., 2006. Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chemistry and Technology, 79(1):152-169.

[49]Hu, Y.H., Suo, Z.G., 2012. Viscoelasticity and poroelasticity in elastomeric gels. Acta Mechanica Solida Sinica, 25(5):441-458.

[50]Huang, J.S., Li, T.F, Foo, C.C., et al., 2012a. Giant, voltage-actuated deformation of a dielectric elastomer under dead load. Applied Physics Letters, 100(4):041911.

[51]Huang, J.S., Lu, T.Q., Zhu, J., et al., 2012b. Large, uni-directional actuation in dielectric elastomers achieved by fiber stiffening. Applied Physics Letters, 100(21):211901.

[52]Huang, J.S., Shian, S., Suo, Z.G., et al., 2013. Maximizing the energy density of dielectric elastomer generators using equi-biaxial loading. Advanced Functional Materials, 23(40):5056-5061.

[53]Huang, Z.P., 2014. A novel constitutive formulation for rubberlike materials in thermoelasticity. Journal of Applied Mechanics, 81(4):041013.

[54]Hunt, S., McKay, T.G., Anderson, I.A., 2014. A self-healing dielectric elastomer actuator. Applied Physics Letters, 104(11):113701.

[55]Joglekar, M.M., 2014. An energy-based approach to extract the dynamic instability parameters of dielectric elastomer actuators. Journal of Applied Mechanics, 81(9):091010.

[56]Jung, K., Kim, K.J., Choi, H.R., 2008. A self-sensing dielectric elastomer actuator. Sensors and Actuators A: Physical, 143(2):343-351.

[57]Kaltseis, R., Keplinger, C., Baumgartner, R., et al., 2011. Method for measuring energy generation and efficiency of dielectric elastomer generators. Applied Physics Letters, 99(16):162904.

[58]Keplinger, C., Li, T.F., Baumgartner, R., et al., 2012. Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation. Soft Matter, 8(2):285-288.

[59]Kim, S., Laschi, C., Trimmer, B., 2013. Soft robotics: a bioinspired evolution in robotics. Trends in Biotechnology, 31(5):287-294.

[60]Klinkel, S., Zwecker, S., Muller, R., 2013. A solid shell finite element formulation for dielectric elastomers. ASME Journal of Applied Mechanics, 80(2):021026.

[61]Knudson, D., 2007. Fundamentals of Biomechanics, 2nd Edition. Springer, New York.

[62]Koh, S.J.A., Zhao, X.H., Suo, Z.G., 2009. Maximal energy that can be converted by a dielectric elastomer generator. Applied Physics Letters, 94(26):262902.

[63]Koh, S.J.A., Keplinger, C., Li, T.F., et al., 2011. Dielectric elastomer generators: how much energy can be converted? IEEE/ASME Transactions on Mechatronics, 16(1):33-41.

[64]Kovacs, G., Duering, L., Michel, S., et al., 2009. Stacked dielectric elastomer actuator for tensile force transmission. Sensors and Actuators A: Physical, 155(2):299-307.

[65]Kuksenok, O., Yashin, V.V., Balazs, A.C., 2008. Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. Physical Review E, 78(4):041406.

[66]Kwon, H.J., Yasuda, K., Gong, J.P., et al., 2014. Polyelectrolyte hydrogels for replacement and regeneration of biological tissues. Macromolecular Research, 22(3):227-235.

[67]La, T.G., Lau, G.K., 2013. Very high dielectric strength for dielectric elastomer actuators in liquid dielectric immersion. Applied Physics Letters, 102(19):192905.

[68]Lawrence, D.B., Cai, T., Hu, Z.B., et al., 2007. Temperature-responsive semipermeable capsules composed of colloidal microgel spheres. Langmuir, 23(2):395-398.

[69]Leng, J.S., Liu, L.W., Liu, Y.J., et al., 2009. Electromechanical stability of dielectric elastomer. Applied Physics Letters, 94(21):211901.

[70]Li, B., Chen, H.L., Qiang J.H., et al., 2012. A model for conditional polarization of the actuation enhancement of a dielectric elastomer. Soft Matter, 8(2):311-317.

[71]Li, T.F., Qu, S.X., Yang, W., 2012. Energy harvesting of dielectric elastomer generators concerning inhomogeneous fields and viscoelastic deformation. Journal of Applied Physics, 112(3):034119.

[72]Li, T.F., Keplinger, C., Baumgartner, R., et al., 2013. Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. Journal of the Mechanics and Physics of Solids, 61(2):611-628.

[73]Li, T.F., Zou, Z.A., Mao, G.Y., et al., 2014. Electromechanical bi-stable behavior of a novel dielectric elastomer actuator. Journal of Applied Mechanics, 81(4):041019.

[74]Liang, X., Cai, S.Q., 2015. Shape bifurcation of a spherical dielectric elastomer balloon under the actions of internal pressure and electric voltage. Journal of Applied Mechanics, 82(10):101002.

[75]Lim, H.L., Hwang, Y., Kar, M., et al., 2014. Smart hydrogels as functional biomimetic systems. Biomaterials Science, 2(5):603-618.

[76]Liu, J.J., Mao, G.Y., Huang, X.Q., et al., 2015. Enhanced compressive sensing of dielectric elastomer sensor using a novel structure. Journal of Applied Mechanics, 81(4):041019.

[77]Liu, L., Chen, H.L., Sheng, J.J., et al., 2014. Experimental study on the dynamic response of inplane deformation of dielectric elastomer under alternating electric load. Smart Materials and Structures, 23(2):025037.

[78]Liu, L.W., Liu, Y.J., Li, B., et al., 2011. Thermo-electro-mechanical instability of dielectric elastomers. Smart Materials and Structures, 20(7):075004.

[79]Liu, L.W., Liu, Y.J., Luo, X.J., et al., 2012. Electromechanical instability and snap-through instability of dielectric elastomers undergoing polarization saturation. Mechanics of Materials, 55:60-72.

[80]Liu, L.W., Zhang, Z., Liu, Y.J., et al., 2014a. Failure modeling of folded dielectric elastomer actuator. Science China: Physics, Mechanics & Astronomy, 57(2):263-272.

[81]Liu, L.W., Yu, K., Liu, Y.J., et al., 2014b. Polar elastic dielectric of large electrocaloric effect and deformation. Mechanics of Materials, 69(1):71-92.

[82]Liu, L.W., Liu, Y.J., Yu, K., et al., 2014c. Thermoelectromechanical stability of dielectric elastomers undergoing temperature variation. Mechanics of Materials, 72:33-45.

[83]Liu, L.W., Zhang, Z., Li, J.R., et al., 2015. Stability of dielectric elastomer/carbon nanotube composites coupling electrostriction and polarization. Composites Part B: Engineering, 78(1):35-41.

[84]Liu, Y.J., Liu, L.W., Zhang, Z., et al., 2008. Comment on method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters, 93(10):106101.

[85]Liu, Y.J., Liu, L.W., Sun, S.H., et al., 2009a. An investigation on electromechanical stability of dielectric elastomers undergoing large deformation. Smart Materials and Structures, 18(9):095040.

[86]Liu, Y.J., Liu, L.W., Zhang, Z., et al., 2009b. Dielectric elastomer film actuators: characterization, experiment and analysis. Smart Materials and Structures, 18(9):095024.

[87]Liu, Y.J., Liu, L.W., Zhang, Z., et al., 2010. Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer. Europhysics Letters, 90(3):36004.

[88]Lochmatter, P., Kovacs, G., Wissler, M., 2007. Characterization of dielectric elastomer actuators based on a visco-hyperelastic film model. Smart Materials and Structures, 16(2):477-486.

[89]Lu, T.Q., Huang, J.S., Jordi, C., et al., 2012. Dielectric elastomer actuators under equal-biaxial forces, uniaxial forces, and uniaxial constraint of stiff fibers. Soft Matter, 8(22):6167-6173.

[90]Lu, T.Q., Foo, C.C., Huang, J.S., et al., 2014. Highly deformable actuators made of dielectric elastomers clamped by rigid rings. Journal of Applied Physics, 115(18):184105.

[91]Lucantonio, A., Nardinocchi, P., 2012. Reduced models of swelling-induced bending of gel bars. International Journal of Solids and Structures, 49(11-12):1399-1405.

[92]Mao, G.Y., Li, T.F., Zou, Z.A., et al., 2014. Prestretch effect on snap-through instability of inflated tubular elastomeric balloons. International Journal of Solids and Structures, 51(11-12):2109-2115.

[93]Mao, G.Y., Huang, X.Q., Liu, J.J., et al., 2015. Dielectric elastomer peristaltic pump module with finite deformation. Smart Materials and Structures, 24(7):075026.

[94]Marckmann, G., Verron, E., 2006. Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry and Technology, 79(5):835-858.

[95]Marcombe, R., Cai, S.Q., Hong, W., et al., 2010. A theory of constrained swelling of a pH-sensitive hydrogel. Soft Matter, 6(4):784-793.

[96]McKay, T., O’Brien, B., Calius, E., et al., 2010. An integrated, self priming dielectric elastomer generator. Applied Physics Letters, 97(6):062911.

[97]McKay, T.G., O’Brien, B.M., Calius, E.P., et al., 2011. Soft generators using dielectric elastomers. Applied Physics Letters, 98(14):142903.

[98]Mooney, M., 1940. A theory of large elastic deformation. Journal of Applied Physics, 11(9):582-592.

[99]Moscardo, M., Zhao, X.H., Suo, Z.G., et al., 2008. On designing dielectric elastomer actuators. Journal of Applied Physics, 104(9):093503.

[100]Mutlu, R., Alici, G., Xiang, X., et al., 2014. Electro-mechanical modelling and identification of electroactive polymer actuators as smart robotic manipulators. Mechatronics, 24(3):241-251.

[101]Nguyen, C.H., Alici, G., Mutlu, R., 2014b. A compliant translational mechanism based on dielectric elastomer actuators. Journal of Mechanical Design, 136(6):061009.

[102]Nguyen, C.T., Phung, H., Nguyen, T.D., et al., 2014a. A small biomimetic quadruped robot driven by multistacked dielectric elastomer actuators. Smart Materials and Structures, 23(6):065005.

[103]Ogden, R.W., 1972. 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, 326(1567):565-584.

[104]O’Halloran, A., O’Malley, F., McHugh, P., 2008. A review on dielectric elastomer actuators, technology, applications, and challenges. Journal of Applied Physics, 104(7):071101.

[105]Otake, M., 2010. Electroactive Polymer Gel Robots: Modelling and Control of Artificial Muscles. Springer, Berlin.

[106]Park, H.S., Nguyen, T.D., 2013. Viscoelastic effects on electromechanical instabilities in dielectric elastomers. Soft Matter, 9(4):1031-1042.

[107]Pelrine, R., Kornbluh, R., Pei, Q.B., et al., 2000. High-speed electrically actuated elastomers with strain greater than 100%. Science, 287(5454):836-839.

[108]Plante, J.S., Dubowsky, S., 2006. Large-scale failure modes of dielectric elastomer actuators. International Journal of Solids and Structures, 43(25-26):7727-7751.

[109]Plante, J.S., Dubowsky, S., 2007. On the performance mechanisms of dielectric elastomer actuators. Sensors and Actuators A: Physical, 137(1):96-109.

[110]Qu, S.X., Suo, Z.G., 2012. A finite element method for dielectric elastomer. Acta Mechanica Solida Sinica, 25(5):459-466.

[111]Qu, S.X., Li, K., Li, T.F., et al., 2012. Rate dependent stress-stretch relation of dielectric elastomers subjected to pure shear like loading and electric field. Acta Mechanica Solida Sinica, 25(5):542-549.

[112]Rivlin, R.S., 1948. 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, 241(835):379-397.

[113]Rotzetter, A.C.C., Schumacher, C.M., Bubenhofer, S.B., et al., 2012. Thermoresponsive polymer induced sweating surfaces as an efficient way to passively cool buildings. Advanced Materials, 24(39):5352-5356.

[114]Shahinpoor, M., 2003. Ionic polymer-conductor composites as biomimetic sensors, robotic actuators and artificial muscles-a review. Electrochimica Acta, 48(14-16):2343-2353.

[115]Shahinpoor, M., Bar-Cohen, Y., Simpson, J.O., et al., 1998. Ionic polymer–metal composites (IPMCs) as biomimetic sensors, actuators and artificial muscles-a review. Smart Materials and Structures, 7(6):R15-R30.

[116]Shahinpoor, M., Kim, K.J., Mojarrad, M., 2007. Artificial Muscles: Applications of Advanced Polymeric Nanocomposites. Taylor & Francis, London.

[117]Shankar, R., Ghosh, T.K., Spontak, R.J., 2007. Dielectric elastomers as next-generation polymeric actuators. Soft Matter, 3(9):1116-1129.

[118]Shian, S., Diebold, R.M., Clarke, D.R., 2013. Tunable lenses using transparent dielectric elastomer actuators. Optics Express, 21(7):8669-8676.

[119]Siboni, M.H., Castañeda, P.P., 2014. Fiber-constrained, dielectric-elastomer composites: finite-strain response and stability analysis. Journal of the Mechanics and Physics of Solids, 68:211-238.

[120]Son, S., Goulbourne, N.C., 2009. Finite deformations of tubular dielectric elastomer sensors. Journal of Intelligent Material Systems and Structures, 20(18):2187-2199.

[121]Son, S.I., Pugal, D., Hwang, T., et al., 2012. Electromechanically driven variable-focus lens based on transparent dielectric elastomer. Applied Optics, 51(15):2987-2996.

[122]Suo, Z.G., 2010. Theory of dielectric elastomers. Acta Mechanica Solida Sinica, 23(6):549-578.

[123]Suo, Z.G., Zhao, X.H., Greene, W.H., 2008. A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids, 56(2):467-486.

[124]Tagarielli, V.L., Hildick-Smith, R., Huber, J.E., 2012. Electro-mechanical properties and electrostriction response of a rubbery polymer for EAP applications. International Journal of Solids and Structures, 49(23-24):3409-3415.

[125]Toh, W., Liu, Z.S., Ng, T.Y., et al., 2013. Inhomogeneous large deformation kinetics of polymeric gels. International Journal of Applied Mechanics, 5(1):1350001.

[126]Toh, W., Ng, T.Y., Liu, Z.S., et al., 2014. Deformation kinetics of pH-sensitive hydrogels. Polymer International, 63(9):1578-1583.

[127]Treloar, L.R.G., 1943. The elasticity of a network of long-chain molecules-II. Transactions of the Faraday Society, 39(36):241-246.

[128]Treloar, L.R.G., 1975. The Physics of Rubber Elasticity, 3rd Edition. Oxford University Press, Oxford, UK.

[129]Vertechy, R., Frisoli, A., Bergamasco, M., et al., 2012. Modeling and experimental validation of buckling dielectric elastomer actuators. Smart Materials and Structures, 21(9):094005.

[130]Wallace, G.G., Spinks, G.M., Kane-Maguire, L.A.P., et al., 2009. Conductive Electroactive Polymers: Intelligent Polymer Systems. Taylor & Francis, London.

[131]Wang, E., Desai, M.S., Lee, S., 2013. Light-controlled graphene-elastin composite hydrogel actuators. Nano Letters, 13(6):2826-2830.

[132]Wang, H.M., Zhu, Y.L., Wang, L., et al., 2012a. Experimental investigation on energy conversion for dielectric electroactive polymer generator. Journal of Intelligent Material Systems and Structures, 23(8):885-895.

[133]Wang, H.M., Cai, S.Q., Carpi, F., et al., 2012b. Computational model of hydrostatically coupled dielectric elastomer actuators. Journal of Applied Mechanics, 79(3):031008.

[134]Wang, H.M., Lei, M., Cai, S.Q., 2013. Viscoelastic deformation of a dielectric elastomer membrane subject to electromechanical loads. Journal of Applied Physics, 113(21):213508.

[135]Wang, J., Nguyen, T.D., Park, H.S., 2014. Electrostatically driven creep in viscoelastic dielectric elastomers. Journal of Applied Mechanics, 81(5):051006.

[136]Wang, M., Guth, E., 1952. Statistical theory of networks of non-Gaussian flexible chains. Journal of Chemical Physics, 20(7):1144-1157.

[137]Wissler, M., Mazza, E., 2005. Modeling of a pre-strained circular actuator made of dielectric elastomers. Sensors and Actuators A: Physical, 120(1):184-192.

[138]Wissler, M., Mazza, E., 2007. Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators. Sensors and Actuators A: Physical, 134(2):494-504.

[139]Wu, P.D., van der Giessen, E., 1993. On improved network models for rubber elasticity and their applications to orientation hardening in glassy-polymers. Journal of the Mechanics and Physics of Solids, 41(3):427-456.

[140]Wu, Z., Zhong, Z., 2013. Inhomogeneous equilibrium swelling of core-shell-coating gels. Soft Materials, 11(2):215-220.

[141]Yamaue, T., Doi, M., 2004. Theory of one-dimensional swelling dynamics of polymer gels under mechanical constraint. Physical Review E, 69(4):041402.

[142]Yamaue, T., Doi, M., 2005. The stress diffusion coupling in the swelling dynamics of cylindrical gels. Journal of Chemical Physics, 122(8):084703.

[143]Yashin, V.V., Balazs, A.C., 2006. Modeling polymer gels exhibiting self-oscillations due to the Belousov-Zhabotinsky reaction. Macromolecules, 39(6):2024-2026.

[144]Yashin, V.V., Kuksenok, O., Dayal, P., et al., 2012. Mechano-chemical oscillations and waves in reactive gels. Reports on Progress in Physics, 75(6):066601.

[145]Yeoh, O.H., 1990. Characterization of elastic properties of carbon black filled rubber vulcanizates. Rubber Chemistry and Technology, 63(5):792-805.

[146]Yong, H.D., He, X.Z., Zhou, Y.H., 2012. Electromechanical instability in anisotropic dielectric elastomers. International Journal of Engineering Science, 50(1):144-150.

[147]Zarzar, L.D., Liu, Q.H., He, X.M., et al., 2012. Multifunctional actuation systems responding to chemical gradients. Soft Matter, 8(32):8289-8293.

[148]Zhao, X.H., Suo, Z.G., 2007. Method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters, 91(6):061921.

[149]Zhao, X.H., Suo, Z.G., 2008a. Electrostriction in elastic dielectrics undergoing large deformation. Journal of Applied Physics, 104(12):123530.

[150]Zhao, X.H., Suo, Z.G., 2008b. Method to analyze programmable deformation of dielectric elastomer layers. Applied Physics Letters, 93(25):251902.

[151]Zhao, X.H., Wang, Q.M., 2014. Harnessing large deformation and instabilities of soft dielectrics: theory, experiment, and application. Applied Physics Reviews, 1(2):021304.

[152]Zhao, X.H., Hong, W., Suo, Z.G., 2007. Electromechanical hysteresis and coexistent states in dielectric elastomers. Physical Review B, 76(13):134113.

[153]Zhao, X.H., Hong, W., Suo, Z.G., 2008. Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core. Applied Physics Letters, 92(5):051904.

[154]Zhao, X.H., Koh, S.J.A., Suo, Z.G., 2011. Nonequilibrium thermodynamics of dielectric elastomers. International Journal of Applied Mechanics, 3(2):203-217.

[155]Zhou, J., Jiang, L., Khayat, R.E., 2013. Failure analysis of a dielectric elastomer plate actuator considering boundary constraints. Journal of Intelligent Material Systems and Structures, 24(14):1667-1674.

[156]Zhu, J., 2015. Instability in nonlinear oscillation of dielectric elastomers. Journal of Applied Mechanics, 82(6):061001.

[157]Zou, Z.A., Li, T.F., Qu, S.X., et al., 2014. Active shape control and phase coexistence of dielectric elastomer membrane with patterned electrodes. Journal of Applied Mechanics, 81(3):031016.