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Dielectric elastomeric actuators (DEAs) have been intensely studied in the recent decades. Their attractive features include large deformation(380%), large energy density(3.4 J/g), light weight, fast response( 1 ms), and high efficiency (80%-90%). They can be used in medical devices, space robotices and energy harvesters. The core part of DEAs is a dielectric elastomeric film with two electordes. When pre-stretched forces are exerted on the film in plane direction and voltage is applied across its thickness, the film achieves a large deformation. Usually the effect of electric field is described by Maxwell stress E2, and the effect of mechanical field is described by free energy function models (such as Neo-Hookean model, Arruda-Boyce model and Gent model). There are deviations in varying degree between every models and tests of dielectric elastomer. No model works perfectly. In the present paper, a new free energy function model is given to reduce the deviation. According to the main models above, an undetermined parameter C(1, 2) is introduced. and i (W/i)= C( 1, 2)(i2- 1-2 2-2), pi = C( 1, 2)( pi2- p1-2p2-2)(i/ pi), i = 1, 2, are assumed. The new i ( W/i) and pi are substituted into the equation of equilibrium of dielectric elastomer film pi + E2 = i ( W/i), i = 1, 2. Under equal-biaxial pre-stretched condition, P1 = P2 = P, p1 = p2 = p, C(1, 2) = C(). The parameter C()= (V2/t0)2/( 2- -4-( p- p-4)(/ p)) is obtained. Through analysing the test results of VHB4905 which contains a series of equal-biaxial pre-stretched tests, the data (, C()) are obtained from the test data (, V). C() =a + beI1-3, (I1 = 12 + 22 + 32) can be determined by data points (, C()). By computing the integral of i ( W/i)= a + beI1-3)(i2- 1-2 2-2), i = 1, 2, a new free energy function W = (a/2)(I1-3) + b[eI1-3(I1-3-1) + 1] (the new model) is achieved. The test results of VHB4905 are fitted by Neo-Hookean, Gent model and the new model. Neo-Hookean model fits well only in small deformation. Gent model fits well only in small-middle deformation, and does not work well when stretch 3.5. The new model fits well in small, middle and large deformation. It is better than Neo-Hookean and Gent model. The new model can give big support in the study of dielectric elastomer materials and structure property, and can be used in engineering practice effectively.
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[2] Sun S, Cao S Q 2012 Acta Phys. Sin. 61 210505(in Chinese) [孙舒, 曹树谦 2012 物理学报 61 210505]
[3] Li H T, Qin W Y, Zhou Z Y, Lan C B 2014 Acta Phys. Sin. 63 220504(in Chinese) [李海涛, 秦卫阳, 周至勇, 蓝春波 2014 物理学报 63 220504]
[4] Qiang L, Zhang R, Tian Q L, Zheng L M 2015 Chin. Phys. B 24 053101
[5] Mckay T, O’Brien B M, Calius E, Anderson I A 2010 Appl. Phys. Lett. 97 062911
[6] Kaltseis R, Keplinger C, Baumgartner R, Kaltenbrunner M, Li T F, Mcachler P, Schwödiauer R, Suo Z G, Bauer S 2011 Appl. Phys. Lett. 99 162904
[7] An P, Guo H, Chen M, Zhao M M, Yang J T, Liu J, Xue C Y, Tang J 2014 Acta Phys. Sin. 63 237306(in Chinese) [安萍, 郭浩, 陈萌, 赵苗苗, 杨江涛, 刘俊, 薛晨阳, 唐军 2014 物理学报 63 237306]
[8] Pelrine R, Kornbluh R, Pei Q, Joseph J 2000 Science 287 836
[9] Zhao X H, Suo Z G 2007 Appl. Phys. Lett. 91 061921
[10] Liu Y J, Liu L W, Zhang Z, Shi L, Leng J S 2008 Appl. Phys. Lett. 93 106101
[11] Zhao X H, Suo Z G 2010 Phys. Rev. Lett. 104 178302
[12] Koh S J A, Keplinger C, Li T, Siegfried B, Suo Z 2011 Mechatronics, IEEE/ASME Transactions on 16 33
[13] Suo Z, Zhu J 2009 Appl. Phys. Lett. 95 232909
[14] Lu T, Huang J, Jordi C, Gabor K, Huang R, David R, Suo Z 2012 Soft Matter 8 6167
[15] Zhu J, Kollosche M, Lu T, Kofod G, Suo Z 2012 Soft Matter 8 8840
[16] Kollosche M, Zhu J, Suo Z, Kofod G 2012 Phys. Rev. E 85 051801
[17] Stoyanov H, Brochu P, Niu X, Lai C, Yun S, Pei Q 2013 RSC Advances 3 2272
[18] Akbari S, Rosset S, Shea H R 2013 EAPAD 8 687
[19] Arruda E M, Boyce M C 1993 J Mech Phys. Solids 41 389
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[1] Park S, Shrout T R 1997 J. Appl. Phys. 82 1804
[2] Sun S, Cao S Q 2012 Acta Phys. Sin. 61 210505(in Chinese) [孙舒, 曹树谦 2012 物理学报 61 210505]
[3] Li H T, Qin W Y, Zhou Z Y, Lan C B 2014 Acta Phys. Sin. 63 220504(in Chinese) [李海涛, 秦卫阳, 周至勇, 蓝春波 2014 物理学报 63 220504]
[4] Qiang L, Zhang R, Tian Q L, Zheng L M 2015 Chin. Phys. B 24 053101
[5] Mckay T, O’Brien B M, Calius E, Anderson I A 2010 Appl. Phys. Lett. 97 062911
[6] Kaltseis R, Keplinger C, Baumgartner R, Kaltenbrunner M, Li T F, Mcachler P, Schwödiauer R, Suo Z G, Bauer S 2011 Appl. Phys. Lett. 99 162904
[7] An P, Guo H, Chen M, Zhao M M, Yang J T, Liu J, Xue C Y, Tang J 2014 Acta Phys. Sin. 63 237306(in Chinese) [安萍, 郭浩, 陈萌, 赵苗苗, 杨江涛, 刘俊, 薛晨阳, 唐军 2014 物理学报 63 237306]
[8] Pelrine R, Kornbluh R, Pei Q, Joseph J 2000 Science 287 836
[9] Zhao X H, Suo Z G 2007 Appl. Phys. Lett. 91 061921
[10] Liu Y J, Liu L W, Zhang Z, Shi L, Leng J S 2008 Appl. Phys. Lett. 93 106101
[11] Zhao X H, Suo Z G 2010 Phys. Rev. Lett. 104 178302
[12] Koh S J A, Keplinger C, Li T, Siegfried B, Suo Z 2011 Mechatronics, IEEE/ASME Transactions on 16 33
[13] Suo Z, Zhu J 2009 Appl. Phys. Lett. 95 232909
[14] Lu T, Huang J, Jordi C, Gabor K, Huang R, David R, Suo Z 2012 Soft Matter 8 6167
[15] Zhu J, Kollosche M, Lu T, Kofod G, Suo Z 2012 Soft Matter 8 8840
[16] Kollosche M, Zhu J, Suo Z, Kofod G 2012 Phys. Rev. E 85 051801
[17] Stoyanov H, Brochu P, Niu X, Lai C, Yun S, Pei Q 2013 RSC Advances 3 2272
[18] Akbari S, Rosset S, Shea H R 2013 EAPAD 8 687
[19] Arruda E M, Boyce M C 1993 J Mech Phys. Solids 41 389
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