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A new free energy model for predicting the qual-biaxial tests of dielectric elastomers

Jiang Shi-Ming

A new free energy model for predicting the qual-biaxial tests of dielectric elastomers

Jiang Shi-Ming
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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.
      PACS:
      Corresponding author: Jiang Shi-Ming, jiangshiming80@163.com
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    [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 63 220504]

    [4]

    Qiang L, Zhang R, Tian Q L, Zheng L M 2015 Chin. Phys. B 24 053101

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    Mckay T, O’Brien B M, Calius E, Anderson I A 2010 Appl. Phys. Lett. 97 062911

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    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 63 237306]

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    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

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    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

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    Suo Z, Zhu J 2009 Appl. Phys. Lett. 95 232909

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    Lu T, Huang J, Jordi C, Gabor K, Huang R, David R, Suo Z 2012 Soft Matter 8 6167

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    Zhu J, Kollosche M, Lu T, Kofod G, Suo Z 2012 Soft Matter 8 8840

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    Kollosche M, Zhu J, Suo Z, Kofod G 2012 Phys. Rev. E 85 051801

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    Stoyanov H, Brochu P, Niu X, Lai C, Yun S, Pei Q 2013 RSC Advances 3 2272

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    Akbari S, Rosset S, Shea H R 2013 EAPAD 8 687

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    Arruda E M, Boyce M C 1993 J Mech Phys. Solids 41 389

  • [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 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 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 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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Publishing process
  • Received Date:  15 February 2015
  • Accepted Date:  08 May 2015
  • Published Online:  05 September 2015

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