Top

Published in:

2013 | OriginalPaper | Chapter

Electro-Elastic Continuum Models for Electrostrictive Elastomers

Authors : R. Vertechy, G. Berselli, V. Parenti Castelli, M. Bergamasco

Published in: Advances in Elastomers I

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A continuum finite-deformation model is described for the study of the isothermal electro-elastic deformations of electrostrictive elastomers. The model comprises general balance equations of motion, electrostatics and electro-mechanical energy, along with phenomenological invariant-based constitutive relations. The model is presented in both Eulerian (spatial) and Lagrangian (material) description. Specialization of the considered model is also presented for “Dielectric Elastomers”, which are a specific class of electrostrictive elastomers having dielectric properties independent of deformation.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Radiation Processing of Elastomers

Available only for authorised users

Zhenyi, M., Scheinbeim, J.I., Lee, J.W., Newman, B.A.: High field electrostrictive response of polymers. J. Polym. Sci. Part B: Polym. Phys. 32(16), 2721–2731 (1994)CrossRef

Zhang, Q.M., Su, J., Kim, C.H., Ting, R., Capps, R.: An experimental investigation of electromechanical responses in a polyurethane elastomer. J. Appl. Phys. 81(6), 2770–2776 (1997)CrossRef

Guillot, F.M., Balizer, E.: Electrostrictive effect in polyurethanes. J. Appl. Polym. Sci. 89(2), 399–404 (2003)CrossRef

Zhang, Q.M., Bharti, V., Zhao, X.: Giant electrostriction and Relaxor Ferroelectric behavior in electron-irradiated Poly(vinylidene fluoride-trifluoroethylene) copolymer. Science 280(5372), 2101–2104 (1998)CrossRef

Bauer, F., Fousson, E., Zhang, Q.M.: Recent advances in highly electrostrictive P(VDF–TrFE–CFE) terpolymers. IEEE Trans. Dielectr. Electr. Insul. 13(5), 1149–1154 (2006)

Su, J., Ounaies, Z., Harrison, J.S., Bar-Cohen, Y., Leary, S.: Electromechanically active polymer blends for actuation. Proc. Smart Struct. Mater. 2000: Electroact. Polym. Actuators Devices (EAPAD) 3987, 65–72 (2000)CrossRef

Pelrine, R., Kornbluh, R., Joseph, J.: Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sens. Actuators A 64, 77–85 (1998)CrossRef

Pelrine, R., Kornbluh, R., Pei, Q., Joseph, J.: High-speed electrically actuated elastomers with strain greater than 100 %. Science 287(5454), 836–839 (2000)CrossRef

Kofod, G., Sommer-Larsen, P., Kornbluh, R., Pelrine, R.: Actuation response of Polyacrylate dielectric elastomers. J. Intell. Mater. Syst. Struct. 14, 787–793 (2003)CrossRef

10.

Mathew, G., Rhee, J.M., Nah, C., Leo, D.J.: Effects of silicone rubber on properties of dielectric acrylate elastomer actuator. Polym. Eng. Sci. 46(10), 1455–1460 (2006)CrossRef

11.

Ludeelerd, P., Niamlang, S., Kunaruksapong, R., Sirivat, A.: Effect of elastomer matrix type on electromechanical response of conductive polypyrrole/elastomer blends. J. Phys. Chem. Solids 71, 1243–1250 (2010)CrossRef

12.

Lehmann, W., Skupin, H., Tolksdorf, C., Gebhard, E., Zentel, R., Krüger, P., Lösche, M., Kremer, F.: Giant lateral electrostriction in ferroelectric liquid-crystalline elastomers. Nature 410, 447–450 (2001)CrossRef

13.

Ha, S.M., Yuan, W., Pei, Q., Pelrine, R., Stanford, S.: Interpenetrating networks of elastomers exhibiting 300 % electrically-induced area strain. Smart Mater. Struct. 16, S280–S287 (2007)CrossRef

14.

Shankar, R., Ghosh, T.K., Spontak, R.J.: Electromechanical response of nanostructured polymer systems with no mechanical pre-strain. Macromol. Rapid Commun. 28, 1142–1147 (2007)CrossRef

15.

Zhang, H., During, L., Kovacs, G., Yuan, W., Niua, X., Pei, Q.: Interpenetrating polymer networks based on acrylic elastomers and plasticizers with improved actuation temperature range. Polym. Int. 59, 384–390 (2010)CrossRef

16.

Liu, B., Shaw, M.T.: Electrorehology of filled silicone elastomers. J. Rheol. 45(6), 641–657 (2001)CrossRef

17.

Carpi, F., De Rossi, D.: Improvement of electromechanical actuating performances of a silicone dielectric elastomer by dispersion of titanium dioxide powder. IEEE Trans. Dielectr. Electr. Insul. 12(4), 835–843 (2005)CrossRef

18.

Puvanatvattana, T., Chotpattananont, D., Hiamtup, P., Niamlang, S., Sirivat, A., Jamieson, A.M.: Eletric field induced stress moduli in polythiophene/polyisoprene elastomer blends. React. Funct. Polym. 66, 1575–1588 (2006)CrossRef

19.

Kunanuruksapong, R., Sirivat, A.: Poly(p-phenylene) and acrylic elastomer blends for electroactive application. Mater. Sci. Eng. A 454–455, 454–460 (2007)

20.

Yuse, K., Guyomar, D., Kanda, M., Seveyrat, L., Guiffard, B.: Development of large-strain and low-powered electro-active polymers (EAPs) using conductive fillers. Sens. Actuators A 165, 147–154 (2011)CrossRef

21.

Madden, J.D.W., Vandesteeg, N.A., Anquetil, P.A., Madden, P.G.A., Takshi, A., Pytel, R.Z., Lafontaine, S.R., Wieringa, P.A., Hunter, I.W.: Artificial muscle technology: physical principles and naval prospects. IEEE J. Oceanic Eng. 29(3), 706–728 (2004)CrossRef

22.

Nalwa, H.S.: Ferroelectric Polymers: Chemistry: Physics, and Applications, ISBN: 0824794680, CRC Press, New York, (1995)

23.

Bar-Cohen, Y.: Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential and Challenges, vol. PM136, ISBN: 0-8194-5297-1. SPIE Press, Washington, (2004)

24.

Kim, K.J., Tadokoro, S.: Electroactive Polymers for Robotic Applications Artificial Muscles and Sensors, ISBN13: 9781846283710, Springer, Berlin, (2007)

25.

Carpi, F., De Rossi,D., Kornbluh, R., Pelrine, R., Sommer-Larsen, P.: Dielectric Elastomers as Electromechanical Transducers: Fundamentals, Materials, Devices, Models and Applications of an Emerging Electroactive Polymer Technology, ISBN13: 9780080474885, Elsevier, Oxford, (2008)

26.

O’Halloran, A., O’Malley, F., McHugh, P.: A review on dielectric elastomer actuators, technology, applications, and challenges. J. Appl. Phys. 104, 071101 (2008)CrossRef

27.

Dubowsky, S., Hafez, M., Lichter, M., Weiss, P., Wingert, A.: Dielectric elastomer actuated systems and methods. US Patent No. 7411331 (2008)

28.

Vertechy, R., Berselli, G., Parenti Castelli, V., Vassura, G.: Optimal design of lozenge-shaped dielectric elastomer linear actuators: mathematical procedure and experimental validation. J. Intell. Mater. Syst. Struct. 21, 503–515 (2010)CrossRef

29.

Maxwell, J.C.: A treatise on Electricity and Magnetism, ISBN13: 9781108014045, Dover Publications Inc., New York, (1891)

30.

Larmor, J.: A dynamical theory of the electric and luminiferous medium. Part III, Relat. Mater. Media Phylosophical Trans. Roy. Soc. London: A 190, 205–493 (1897)CrossRef

31.

Einstein, A., Laub, J.: Uber die Elektromagnmetischen Felde auf Ruhende Korpen Ausgeubten Ponderomotorishen Krafte. Ann. Phys. 331(8), 541–550 (1908)CrossRef

32.

Minkowski, H.: Die Glundgleichungen fur die elektromagnetischen Vorgange in bewegten Korper. Math. Ann. 68(4), 472–525 (1909)CrossRef

33.

Lorentz, H.A., The Theory of Electrons and Its Application to the Phenomena of Light and Radiat Heat, 2nd edn. ISBN13: 9780486495583, Dover Publications Inc., New York, (1916)

34.

Livens, G.H.: The Theory of Electricity, 2nd edn. ISBN 13: 9781178439892, Cambridge University Press, London, (1926)

35.

Stratton, J.A.: Electromagnetic Theory, ISBN13: 9780070621503, McGraw-Hill Book Co., New York, (1941)

36.

Smith-White, W.B.: On the mechanical forces in dielectrics. Philos. Mag. Ser. 7 40(303), 466–479 (1949)

37.

Panofsky, W.K.H., Phillips, M.: Classical Electricity and Magnetism, 2nd edn. ISBN13: 9780486439242, Dover Publication Inc., New York, (1955)

38.

Toupin, R.A.: The elastic dielectrics. J. Rational Mech. Anal. 5, 849–915 (1956)

39.

Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media, ISBN13: 9780750626347, Addison-Wesley, New York, (1960)

40.

Fano, R.M., Chu, L.J., Adler, R.B.: Electromagnetic Fields, Energy, and Forces, ISBN13: 9780262561709, Wiley, New York, (1960)

41.

Toupin, R.A.: A dynamical theory of elastic dielectrics. Int. J. Eng. Sci. 1, 101–126 (1963). Pergamon Press, NYCrossRef

42.

Becker, R.: Electromagnetic Fields and Interactions. English edition: Sauter, F. (Electromagnetic theory and relativity, Vol. 1. (Trans: Knudson, A.W.) ISBN13: 9780216874169, Blackie, London, (1964)

43.

Chu, L.J., Haus, H.A., Penfield, P.: The force density in polarizable and magnetizable fluids. Proc. IEEE 54(7), 920–935 (1966)CrossRef

44.

Grindlay, J.: Elastic dielectric. Phys. Rev. 143(2), 637–645 (1966)CrossRef

45.

Penfield, P., Haus, H.A.: Electrodynamics of moving media, ISBN13: 9780262160193. The MIT Press, Cambridge (1967)

46.

Lax, M., Nelson, D.F.: Linear and nonlinear electrodynamics in elastic anisotropic dielectrics. Phys. Rev. B 4, 3694–3731 (1971)CrossRef

47.

De Groot, S.R., Suttorp, L.G.: Foundation of Electrodynamics, ISBN13: 9780720402483, North-Holland Publication Co., Amsterdam, (1972)

48.

Van de Ven, A.A.F.: Interaction of electromagnetic and elastic fields in solids. Ph.D. Thesis, Technical University of Eindhoven, The Netherlands, (1975)

49.

Pao, Y.H., Hutter, K.: Electrodynamics for moving elastic solids and viscous fluids. Proc. IEEE 63(7), 1011–1021 (1975)CrossRef

50.

Robinson, F.N.H.: Electromagnetic stress and momentum in matter. Phys. Rep. 16(6), 313–354 (1975)CrossRef

51.

Tiersten, H.F., Tsai, C.F.: On the interaction of the electromagnetic field with heat conducting deformable insulator. J. Math. Phys. 13(3), 361–378 (1972)CrossRef

52.

Pao, Y.H.: Electromagnetic Forces in Deformable Media, Mechanics Today, vol. 4. Pergamon Press Inc, New York (1978)

53.

Hutter, K., Van de Ven, A.A.F.: Field matter interactions in thermoelastic solids. Lecture Notes in Physics, Vol. 710, ISBN: 9783540372394, Springer, Berlin, (1978)

54.

Eringen, A.C., Maugin, G.A.: Electrodynamics of Continua I: Foundations and solid media, ISBN: 0387969365, Springer, Berlin, (1990)

55.

Green, A.E., Naghdi, P.M.: A unified procedure for construction of theories of deformable media. II. Generalized Continua. Proc. Roy. Soc. London A 448(1934), 357–377 (1995)CrossRef

56.

Yang, J.S., Batra, R.C.: Mixed variational principles in non-linear electroelasticity. Int. J. Non-Linear Mech. 30(5), 719–725 (1995)CrossRef

57.

Rajagopal, K.R., Wineman, A.: A constitutive equation for non-linear electro-active solids. Acta. Mech. 135(3–4), 219–228 (1999)CrossRef

58.

Kovetz, A.: Electromagnetic Theory, ISBN13: 9780198506034, Oxford University Press, Oxford, (2000)

59.

Bobbio, S.: Electrodynamics of Materials: Forces, Stresses, and Energies in Solids and Fluids, ISBN13: 9780121082604, Academic, San Diego, (2000)

60.

Dorfmann, A., Ogden, R.W.: Nonlinear electroelasticity. Acta Mech. 174, 167–183 (2005)CrossRef

61.

McMeeking, R.M., Landis, C.M.: Electrostatic forces and stored energy for deformable dielectric materials. J. Appl. Mech. 72, 581–590 (2005)CrossRef

62.

Bustamante, R., Ogden, R.W.: Universal relations for nonlinear electroelastic solids. Acta Mech. 182, 125–140 (2006)CrossRef

63.

Ericksen, J.L.: Theory of elastic dielectric revisited. Arch. Ration. Mech. Anal. 183(2), 299–313 (2007)CrossRef

64.

Ericksen, J.L.: On formulating and assessing continuum theories of electromagnetic fields in elastic materials. J. Elast. 87(2–3), 95–108 (2007)CrossRef

65.

Suo, Z., Zhao, X., Greene, W.H.: A nonlinear field theory of deformable dielectrics. J. Mech. Phys. Solids 56(2), 467–486 (2008)CrossRef

66.

Bustamante, R., Dorfmann, A., Ogden, R.W.: Nonlinear electroelastostatics: a variational framework. Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 60(1), 154–177 (2009)CrossRef

67.

Trimarco, C.: On the lagrangian electrostatics of elastic solids. Acta Mech. 204(3–4), 193–201 (2009)CrossRef

68.

Cade, R.: On mechanical action in dielectrics. Proc. Phys. Soc.: Section A 64, 665 (1951)CrossRef

69.

Smith-White, W.B.: Reply to on mechanical action in dielectrics. Proc. Phys. Soc.: Section A 65, 289 (1952)CrossRef

70.

Cade, R.: On mechanical action in dielectrics. Proc. Phys. Soc.: Section A 65, 287 (1952)CrossRef

71.

Hakim, S.S.: Mechanical forces in dielectrics. Proc. IEEE: Part C: Monographs 109(15), 158–161 (1962)CrossRef

72.

Vertechy, R., Frisoli, A., Bergamasco, M., Carpi, F., Frediani, G., De Rossi, D., Modeling and experimental validation of buckling dielectric elastomer actuators. Smart. Mater. Struct. ISSN 0964-1726, 21(9), 94005 (2012). doi: 10.1088/0964-1726/21/9/094005

73.

Vertechy, R., Berselli, G., Parenti Castelli, V., Bergamasco, M., Continuum thermo-electro-mechanical model for electrostrictive elastomers. J Intell. Mater. Syst. Struct. 24(6), 761–778 (2013). doi: 10.1177/1045389X12455855

74.

Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd revised edition, ISBN13: 9780201408409, Westview Press, Cambridge, (1978)

75.

Eringen, A.C.: Mechanics of Continua, ISBN13: 9780882756639, Krieger Publication Co., New York, (1980)

76.

Eringen, A.C., Maugin, G.A.: Electrodynamics of Continua II: Fluids and complex media, ISBN: 0387970053, Springer, Berlin, (1990)

77.

Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, 2nd edn. Springer, Berlin (1992)CrossRef

78.

Spencer, A.J.M.: Theory of invariants. In: Eringen, A.C. (ed.) Continuum Physics, vol. 1, pp. 239–353. Academic, New York (1971)

79.

Wang, C.C.: On representation for isotropic functions I & II. Arch. Ration. Mech. Anal. 33, 249–287 (1969)CrossRef

80.

Smith, G.F.: On a fundamental error in two papers of C.C. Wang ‘on representation for isotropic functions I & II’. Arch. Ration. Mech. Anal. 36, 161–165 (1970)CrossRef

81.

Wang, C.C.: A new representation theorem for isotropic functions I & II. Arch. Ration. Mech. Anal. 36, 166–223 (1970)CrossRef

82.

Smith, G.F.: On isotropic functions of symmetric tensors. Int. J. Eng. Sci. 19, 899–916 (1971)CrossRef

83.

Yeoh, O.H.: Characterization of elastic properties of carbon-black filled rubber vulcanizates. Rubber Chem. Technol. 63, 792–805 (1990)CrossRef

Title: Electro-Elastic Continuum Models for Electrostrictive Elastomers
Authors: R. Vertechy
G. Berselli
V. Parenti Castelli
M. Bergamasco
Publisher: Springer Berlin Heidelberg
Book: Advances in Elastomers I
Print ISBN: 978-3-642-20924-6

Electronic ISBN: 978-3-642-20925-3

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-642-20925-3_14

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Premium Partners