Continuum thermo-electro-mechanical model for electrostrictive elastomers

Journal of Intelligent Material Systems and Structures

Volumn 24, Issue 6, 2013, Pages 761-778

  Vertechy, Rocco ^a   Berselli, Giovanni ^b   Castelli, Vincenzo Parenti ^c   Bergamasco, Massimo ^a  

^a SCUOLA SUPERIORE SANT ANNA   (Italy)

^b UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^c UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

actuator; dielectric elastomers; Electroactive polymers; electrostrictive; thermo electro elasticity

Indexed keywords

CONSTITUTIVE RELATIONS; DIELECTRIC ELASTOMERS; ELECTRO-ACTIVE POLYMERS; ELECTROSTRICTIVE; MATERIAL PARAMETER; MECHANICAL STIMULUS; THERMO-ELECTRO-ELASTIC; THERMO-ELECTRO-ELASTICITY;

ACTUATORS; CONDUCTING POLYMERS; CONTINUUM MECHANICS; DIELECTRIC MATERIALS; PLASTICS;

ELASTOMERS;

EID: 84875716404     PISSN: 1045389X     EISSN: 15308138     Source Type: Journal    
DOI: 10.1177/1045389X12455855     Document Type: Conference Paper

References (88)

1. Abraham R, Marsden JE Foundations of Mechanics. 1978 ) Foundations of Mechanics. 2nd rev. ed.Cambridge, MA: Westview Press. Cambridge, MA: Westview Press ; 1978 :
2. Bar-Cohen Y Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential and Challenges. Washington, DC: SPIE Press ; 2004 :
3. Bauer F, Fousson E, Zhang QM. Recent advances in highly electrostrictive P(VDF-TrFE-CFE) terpolymers. IEEE Transactions on Dielectrics and Electrical Insulation. 2006 ; 13 (5). 1149-1154
4. Becker R Electromagnetic Fields and Interactions, Electromagnetic Theory and Relativity. Sauter F, ed. London: Blackie ; 1964 :
5. Berselli G, Vertechy R, Vassura G, et al. Optimal synthesis of conically-shaped dielectric elastomer linear actuators: design methodology and experimental validation. IEEE Transactions on Mechatronics. 2011 ; 16 (1). 67-79
6. Berselli G, Vertechy R, Babic M, et al. Dynamic modeling and experimental evaluation of a constant-force dielectric elastomer actuator. Journal of Intelligent Material Systems and Structures. 2012 ; 24 (6). 779-791
7. Bobbio S Electrodynamics of Materials: Forces, Stresses, and Energies in Solids and Fluids. San Diego, CA: Academic Press ; 2000 :
8. Bustamante R, Dorfmann A, Ogden RW. Nonlinear electroelastostatics: a variational framework. Zeitschrift fur Angewandte Mathematik und Physik. 2009 ; 60 (1). 154-177
9. Carpi F, De Rossi D. Improvement of electromechanical actuating performances of a silicone dielectric elastomer by dispersion of titanium dioxide powder. IEEE Transactions on Dielectrics and Electrical Insulation. 2005 ; 12 (4). 835-843
10. Carpi F, De Rossi D, Kornbluh R, et al Dielectric Elastomers as Electromechanical Transducers: Fundamentals, Materials, Devices, Models and Applications of an Emerging Electroactive Polymer Technology. Oxford: Elsevier ; 2008 :
11. Chadwick P, Creasy CFM. Modified entropic elasticity of rubber-like materials. Journal of the Mechanics and Physics of Solids. 1984 ; 32 (5). 337-357
12. Chu LJ, Haus HA, Penfield P. The force density in polarizable and magnetizable fluids. Proceedings of the IEEE. 1966 ; 54 (7). 920-935
13. De Groot SR, Suttorp LG Foundation of Electrodynamics. Amsterdam: North-Holland Publishing Co ; 1972 :
14. Dorfmann A, Ogden RW. Nonlinear electroelasticity. Acta Mechanica. 2005 ; 174 (3-4). 167-183
15. Dubowsky S, Hafez M, Lichter M, et al. Dielectric elastomer actuated systems and methods. 2008 ;:
16. Einstein A, Laub J. Uber die Elektromagnmetischen Felde auf Ruhende Korpen Ausgeubten Ponderomotorishen Krafte. Annalen der Physik. 1908 ; 331 (8). 541-550
17. Ericksen JL. Theory of elastic dielectric revisited. Archive for Rational Mechanics and Analysis. 2007 ; 183 (2). 299-313
18. Eringen AC Mechanics of Continua. New York: Krieger Publishing Co ; 1980 :
19. Eringen AC, Maugin GA Electrodynamics of Continua I: Foundations and Solid Media. Berlin: Springer-Verlag ; 1990 :
20. Fano RM, Chu LJ, Adler RB Electromagnetic Fields, Energy, and Forces. New York: John Wiley & Sons Inc. ; 1960 :
21. Green AE, Naghdi PM. A unified procedure for construction of theories of deformable media. I. Classical continuum physics. Proceedings of the Royal Society of London Series A: Mathematical Physical and Engineering Sciences. 1995 ; 448 (1934). 335-356
22. Grindlay J. Elastic dielectric. Physical Review. 1966 ; 143 (2). 637-645
23. Guillot FM, Balizer E. Electrostrictive effect in polyurethanes. Journal of Applied Polymer Science. 2003 ; 89 (2). 399-404
24. Ha SM, Yuan W, Pei Q, et al. Interpenetrating networks of elastomers exhibiting 300% electrically-induced area strain. Smart Materials and Structures. 2007 ; 16 (2). S280 - S287
25. Heaviside O Electromagnetic Theory. London: The Electrician Publishing Co ; 1893-1912 :
26. Holzapfel GA Nonlinear Solid Mechanics: A Continuum Approach for Engineering. New York: John Wiley & Sons ; 2001 :
27. Holzapfel GA, Simo JC. Entropic elasticity of isotropic rubber-like solids at finite strains. Computer Methods in Applied Mechanics and Engineering. 1996 ; 132 (1-2). 17-44
28. Hutter K. On thermodynamics and thermostatics of viscous thermoelastic solids in the electromagnetic fields. A Lagrangian formulation. Archive for Rational Mechanics and Analysis. 1975 ; 58 (4). 339-368
29. Hutter K. A thermodynamic theory of fluids and solids in the electromagnetic fields. Archive for Rational Mechanics and Analysis. 1977 ; 64 (3). 269-298
30. Hutter K, Van De Ven AAF Field Matter Interactions in Thermoelastic Solids. Lecture Notes in Physics 710. Berlin: Springer-Verlag ; 1978 :
31. Jean-Mistral C, Sylvestre A, Basrour S, et al. Dielectric properties of polyacrylate thick films used in sensors and actuators. Smart Materials and Structures. 2010 ; 19 (7). 075019
32. Joule JP. On some thermo-dynamic properties of solids. Philosophical Transactions of the Royal Society of London. 1859 ; 149: 91-131
33. Kim KJ, Tadokoro S Electroactive Polymers for Robotic Applications Artificial Muscles and Sensors. Berlin: Springer-Verlag ; 2007 :
34. Kofod G, Sommer-Larsen P, Kornbluh R, et al. Actuation response of polyacrylate dielectric elastomers. Journal of Intelligent Material Systems and Structures. 2003 ; 14 (12). 787-793
35. Krakovský I, Romijn T, Posthuma De Boer A. A few remarks on the electrostriction of elastomers. Journal of Applied Physics. 1999 ; 85 (1). 628
36. Kunanuruksapong R, Sirivat A. Electrical properties and electromechanical responses of acrylic elastomers and styrene copolymers: effect of temperature. Applied Physics A-Materials Science & Processing. 2008 ; 92 (2). 313-320
37. Landau LD, Lifshitz EM Electrodynamics of Continuum Media. 1960 ) Electrodynamics of Continuum Media. 2nd ed.Boston, MA: Butterworth-Heinemann. Boston, MA: Butterworth-Heinemann ; 1960 :
38. Larmor J. A dynamical theory of the electric and luminiferous medium. Part III, relations with material media. Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences. 1897 ; 190: 205-493
39. Lax M, Nelson DF. Linear and nonlinear electrodynamics in elastic anisotropic dielectrics. Physical Review B. 1971 ; 4 (10). 3694-3731
40. Lehmann W, Skupin H, Tolksdorf C, et al. Giant lateral electrostriction in ferroelectric liquid-crystalline elastomers. Nature. 2001 ; 410: 447-450
41. Liu B, Shaw MT. Electrorheology of filled silicone elastomers. Journal of Rheology. 2001 ; 45 (6). 641-657
42. Liu L, Liu Y, Li B, et al. Thermo-electro-mechanical instability of dielectric elastomers. Smart Materials and Structures. 2011 ; 20 (7). 075004
43. Livens GH The Theory of Electricity. 1926 ) The Theory of Electricity. 2nd ed.London: Cambridge University Press. London: Cambridge University Press ; 1926 :
44. Lorentz HA The Theory of Electrons and Its Application to the Phenomena of Light and Radiant Heat. 1916 ) The Theory of Electrons and Its Application to the Phenomena of Light and Radiant Heat. 2nd ed.New York: Dover Publications Inc. New York: Dover Publications Inc ; 1916 :
45. Ludeelerd P, Niamlang S, Kunaruksapong R, et al. Effect of elastomer matrix type on electromechanical response of conductive polypyrrole/elastomer blends. Journal of Physics and Chemistry of Solids. 2010 ; 71 (9). 1243-1250
46. McMeeking RM, Landis CM. Electrostatic forces and stored energy for deformable dielectric materials. Journal of Applied Mechanics. 2005 ; 72 (4). 581-590
47. McMeeking RM, Landis CN, Jimenez SMA. A principle of virtual work for combined electrostatic and mechanical loading of materials. International Journal of Non-Linear Mechanics. 2007 ; 42 (6). 831-838
48. Madden JDW, Vandesteeg NA, Anquetil PA, et al. Artificial muscle technology: physical principles and naval prospects. IEEE Journal of Oceanic Engineering. 2004 ; 29 (3). 706-728
49. Mathew G, Rhee JM, Nah C, et al. Effects of silicone rubber on properties of dielectric acrylate elastomer actuator. Polymer Engineering and Science. 2006 ; 46 (10). 1455-1460
50. Maxwell JC A Treatise on Electricity and Magnetism. New York: Dover Publications Inc ; 1891 :
51. Michel S, Zhang XQ, Wissler M, et al. A comparison between silicone and acrylic elastomers as dielectric materials in electroactive polymer actuators. Polymer International. 2010 ; 59 (3). 391-399
52. Minkowski H. Die Glundgleichungen fur die elektromagnetischen Vorgange in bewegten Korper. Mathematische Annalen. 1909 ; 68 (4). 472-525
53. Moller C The Theory of Relativity. London: Oxford University Press ; 1972 :
54. Nalwa HS Ferroelectric Polymers: Chemistry: Physics, and Applications. New York: CRC Press ; 1995 :
55. Nam J, Choi HR, Koo JC, et al Electroactive Polymers for Robotic Applications. Kim KJ Tadokoro S, ed. London: Springer-Verlag ; 2007: 37-48.
56. Neese B, Chu B, Lu SG, et al. Large electrocaloric effect in ferroelectric polymers near room temperature. Science. 2008 ; 321 (5890). 821-823
57. 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
58. Panofsky WKH, Phillips M Classical Electricity and Magnetism. 1955 ) Classical Electricity and Magnetism. 2nd ed.New York: Dover Publication Inc. New York: Dover Publication Inc ; 1955 :
59. Pao YH Mechanics Today. Nemat-Nasser S, ed. New York: Pergamon Press Inc. ; 1978: 209-306.
60. Pao YH, Hutter K. Electrodynamics for moving elastic solids and viscous fluids. Proceedings of the IEEE. 1975 ; 63 (7). 1011-1021
61. Pelrine R, Kornbluh R, Joseph J. Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sensors and Actuators A: Physical. 1998 ; 64 (1). 77-85
62. Pelrine R, Kornbluh R, Pei Q, et al. High-speed electrically actuated elastomers with strain greater than 100%. Science. 2000 ; 287 (5454). 836-839
63. Penfield P, Haus HA Electrodynamics of Moving Media. Cambridge, MA: The MIT Press ; 1967 :
64. Pennisi S, Trovato M. On the irreducibility of Professor G.F. Smith's representations for isotropic functions. International Journal of Engineering Science. 1987 ; 25 (8). 1059-1065
65. Puvanatvattana T, Chotpattananont D, Hiamtup P, et al. Electric field induced stress moduli in polythiophene/polyisoprene elastomer blends. Reactive & Functional Polymers. 2006 ; 66 (12). 1575-1588
66. Robinson FNH. Electromagnetic stress and momentum in matter. Physics Reports. 1975 ; 16 (6). 313-354
67. Saad ALG, Younan AF. Rheological, mechanical and electrical properties of natural rubber-white filler mixtures reinforced with nylon 6 short fibers. Polymer Degradation and Stability. 1995 ; 50 (2). 133-140
68. Shankar R, Ghosh TK, Spontak RJ. Electromechanical response of nanostructured polymer systems with no mechanical pre-strain. Macromolecular Rapid Communications. 2007 ; 28 (10). 1142-1147
69. Sheng J, Chen H, Li B. Effect of temperature on the stability of dielectric elastomers. Journal of Physics D: Applied Physics. 2011 ; 44 (36). 365406
70. Sircar AK, Wells JL. Thermal conductivity of elastomer vulcanizates by differential scanning calorimetry. Rubber Chemistry and Technology. 1981 ; 55: 191-207
71. Smith GF. On isotropic functions of symmetric tensors. International Journal of Engineering Science. 1971 ; 9 (10). 899-916
72. Spencer AJM Continuum Physics. Eringen AC, ed. New York: Academic Press ; 1971: 239-353.
73. Stratton JA Electromagnetic Theory. New York: McGraw-Hill Book Co ; 1941 :
74. Su J, Ounaies Z, Harrison JS, et al. Electromechanically active polymer blends for actuation. Proceedings of smart structures and materials 2000: electroactive polymer actuators and devices (EAPAD) ; 2000 Newport Beach ; 2000. 65.
75. Suo Z, Zhao X, Greene WH. A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids. 2008 ; 56 (2). 467-486
76. Tiersten HF, Tsai CF. On the interaction of the electromagnetic field with heat conducting deformable insulator. Journal of Mathematical Physics. 1972 ; 13 (3). 361-378
77. Toupin RA. The elastic dielectrics. Journal of Rational Mechanics and Analysis. 1956 ; 5: 849-915
78. Toupin RA. A dynamical theory of elastic dielectrics. International Journal of Engineering Science. 1963 ; 1 (1). 101-126
79. Treloar LRG The Physics of Rubber Elasticity. 2005 ) The Physics of Rubber Elasticity. 3rd ed.London: Oxford University Press. London: Oxford University Press ; 2005 :
80. Trimarco C. On the Lagrangian electrostatics of elastic solids. Acta Mechanica. 2009 ; 204 (3-4). 193-201
81. Truesdell C, Noll W The Non-Linear Field Theories of Mechanics. 1992 ) The Non-Linear Field Theories of Mechanics. 2nd ed.Berlin: Springer-Verlag. Berlin: Springer-Verlag ; 1992 :
82. Vertechy R, Berselli G, Parenti Castelli V, et al. Optimal design of lozenge-shaped dielectric elastomer linear actuators: mathematical procedure and experimental validation. Journal of Intelligent Material Systems and Structures. 2010 ; 21 (5). 503-515
83. Yang JS, Batra RC. Mixed variational principles in non-linear electroelasticity. International Journal of Non-Linear Mechanics. 1995 ; 30 (5). 719-725
84. Yuse K, Guyomar D, Kanda M, et al. Development of large-strain and low-powered electro-active polymers (EAPs) using conductive fillers. Sensors and Actuators A-Physical. 2011 ; 165 (2). 147-154
85. Zhang H, During L, Kovacs G, et al. Interpenetrating polymer networks based on acrylic elastomers and plasticizers with improved actuation temperature range. Polymer International. 2010 ; 59 (3). 384-390
86. Zhang QM, Bharti V, Zhao X. Giant electrostriction and relaxor ferroelectric behavior in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) Copolymer. Science. 1998 ; 280 (5372). 2101-2104
87. Zhang QM, Su J, Kim CH, et al. An experimental investigation of electromechanical responses in a polyurethane elastomer. Journal of Applied Physics. 1997 ; 81 (6). 2770-2776
88. Zhenyi M, Scheinbeim JI, Lee JW, et al. High field electrostrictive response of polymers. Journal of Polymer Science Part B-Polymer Physics. 1994 ; 32 (16). 2721-2731