Constitutive modeling of electrostrictive polymers using a hyperelasticity-based approach

Journal of Applied Mechanics, Transactions ASME

Volumn 77, Issue 1, 2010, Pages 1-5

  Richards, A W ^a   Odegard, G M ^a  

^a Michigan Technological University   (United States)

Author keywords

Electroactive materials; Electrostriction; MEMS; Polyurethane elastomers

Indexed keywords

CONSTITUTIVE MODELING; ELECTROACTIVE MATERIAL; ELECTROACTIVE MATERIALS; ELECTROMECHANICAL BEHAVIOR; ELECTROSTRICTIVE MATERIALS; ELECTROSTRICTIVE POLYMERS; EMPIRICAL DATA; HYPER ELASTIC; HYPER-ELASTICITY; POLYURETHANE ELASTOMERS; SIMPLE FUNCTIONAL FORMS; TRANSVERSELY ISOTROPIC; TRANSVERSELY ISOTROPIC MATERIALS;

BIOLOGICAL MEMBRANES; CONSTITUTIVE EQUATIONS; CONSTITUTIVE MODELS; ELASTOMERS; ELECTROSTRICTION; POLYMERS; RUBBER;

FUNCTIONAL POLYMERS;

EID: 77955234650     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3173766     Document Type: Article

References (66)

1. Bauer, F., Fousson, E., and Zhang, Q. M., 2006, "Recent Advances in Highly Electrostrictive P(VDF-TrFE-CFE) Terpolymers,"IEEE Trans. Dielectr. Electr. Insul., 13(5), pp. 1149-1154.
2. Bauer-Gogonea, S., Camacho-Gonzalez, F., Schwodiauer, R., Ploss, B., and Bauer, S., 2007, "Nonlinear Capacitance Dilatometry for Investigating Elastic and Electromechanical Properties of Ferroelectrets,"Appl. Phys. Lett., 91(12), p. 122901.
3. Beom, H. G., Kim, Y. H., Kim, C. B., and Cho, C., 2008, "Modified Boundary Layer Analysis of an Electrode in an Electrostrictive Material,"Arch. Appl. Mech., 78(3), pp. 191-209.
4. Butkewitsch, S., and Scheinbeim, J., 2006, "Dielectric Properties of a Hydrated Sulfonated Poly(Styrene-Ethylene/Butylenes-Styrene) Triblock Copolymer,"Appl. Surf. Sci., 252(23), pp. 8277-8286.
5. Diaconu, I., Dorohoi, D. O., and Topoliceanu, F., 2006, "Electrostriction of a Polyurethane Elastomer-Based Polyester,"IEEE Sens. J., 6(4), pp. 876-880.
6. Dubois, P., Rosset, S., Koster, S., Stauffer, J., Mikhailov, S., Dadras, M., de Rooij, N. F., and Shea, H., 2006, "Microactuators Based on Ion Implanted Dielectric Electroactive Polymer (EAP) Membranes,"Sens. Actuators, A, 130-131, pp. 147-154.
7. Galler, N., Ditlbacher, H., Steinberger, B., Hohenau, A., Dansachmuller, M., Camacho-Gonzales, F., Bauer, S., Krenn, J. R., Leitner, A., and Aussenegg, F. R., 2006, "Electrically Actuated Elastomers for Electro-Optical Modulators,"Appl. Phys. B: Lasers Opt., 85(1), pp. 7-10.
8. Ha, J. Y., Jeong, D. Y., Kim, J. S., and Yoon, S. J., 2007, "Fabrication of an Optical Grating Using High Electrostrictive Strain Polymer as a Template,"J. Opt. A, Pure Appl. Opt., 9(2), pp. 170-173.
9. Xu, H., Shen, D., and Zhang, Q., 2007, "Structural and Ferroelectric Response in Vinylidene Fluoride/Trifluoroethylene/Hexafluoropropylene Terpolymers,"Polymer, 48(7), pp. 2124-2129.
10. Kim, B. H., Choi, H. J., Park, H. S., Jeong, Y. D., Do Jeong, H., Lee, J. O., and Jo, N. J., 2006, "Preparation and Properties of Polyurethane/MMT Nanocomposite Actuators,"Compos. Interfaces, 13(2-3), pp. 285-297.
11. Lam, T. Y., Lau, S. T., Chao, C., Chan, H. L. W., Choy, C. L., Cheung, W. Y., and Wong, S. P., 2007, "Characterization of Proton Irradiated Copolymer Thin Films for Microelectromechanical System Applications,"Appl. Phys. Lett., 90(4), p. 043511.
12. Li, Z. M., Wang, Y. H., and Cheng, Z. Y., 2006, "Electromechanical Properties of Poly(Vinylidene-Fluoride-Chlorotrifluoroethylene) Copolymer,"Appl. Phys. Lett., 88(6), p. 062904.
13. Pimpin, A., Suzuki, Y., and Kasagi, N., 2007, "Microelectrostrictive Actuator With Large Out-of-Plane Deformation for Flow-Control Application,"J. Microelectromech. Syst., 16(3), pp. 753-764.
14. Ren, K., Liu, Y. M., Hofmann, H., Zhang, Q. M., and Blottman, J., 2007, "An Active Energy Harvesting Scheme With an Electroactive Polymer,"Appl. Phys. Lett., 91(13), p. 132910.
15. Zhang, S., Huang, C., Klein, R. J., Xia, F., Zhang, Q. M., and Cheng, Z. Y., and 2007, "High Performance Electroactive Polymers and Nano-Composites for Artificial Muscles,"J. Intell. Mater. Syst. Struct., 18(2), pp. 133-145.
16. Spillmann, C. M., Ratna, B. R., and Naciri, J., 2007, "Anisotropic Actuation in Electroclinic Liquid Crystal Elastomers,"Appl. Phys. Lett., 90(2), p. 021911.
17. Xia, F., Tadigadapa, S., and Zhang, Q. M., 2006, "Electroactive Polymer Based Microfluidic Pump,"Sens. Actuators, A, 125(2), pp. 346-352.
18. Zhang, S. H., Neese, B., Ren, K. L., Chu, B. J., Xia, F., Xu, T., Tadigadapa, S., Wang, Q., Zhang, Q. M., and Bauer, F., 2006, "Relaxor Ferroelectric Polymers, Thin Film Devices, and Ink-Jet Microprinting for Thin Film Device Fabrication,"Ferroelectrics, 342, pp. 43-56.
19. Zhang, Q. M., Li, H. F., Poh, M., Xia, F., Cheng, Z. Y., Xu, H. S., and Huang, C., 2002, "An All-Organic Composite Actuator Material With a High Dielectric Constant,"Nature (London), 419(6904), pp. 284-287.
20. Guillot, F. M., and Balizer, E., 2003, "Electrostrictive Effect in Polyurethanes,"J. Appl. Polym. Sci., 89(2), pp. 399-404.
21. Shkel, Y. M., and Klingenberg, D. J., 1998, "Electrostriction of Polarizable Materials: Comparison of Models With Experimental Data,"J. Appl. Phys., 83(12), pp. 7834-7843.
22. Shankar, R., Ghosh, T. K., and Spontak, R. J., 2007, "Electroactive Nanostructured Polymers as Tunable Actuators,"Adv. Mater., 19(17), pp. 2218-2223.
23. Su, J., Ounaies, Z., and Harrison, J. S., 1999, "Ferroelectric and Piezoelectric Properties of Blends of Poly(Vinylidene Fluoride-Trifluorethylene) and a Graft Elastomer,"Proceedings of the Materials Research Society Symposium,Q.M. Zhang, T. Furukawa, Y. Bar-Cohen, and J. Scheinbeim, eds., Materials Research Society, Boston, MA, pp. 95-100.
24. Lorberg, H., 1884, "Ueber Electrostriction,"Ann. Phys. Chem., 21, pp. 300-329.
25. Sacerdote, M. P., 1899, "Deformations Electriques Des Dielectriques Solides Isotropes,"J. Phys. Theor. Appl., 8(1), pp. 457-471.
26. Sacerdote, M. P., 1901, "Sur un Cas Particulier de Deformation Electrique D'un Dielectrique Solide Isotrope,"J. Phys. Theor. Appl., 10, pp. 196-200.
27. Adams, E. P., 1911, "On Electrostriction,"Philos. Mag., 6(22), pp. 889-900.
28. Kemble, E. C., 1916, "Note on the End Effect in the Electrostriction of Cylindrical Condensers,"Phys. Rev., 7(6), pp. 614-624.
29. Pauthenier, M., 1926, "Mesure Photgraphique de l'electrostriction dans le cas du Tetrachlorure de Carbone,"C. R. Hebd. Seances Acad. Sci., 182, pp. 121-123.
30. Cady, W. G., 1929, "Electroelastic and Pyroelectric Phenomena,"International Critical Tables of Numerical Data, Physics, Chemistry and Technology, E. W. Washburn, ed., McGraw-Hill, New York, pp. 207-212.
31. Pauthenier, M., 1924, "L"Electrostriction Dans Les Liquides Tres Peu Birefringents,"J. Phys. Radium, 5, pp. 312-320.
32. Bruhat, M. M. G., and Pauthenier, M., 1925, "Sur la Theorie del'Electrostriction dans les Liquides Isolants,"J. Phys. Radium, 6(1), pp. 1-9.
33. Ze, N. T., 1928, "Etude Experimentale des Deformations et des Changements de proprietes Optiques du Quartz Sous L'Influence du Champ Electrique,"J. Phys. Radium, 9(1), pp. 13-37.
34. Stratton, J. A., 1941, Electromagnetic Theory, McGraw-Hill, New York.
35. Mason, W. P., 1950, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York.
36. von Hippel, A. R., 1954, Dielectrics and Waves, Chapman and Hall, New York.
37. Devonshire, A. F., 1954, "Theory of Ferroelectrics,"Adv. Phys., 3(10), pp. 85-130.
38. Nye, J. F., 1957, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Clarendon, Oxford.
39. Landau, L. D., and Lifshitz, E. M., 1960, Electrodynamics of Continuous Media, Pergamon, New York.
40. Eringen, A. C., 1962, Nonlinear Theory of Continuous Media, McGraw-Hill, New York.
41. Toupin, R. A., 1956, "The Elastic Dielectric,"Journal of Rational Mechanics and Analysis, 5, pp. 850-915.
42. Baumhauer, J. C., and Tiersten, H. F., 1973, "Nonlinear Electroelastic Equations for Small Fields Superposed on a Bias,"J. Acoust. Soc. Am., 54(4), pp. 1017-1034.
43. Van Sterkenburg, S. W. P., 1991, "Measurement of the Electrostrictive Tensor of 8 Alkali-Halides,"J. Phys. D, 24(10), pp. 1853-1857.
44. Meng, Z. Y., and Cross, L. E., 1985, "Determination of the Electrostriction Tensor Components in Single-Crystal CaF2 From the Uniaxial-Stress Dependence of the Dielectric Permittivity,"J. Appl. Phys., 57(2), pp. 488-491.
45. Damjanovic, D., 1998, "Ferroelectric, Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics,"Rep. Prog. Phys., 61(9), pp. 1267-1324.
46. Sundar, V., and Newnham, R. E., 1992, "Electrostriction and Polarization,"Ferroelectrics, 135(1-4), pp. 431-446.
47. Tiersten, H. F., 1971, "On the Nonlinear Equations of Thermo-Electroelasticity,"Int. J. Eng. Sci., 9, pp. 587-604.
48. McMeeking, R. M., Landis, C. M., and Jimenez, S. M. A., 2007, "A Principle of Virtual Work for Combined Electrostatic and Mechanical Loading of Materials,"Int. J. Non-Linear Mech., 42(6), pp. 831-838.
49. McMeeking, R. M., and Landis, C. M., 2005, "Electrostatic Forces and Stored Energy for Deformable Dielectric Materials,"Trans. ASME, J. Appl. Mech., 72(4), pp. 581-590.
50. Dorfmann, A., and Ogden, R. W., 2005, "Nonlinear Electroelasticity,"Acta Mech., 174(3-4), pp. 167-183.
51. Pao, Y. H., 1978, "Electromagnetic Forces in Deformable Continua,"Mechanics Today, Vol. 4, S. Nemat-Nasser, ed., Pergamon, New York, pp. 209-305.
52. Maugin, G. A., 1988, Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam.
53. Eringen, A. C., and Maugin, G. A., 1990, Electrodynamics of Continua: I Foundations and Solid Media, Springer, New York.
54. Eringen, A. C., and Maugin, G. A., 1990, Electrodynamics of Continua: II Fluids and Complex Media, Springer, New York.
55. Hutter, K., van de Ven, A. A. F., and Ursescu, A., 2006, Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids, Springer, New York.
56. Zhao, X. H., and Suo, Z. G., 2008, "Electrostriction in Elastic Dielectrics Undergoing Large Deformation,"J. Appl. Phys., 104(12), p. 123530.
57. Truesdell, C. A., and Toupin, R. A., 1960, "The Classical Field Theories,"Encyclopedia of Physics, Vol. III/1, S. Flugge, ed., Springer-Verlag, Berlin, Germany.
58. Truesdell, C., and Noll, W., 2004, The Non-Linear Field Theories of Mechanics, Springer-Verlag, New York.
59. Eringen, A. C., 1999, Microcontinuum Field Theories, Springer-Verlag, New York.
60. de Groot, S. R., and Suttorp, L. G., 1972, Foundations of Electrodynamics, American Elsevier, New York.
61. Eringen, A. C., 1967, Mechanics of Continua, Wiley, New York.
62. Suo, Z. G., Zhao, X. H., and Greene, W. H., 2008, "A Nonlinear Field Theory of Deformable Dielectrics,"J. Mech. Phys. Solids, 56(2), pp. 467-486.
63. Bustamante, R., Dorfmann, A., and Ogden, R. W., 2008, "Nonlinear Electroelastostatics: A Variational Framework,"ZAMP, 60(1), pp. 154-177.
64. Spencer, A. J. M., 1971, "Theory of Invariants,"Continuum Physics,Vol.1,A. C. Eringen, ed., Academic, New York, pp. 239-353.
65. Guillot, F. M., Jarzynski, J., and Balizer, E., 2001, "Measurement of Electrostrictive Coefficients of Polymer Films,"J. Acoust. Soc. Am., 110(6), pp. 2980-2990.
66. Anand, L., 1986, "Moderate Deformations in Extension Torsion of Incompressible Isotropic Elastic-Materials,"J. Mech. Phys. Solids, 34(3), pp. 293-304.