Theoretical Estimation of Stability of Dielectric Elastomers

Asha Dahiya, O. P. Thakur

School of Applied Sciences, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India.

DOI: 10.4236/wjcmp.2012.24036                

Abstract

When dielectric elastomers sandwiched between compliant electrodes and high electric voltage is applied to the dielectric elastomers. Then due to the electrostatic force between the electrodes the elastomers expands in plane and contract out of plane so that it becomes thinner. As the thickness decreases we observe the increase in the applied electric voltage with the positive feedback effect. This positive feedback leads the electrical as well as mechanical breakdown of elastomer. By applying a mechanical pre-stretch the mechanical stability of dielectric elastomers gets also increased. In this paper, a new generalized set of strain/stretch variables q_r^N has been introduced to get the expression for second order elastic moduli for the ideal electro elastic material deformed to orthorhombic structure. The strength of a loaded crystal determined from the new moduli has been compared with the strength of classical (Green, Stretch) moduli. It has been observed that the use of incorrect formula by ignoring shear strain leads to incorrect estimation of stability. This problem has been resolved by considering stretch variable in tensor form as generally observed in the process of electrostriction in the elastomers.

Keywords

Elastomers; Electromechanical Stability; Energy Convexity; Mechanical Strength; Generalised Variable

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. E. Pelrine, R. D. Kornbluh, Q. B. Pei, et al., “High-Speed Electrically Actuated Elastomers with Strain Greater than 100%,” Science, Vol. 287, No. 5454, 2000, pp. 836-839. doi:10.1126/science.287.5454.836
[2]	E. Smela, O. Inganaas and I. Lundstrom, “Controlled Folding of Micrometer-Size Structures,” Science, Vol. 268, No. 5218, 1995, pp. 1735-1738. doi:10.1126/science.268.5218.1735
[3]	R. E. Pelrine, R. D. Kornbluh and J. P. Joseph, “Electrostriction of Polymer Dielectrics with Compliant Electrodes as a Means of Actuation,” Sensors and Actuators A: Physical, Vol. 64, No. 1, 1998, pp. 77-85. doi:10.1016/S0924-4247(97)01657-9
[4]	J. S. Plante and S. Dubowsky, “On the Properties of Dielectric Elastomer Actuators and Their Design Implications,” Smart Materials and Structures, Vol. 16, No. 20, 2007, pp. S227-S236. doi:10.1088/0964-1726/16/2/S05
[5]	E. M. Arrude and M. C. Boyce, “A Three-Dimensional Constitutive Model for the Large Stretch Behaviour of Rubber Elastic Materials,” Journal of the Mechanics and Physics of Solids, Vol. 41, No. 2, 1993, pp. 389-412. doi:10.1016/0022-5096(93)90013-6
[6]	X. H. Zhao and Z. G. Suo, “Method to Analyse Electromechanical Stability of Dielectric Elastomers,” Applied Physics Letter, Vol. 91, No. 6, 2007, Article ID: 061921. doi:10.1063/1.2768641
[7]	X. H. Zhao, W. Hong and Z. G. Suo, “Electromechanical Coexistent States and Hysteresis in Dielectric Elastomers,” Physical Review B, Vol. 76, No. 13, 2007, Article ID: 134113. doi:10.1103/PhysRevB.76.134113
[8]	Z. G. Suo, X. H. Zhao and W. H. Greene, “A Nonlinear Field Theory of Deformable Dielectrics,” Journal of the Mechanics and Physics of Solids, Vol. 56, No. 2, 2008, pp. 476-486. doi:10.1016/j.jmps.2007.05.021
[9]	J. Zhou, W. Hong, X. H. Zhao, et al., “Propagation of Instability in Dielectric Elastomers,” International Journal of Solids and Structures, Vol. 45, No. 13, 2008, pp. 3739-3750. doi:10.1016/j.ijsolstr.2007.09.031
[10]	A. N. Norrisa, “Comment on Method to Analyse Electromechanical Stability of Dielectric Elastomers,” Applied Physics Letters, Vol. 92, No. 2, 2007, Article ID: 026101. doi:10.1063/1.2833688
[11]	R. Diaz-Calleja, E. Riande and M. J. Sanichis, “On Electromechanical Stability of Dielectric Elastomers,” Applied Physics Letters, Vol. 93, No. 10, 2008, Article ID: 101902. doi:10.1063/1.2972124
[12]	Y. J. Liu, L. W. Liu, Z. Zhang, et al., “Comment on Method to Analyse Electromechanical Stability of Dielectric Elastomers,” Applied Physics Letters, Vol. 93, No. 10, 2008, Article ID: 106101. doi:10.1063/1.2979236
[13]	O. P. Thakur and A. K. Singh, “Electrostriction and Electromechanical Coupling in Elastic Dielectrics at Nanometric Interfaces,” Materials Science—Poland, Vol. 27, No. 3, 2009, pp. 839-850.
[14]	O. P. Thakur and A. K. Singh, “Error in Estimation of Electrically Induced Deformation in Elastic Dielectric,” Material Science Research Journal, Vol. 2, No. 3-4, 2009, pp. 307-319.
[15]	J. A. Stratton, “Electromagnetic Theory,” McGraw-Hill, New York, 1941.
[16]	L. D. Landu and L. M. Lifeshitz, “Theory of Elasticity,” Pergamon Press, Oxford, 1970.
[17]	L. D. Landu and L. M. Lifeshitz, “Electrodynamics of Continuous Media,” 2nd Edition, Pergamon Press, Oxford, 1984.
[18]	K. P. Thakur, R. K. Jha and O. P. Thakur, “Convexity of Internal Energy of Cubic Crystal Deformed to Orthorhombic Structure,” Springer (Pramana)—Journal of Physics, Vol. 34, No. 3, 1990, pp. 201-215.
[19]	O. P. Thakur, “Theoretical Mechanical Strength of Metals,” Proceeding of 34th Congress of Indian Society of Theoretical & Applied Mechanics, Coimbatore, December 1989, pp. 73-82.