Electrostrictive materials convert electrical energy into mechanical energy and vice versa. They are extensive applied as intelligent materials in the engineering structures. The governing equations in electrostrictive media under the quasistatic electric field are very important for the measurement of material constants and the research on the strength and function. But some theoretical problems should be further clarified. In this paper, the electric force acting on the material is studied and the complete governing equations will be given. In this paper a possible method to measure electrostrictive coefficients is also discussed. 1. Introduction The measurement method of material constants in an electrostrictive material is somewhat controversial between authors. Shkel and Klingenberg [1] considered that “The ultimate deformation depends on the elastic properties of the fixtures attached to the material (e.g., the electrodes). The (electrostrictive) coefficients are therefore not strictly material parameters, but rather characteristics of the entire system.” Zhang et al. [2] pointed out that “In general in a nonpiezoelectric material such as the polyurethane elastomers investigated, the electric field induced strain can be caused by the electrostrictive effect and also by the Maxwell stress effect. The electrostrictive effect is the direct coupling between the polarization and mechanical response in the material. … On the other hand Maxwell stress, which is due to the interaction between the free charges on the electrodes (Coulomb interaction) and to electrostatic forces that arise from dielectric inhomogeneities.” Guillot et al. [3] considered that “strictly speaking, the Maxwell stress tensor does not belong to the electrostrictive equations, but that it should be taken into account in the measurements. … it is possible to factor out its contribution to the total response of the film and therefore to identify the isolated contribution due to the (electrostrictive) tensor only.” Thakur and Singh [4] considered that: “In most of the recent experiments concerning determination of electrostrictive parameters in elastic dielectrics, several researchers used incorrect equations without considering the contribution from the edge effect, the shear stress and suitable boundary conditions. This led to wrong predictions of experimental results particularly for materials with high Poisson ratios. Errors in the estimation of induced strains, varying from an underestimation of 202% to an overestimation of 168%, have been pointed out in the case of polycarbonate
Q. M. Zhang, J. Su, C. H. Kim, R. Ting, and R. Capps, “An experimental investigation of electromechanical responses in a polyurethane elastomer,” Journal of Applied Physics, vol. 81, no. 6, pp. 2770–2776, 1997.
F. M. Guillot, J. Jarzynski, and E. Balizer, “Measurement of electrostrictive coefficients of polymer films,” Journal of the Acoustical Society of America, vol. 110, no. 6, pp. 2980–2990, 2001.
O. P. Thakur and A. K. Singh, “Electrostriction and electromechanical coupling in elastic dielectrics at nanometric interfaces,” Materials Science- Poland, vol. 27, no. 3, pp. 839–850, 2009.
Q. Jiang and Z. B. Kuang, “Stress analysis in two dimensional electrostrictive material with an elliptic rigid conductor,” European Journal of Mechanics A, vol. 23, no. 6, pp. 945–956, 2004.
Q. Jiang and Z. B. Kuang, “Stress analysis in a cracked infinite electrostrictive plate with local saturation electric fields,” International Journal of Engineering Science, vol. 44, no. 20, pp. 1583–1600, 2006.
R. M. McMeeking and C. M. Landis, “Electrostatic forces and stored energy for deformable dielectric materials,” Journal of Applied Mechanics, vol. 72, no. 4, pp. 581–590, 2005.
Z. B. Kuang, “Some variational principles in elastic dielectric and elastic magnetic materials,” European Journal of Mechanics A, vol. 27, no. 3, pp. 504–514, 2008.
Z. B. Kuang, “Some variational principles in electroelastic media under finite deformation,” Science in China, Series G, vol. 51, no. 9, pp. 1390–1402, 2008.
Z. B. Kuang, “Internal energy variational principles and governing equations in electroelastic analysis,” International Journal of Solids and Structures, vol. 46, no. 3-4, pp. 902–911, 2009.
Z. B. Kuang, “Physical variational principle and thin plate theory in electro-magneto-elastic analysis,” International Journal of Solids and Structures, vol. 48, no. 2, pp. 317–325, 2011.
Z. B. Kuang, “Some thermodynamic problems in continuum mechanics,” in Thermodynamics—Kinetics of Dynamic Systems, J. C. M. Piraján, Ed., InTech Open Access Publisher, Rijeka, Croatia, 2011.