A finite element method for electrostrictive ceramic devices

A nonlinear, static finite element technique is developed and implemented for electrostrictive ceramic solids. This numerical method is based on Toupin's elastic dielectric theory and models full electromechanical coupling in the solid via the Maxwell stress and constitutive equations [Toupin, R. A. (1956). The elastic dielectric. J. Rational Mech. Anal. 5, 849-915; Toupin, R. A. (1963). A dynamical theory of elastic dielectrics. Int. J. Engng Sci. 1, 101-126]. The formulation incorporates the constitutive model of Hom and Shankar [(1994). A fully coupled constitutive model for electrostrictive ceramic materials. J. Intell. Mater. Syst. Struct. 5, 795-801]. This model simulates polarization saturation at high electric fields and nonlinear coupling of the mechanical and electric field variables. The finite element technique is demonstrated by solving the problem of a multilayered actuator constructed from a lead-magnesium-niobate electrostrictor. Both the electric field and stress state are computed near the tip of an internal electrode. The results show that the nonlinear dielectric behavior significantly alters the electric field near the rip to form a stress singularity. An analytical solution of the internal electrode problem is presented and compared with the finite element predictions for verification. The comparison shows a good qualitative agreement between the two solutions. Finally, the numerical results are used to examine crack nucleation and growth from the electrode tip.