A FINITE-ELEMENT METHOD FOR ELECTROSTRICTIVE CERAMIC DEVICES

A nonlinear, static finite element technique is developed and implemen ted for electrostrictive ceramic solids. This numerical method is base d on Toupin's elastic dielectric theory and models full electromechani cal coupling in the solid via the Maxwell stress and constitutive equa tions [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 incorpor ates the constitutive model of Hom and Shankar [(1994). A fully couple d 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 mecha nical and electric field variables. The finite element technique is de monstrated by solving the problem of a multilayered actuator construct ed from a lead-magnesium-niobate electrostrictor. Both the electric fi eld and stress state are computed near the tip of an internal electrod e. The results show that the nonlinear dielectric behavior significant ly alters the electric field near the rip to form a stress singularity . An analytical solution of the internal electrode problem is presente d and compared with the finite element predictions for verification. T he comparison shows a good qualitative agreement between the two solut ions. Finally, the numerical results are used to examine crack nucleat ion and growth from the electrode tip.