Finite-element modeling of lead magnesium niobate electrostrictive materials: dynamic analysis

A finite-element model is proposed for the time-domain analysis of electrostrictive materials. Hom's material model, developed for lead magnesium niobate (PMN) ceramics, is used. It includes the quadratic dependence of strain with polarization, the saturation of polarization, assumes constant temperature, and excludes hysteresis. The theoretical formulation is justified by the principle of virtual works. The numerical model is obtained after discretization in space and time. The validation is performed by comparing numerical results with semianalytical results for an electrostrictive spherical shell subjected to a step in voltage or in charge. From these results, a method to compute the coupling coefficient of electrostrictive materials, based on Ikeda's definition, is proposed and applied to a bar with parallel electric field.