Ferroelectric materials for piezoelectric actuators by optimal design

Abstract

Optimization methods provide a systematic means of designing heterogeneous materials with tailored properties and microstructures focussing on a specific objective. An optimization procedure incorporating a continuum modeling is used in this work to identify the ideal orientation distribution of ferroelectrics (FEs) for application in piezoelectric actuators. Piezoelectric actuation is dictated primarily by the piezoelectric strain coefficients d iμ . Crystallographic orientation is inextricably related to the piezoelectric properties of FEs. This suggests that piezoelectric properties can be tailored by a proper choice of the parameters which control the orientation distribution. Nevertheless, this choice is complicated and it is impossible to analyze all possible combinations of the distribution parameters or the angles themselves. Stochastic optimization combined with a generalized Monte Carlo scheme is used to optimize the objective functions, the effective piezoelectric coefficients d 31 and d 15. The procedure is applied to heterogeneous, polycrystalline, FE ceramics which are essentially an aggregate of variously oriented grains (crystallites). Global piezoelectric properties are calculated using the homogenization method at each grain configuration chosen by the optimization algorithm. Optimal design variables and microstructure that would generate polycrystalline configurations that multiply the macroscopic piezoelectricity are identified.