Spectral Methods for Electromechanical Coupling in Ferroelectrics

Abstract eng:
Recent advances in fast numerical methods to compute the mechanical response of heterogeneous microstructures have allowed the solution of hitherto intractable systems. In particular the use of an iterative Fourier Spectral Method as opposed to the traditional Finite Element Method has gained significant interest in the periodic homogenisation of microstructures. In this paper, a method is presented to solve a periodic boundary value problem involving electromechanical coupling in a polycrystalline ferroelectric microstructure. In addition to the mechanical response of the structure, this method provides insight into the kinetics of domain wall motion in a complex microstructure. Time hysteresis curves for the electric displacement and strain evolution resulting from a saw-tooth electric loading are presented, and are shown to qualitatively match experimental results. An overview of the diverse applications of this method is also provided.

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