FFT-based Galerkin and level-set methods for the homogenized evolution of domain nuclei in ferroelectrics

We introduce an FFT-based Galerkin homogenization scheme, which, in combination with the level-set method, allows us to study the evolution of ferroelectric domain nuclei in the experimentally relevant stress-driven setting. Our proposed framework includes an accelerated FFT-solver for solving the electromechanically coupled balance laws and a unified regularized driving force formulation for the level-set method (overcoming the main deficiencies of existing ferroelectric phase-field formulations).

We use this new scheme to simulate the long-term evolution of 180° and 90° domain nuclei in a periodic cell of both barium titanate and lead titanate, shedding light onto the distinct contributions of the electrical and mechanical fields onto the nucleus’ geometric changes including needle-like and polygonal shapes. Piezoelectricity connects those two effects and further affects fine feature adjustments of the evolving nucleus, classically not captured by analytical or phase-field models.