  Understanding the dynamic behavior of the domain structure is critical to the
design and application of super-elastic freestanding ferroelectric thin films.
The phase-field simulation is currently a powerful tool for observing,
exploring, and revealing domain switching behavior and phase transition in
ferroelectric materials at the mesoscopic scale. The present review summarizes
the recent progress of phase-field methods in the theoretical interpretation,
mechanical response, and domain structure evolution of freestanding
ferroelectric thin films, wrinkled structures, and nano-springs. Furthermore,
the strong coupling relationship between strain and ferroelectric polarization
in super-elastic ferroelectric nanostructures is confirmed and discussed, which
brings new design strategies for strain engineering of freestanding
ferroelectric thin film systems. To further promote the innovative development
and application of the freestanding ferroelectric thin film system, the review
ends with a summary and an outlook on the theoretical model of the freestanding
ferroelectric thin film.

Materials Science;Applied Physics