Résumé :

Ferroelectric ceramics are a prime example of multifunctional materials where mechanical and electrical properties are intrinsically coupled. They exhibit a spontaneous electric polarization that can be reversed under the application of an electrical or mechanical loading. The switching process consists of the nucleation and growth of domains of constant polarization, corresponding to the different variants of the crystallographic phase of the ferroelectrics (e.g., tetragonal phase in BaTiO3). Simulations of the evolution of polarization domains at the mesoscale use phase-field models where the physical fields evolve steeply but continuously across polarization domains. Existing phase-field model are based on the Allen-Cahn equation which assumes, unlike experimental evidence, a linear relation between the velocity of domain walls and their conjugate driving force. As a faithful modeling of the kinetics is required for understanding high-rate switching, we develop in this work a phase-field formulation that accounts for the non-linear kinetics of domain walls.

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