Nonlinear electromechanical coupling in ferroelectric materials: large deformation and hysteresis

Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external electric field. To extend the operational range of sensors and actuators, an accurate understanding of the evolution of the material's state of polarization is imperative, which requires both physical and geometric nonlinearities to be taken into account. Moreover, polymeric smart materials like PVDF allow significantly larger deformation as compared to conventional piezoelectric ceramics. The electromechanical coupling in piezoelectric materials manifests in ferroelectric and ferroelastic hystereses, which are related to both reversible and irreversible processes. Focusing on the latter, we transfer phenomenological models for domain switching in ferroelectric materials to the geometrically nonlinear regime. For this purpose, we follow related concepts of geometrically nonlinear elastoplasticity, where the concept of a multiplicative decomposition of the deformation gradient plays a key role. Accordingly, an additional deformation path that describes the evolution of the poled state from the unpoled referential configuration is introduced. The constitutive response of the material to mechanical and electrical loads is discussed, and dissipative internal forces that drive the evolution of the remanent polarization are derived within a thermodynamical framework and the principle of maximum dissipation.