Superelastic electromechanical behaviors in ferroelectric PbTiO3 ceramics under coupled mechanical-electric fields: Higher-order piezoelectric constitutive equations from first-principles

With the recent discovery of superelastic behaviors of ferroelectric (piezoelectric) ceramics, understanding their non-linear mechanical and electromechanical responses under high stress and electric field conditions is crucial for engineering and designing advanced piezoelectric devices, such as ultrasmall actuator systems. In this study, we carry out first-principles finite electric field calculations to clarify the mechanical and electromechanical properties under the electric field for typical ferroelectric ceramics of PbTiO3. Superelastic-like non-linear deformation behavior is enhanced or suppressed depending on the electric field direction, suggesting the possible design of superelasticity. We clarified that positive and negative electric fields to spontaneous polarization promote and inhibit deformation due to strain loading, thereby providing tunable superelasticity. We also investigate the mechanical loading and electric field dependence of the piezoelectric coefficient of PbTiO3. The tunable piezoelectric response can be provided with a coupling of mechanical loading and electric field. Finally, we present higher-order piezoelectric constitutive equations applicable for superelastic-like non-linear deformations under an electric field. The present results will open promising paradigms for functional piezoelectric devices, and the proposed piezoelectric constitutive equations broaden the design scope through finite element method analysis.