Buckling analysis of stretchable ferroelectric thin film on elastomeric substrates

The thin stiff films on pre-stretched compliant substrates can form wrinkles, which can be controlled in micro and nanoscale systems to generate smart structures. Recently, buckled piezoelectric/ferroelectric nanoribbons have been reported to show an enhancement in the piezoelectric effect and stretchability, which can be applied in energy harvesting devices, sensors and memory devices instead of polymeric polyvinylidine fluoride (PVDF). This paper studies the buckling and post-buckling process of ferroelectric thin films bonded to the pre-stretched soft layer, which in turn lies on a rigid support. Nonlinear electromechanical equations for the buckling of thin piezoelectric plates are deduced and employed to model the ferroelectric film poled in the thickness direction. Two buckling modes are analyzed and discussed: partially de-adhered buckling and fully adhered buckling. Transition from one buckling mode to the other is predicted and the effect of piezoelectricity on the critical buckling condition of piezoelectric film is examined.