Modeling and analysis of the static bending of piezoelectric nanowires with the consideration of surface effects

In this paper, the Euler–Bernoulli beam model was used to analyze the influence of surface effect on the bending of piezoelectric nanowires based on surface energy density theory. The governing equations and boundary conditions of fixed–fixed nanowire and cantilever nanowire are derived in detail using the principle of minimum potential energy. The analytical solutions for the deflection, effective bending stiffness and induced charge are obtained. The results show that compared with the classical elastic beam theory, due to the influence of surface effect, the cantilever nanowires soften and the induced charges increase, while the fixed nanowires strengthen and the induced charges decrease. This research has a certain guiding significance for the design of piezoelectric wire-based nano-devices and the characterization of the mechanical properties of nanowires.