Global sensitivity analysis of electromechanical coupling behaviors for flexoelectric nanostructures

Recent research shows that flexoelectricity may prominently affect the electromechanical coupling responses of elastic dielectrics at the nanoscale. From the perspective of devices design, it is urgent to know how the input parameters affect the electromechanical coupling behaviors of flexoelectric nanostructures. In this work, global sensitivity analysis is applied to elastic dielectric nanoplates to decompose the attribution of each of the parameters. Meanwhile, the existing hierarchical regression is found not suitable for simultaneously evaluating the multicollinearity and high dimensionality problems, when global sensitivity analysis of flexoelectric nanostructures is obtained combining polynomial chaos expansion (PCE). In order to overcome the above issues, the following strategies is proposed: 1) First, an adaptive sparse scheme is employed to build the sparse PCE. The number of terms of the PCE is decreased through choosing the most related polynomials with respect to a given model output. 2) Then, the hierarchical regression can be carried out iteratively via combining with the adaptive-sparse scheme. 3) Finally, the Sobol sensitivity indices are calculated through using these procedures. Further, Sobol sensitivity indices reveal that the thickness is the decisive input parameter that strongly affects the buckling and vibration responses of the flexoelectric nanoplate; the flexoelectric coefficients is the next key parameter that affect the buckling and vibration responses of flexoelectric nanoplate. Our finding also demonstrates that the influence of the flexoelectric coefficient is much stronger than that of the piezoelectric coefficient, which revealed the domination of the flexoelectric effect in ultra-thin piezoelectric nanostructures.