Size-dependent dynamic electromechanical behavior of an isotropic dielectric nanotube under torsional and electrical loading: a strain gradient elasticity approach
摘要
In this manuscript, we investigate both the direct and converse flexoelectric effects in an elastic, isotropic dielectric nanotube. To examine these phenomena, we consider two loading scenarios applied at the lateral surface of the nanotube: a mechanical moment (torsional loading) and distributed electric charges. The ends of the nanotube are assumed to be subject to fixed mechanical or electrical boundary conditions, depending on the case. The governing field equations are derived using a variational approach based on the strain energy functional and the virtual work of external forces. All boundary conditions, both mechanical and electrical, are assumed to be satisfied a priori. The formulation is developed in a general form and later specialized according to the geometry of the nanotube. We compare the mechanical responses induced by the applied moment to the electrical responses induced by surface charges, with a particular focus on the influence of the ratio between the material length scale and the micro-inertia length scale. The results are presented graphically and analyzed in detail. In summary, the study highlights that the internal length scale of the material plays a significant role in the flexoelectric response, especially when it is comparable to or smaller than the macroscopic dimensions of the structure. Furthermore, Saint-Venant's principle is found to be applicable to both the mechanical and electrical responses in this context.