Couple Stress-Based Flexoelectric Theory in Orthogonal Curvilinear Coordinates and its Application to an Infinitely Long Dielectric Cylinder

Abstract

In this paper, the formulations of the couple stress based flexoelectric theory in orthogonal curvilinear coordinates are presented. By following the two rules of transforming tensor equations from Cartesian coordinates to curvilinear ones: replacing the partial differentiation symbol with the covariant differentiation symbol and ensuring that the identical indices are positioned diagonally, the governing equations, constitutive equations and boundary conditions in orthogonal curvilinear coordinates are obtained. Then the couple stress based flexoelectric theory is specified for cylindrical coordinates. The flexoelectric responses of an infinitely long dielectric cylinder under a uniform electric field are analyzed. Numerical results show that the radial displacement increases rapidly as the mechanical length scale parameter [Formula: see text] increases. When [Formula: see text] is larger than 5[Formula: see text][Formula: see text]m, the circumferential displacement decreases rapidly. [Formula: see text] has a large effect on the induced displacements but a small effect on the induced electric potential, while the electrical length scale parameter [Formula: see text] has a small effect on both the induced displacements and the induced electric potential.