Modeling direct and converse flexoelectricity in soft dielectric rods with application to the follower load

Abstract

Dielectric rods have been employed in various electromechanical applications, including energy harvesters and sensors. This paper develops a general framework to model large deformations in dielectric rods, considering both direct and converse flexoelectric effects. Initially, we derive the governing differential equations for a three-dimensional dielectric continuum solid to model large deformations, incorporating converse flexoelectricity. Then, we derive the equilibrium equations for the flexoelectric strain-gradient special Cosserat rod. Subsequently, we establish its constitutive relations and identify the corresponding work conjugates. To solve these governing differential equations numerically, we implement a quaternion-based numerical approach and obtain flexoelectricity-based solutions corresponding to the follower load. Moreover using these constitutive relations, we have also obtained nonlinear analytical solutions for bending under the follower load that show an excellent agreement with our numerical results. Bending under the follower load is also compared with the transverse load to understand the electric field generation. Unlike, under the application of the transverse load, where the electric field increases monotonically, for the follower load, the electric field gradually switches its sign. The role of direct and converse flexoelectric coefficients has also been examined, and several interesting conclusions have been drawn. Finally, we analyze the effect of mechanical and electrical length scale parameters. The electromechanical response from the follower load can be utilized to fabricate flexoelectric sensors for nanoelectromechanical systems.