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A flexoelectric theory with rotation gradient and electric field gradient effects for isotropic dielectrics

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Abstract

In this study, a flexoelectric theory within the context of the couple stress theory is developed for isotropic dielectrics to capture the size-dependent flexoelectric behaviors. In this theory, the electric enthalpy density depends on the strain, the symmetric part and the dual vector of the antisymmetric part of the rotation gradient, the electric field and its gradient. The constitutive relations are obtained by means of it. The governing equations and boundary conditions are derived from the variational principle. Based on this theory, the electromechanical responses of a cantilever beam and an infinite length tube are solved. For the beam problem, numerical results show that the force-induced electric potential increases with the increasing flexoelectric coefficient and decreasing electrical scale parameters and exhibits obvious size dependency. A positive voltage makes the beam bend upward, while a negative voltage makes the beam bend downward, and the deflection increases with the applied voltage. Besides, the rotation gradient effect is significant when the ratio of beam thickness to material mechanical scale parameters is smaller. For the tube problem, numerical results show that the radial displacement is reduced, and the radial electric field becomes smoothed out owing to the flexoelectric effect. The gradient of the radial electric field increases with the decreasing electrical scale parameters. Moreover, this problem is not affected by the rotation gradient effect.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (2018YFB0703500).

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Authors and Affiliations

  1. Key Laboratory of High Efficiency and Clean Mechanical Manufacture of Ministry of Education, School of Mechanical Engineering, Shandong University, **an, 250061, China

    Juanjuan Li, Shenjie Zhou & Kanghui Wu

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  1. Juanjuan Li
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  2. Shenjie Zhou
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Correspondence to Shenjie Zhou.

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Li, J., Zhou, S. & Wu, K. A flexoelectric theory with rotation gradient and electric field gradient effects for isotropic dielectrics. Arch Appl Mech 93, 1809–1823 (2023). https://doi.org/10.1007/s00419-022-02357-1

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