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首页> 外文期刊>Journal of Physics, D. Applied Physics: A Europhysics Journal >A reformulated flexoelectric theory for isotropic dielectrics
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A reformulated flexoelectric theory for isotropic dielectrics

机译：各向同性电介质的重构柔电理论

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摘要

In flexoelectricity, a strain gradient can induce polarization and a polarization gradient can induce mechanical stress. In this paper, in order to identify the contributions of each strain gradient component, the flexoelectric theory is reformulated by splitting the strain gradient tensor into mutually independent parts. Two sets of orthogonal higher-order deformation metrics are inherited and perfected to reformulate the internal energy density for isotropic materials. The deviatoric stretch gradient and the symmetric part of the rotation gradient are proved to disappear in the coupling of strain gradient to polarization and, moreover, the independent higher-order constants associated with the coupling of strain gradient to strain gradient reduce from five to three. The constitutive relations are then reformulated in terms of the new deformation and electric field metrics, and the governing equations and boundary conditions are derived according to the variational principle of electric enthalpy. On the basis of the present simplified flexoelectric theory, a flexoelectric Bernoulli-Euler beam theory is specified. Solutions for a cantilever subjected to a force at the free end and a voltage cross the thickness are constructed and the size-dependent direct and inverse flexoelectric effects are captured.
机译：在柔电中，应变梯度会引起极化，而极化梯度会引起机械应力。在本文中，为了确定每个应变梯度分量的贡献，通过将应变梯度张量分成相互独立的部分来重新构造柔电理论。继承并完善了两组正交的高阶变形度量，以重新形成各向同性材料的内部能量密度。事实证明，在应变梯度与极化的耦合中，偏斜拉伸梯度和旋转梯度的对称部分消失了;此外，与应变梯度与应变梯度的耦合相关的独立高阶常数从5减小为3。然后根据新的变形和电场度量重新构造本构关系，并根据电焓的变分原理推导控制方程和边界条件。基于当前简化的柔电理论，提出了柔电的Bernoulli-Euler梁理论。构造了悬臂的解决方案，该悬臂的自由端受力，且电压跨过厚度，并捕获了尺寸相关的正和反柔电效应。

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