A reformulated flexoelectric theory for isotropic dielectrics
A reformulated flexoelectric theory for isotropic dielectrics
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DOI：
10.1088/0022-3727/48/46/465502
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发表时间：
2015-11-25
影响因子：
3.4
通讯作者：
Chen, Xi
中科院分区：
文献类型：
--
作者：
Li, Anqing;Zhou, Shenjie;Chen, Xi
在挠曲电性中，应变梯度可以引起极化，并且极化梯度可以引起机械应力。本文通过将应变梯度张量分解为相互独立的部分，对挠曲电理论进行了重新表述，以确定各应变梯度分量的贡献。继承和完善了两组正交高阶变形度量，重新表述了各向同性材料的内能密度。证明了在应变梯度与极化的耦合中，偏拉伸梯度和旋转梯度的对称部分消失了，而且与应变梯度与应变梯度的耦合相关的独立高阶常数从5个减少到3个.根据新的变形和电场度规重新建立了本构关系，并根据电焓变分原理导出了控制方程和边界条件。在现有弯电简化理论的基础上，提出了弯电Bernoulli-Euler梁理论。悬臂梁的自由端受到的力和跨厚度的电压的解决方案被构造和大小相关的直接和逆挠曲电效应被捕获。
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.