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A flexoelectric spherical microshell model incorporating the strain gradient effect

机译：包含应变梯度效应的柔电球形微壳模型

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In this paper, a size-dependent flexoelectric spherical microshell model is proposed considering flexoelectric effect and strain gradient effect. By means of the variation principle, explicit expressions of the governing equations and the boundary conditions are deduced. Solving corresponding governing equations, analytical solutions of both direct and converse flexoelectric responses in static axisymmetric bending problem are obtained. Then, the flexoelectric responses in barium strontium titanate spherical microshells with and without a circular top opening are numerically investigated. Both the direct and converse flexoelectric responses are found to vary non-monotonically as the central angle increases. The converse flexoelectric bending is examined to exist even in clamped spherical microshells, which is different from the case of flat structures. In addition, for all cases, the strain gradient effect will highly reduce the flexoelectric responses, particularly when the thickness approaches the material internal scale constants. (C) 2019 Elsevier Inc. All rights reserved.
机译：本文提出了一种基于尺寸的柔性电球形微壳模型，该模型考虑了柔性电效应和应变梯度效应。利用变分原理，推导了控制方程和边界条件的明确表达式。通过求解相应的控制方程，可以得到静态轴对称弯曲问题中正，反柔电响应的解析解。然后，数值研究了钛酸钡锶锶球形微壳中是否具有圆形顶部开口。随着中心角的增加，直接和相反的柔电响应都发现非单调变化。甚至在夹紧的球形微壳中也检测到了相反的柔电弯曲，这与平面结构的情况不同。此外，在所有情况下，应变梯度效应都将极大地降低柔电响应，尤其是当厚度接近材料内部尺度常数时。 （C）2019 Elsevier Inc.保留所有权利。

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