Abstract We study flexoelectric couplings in the second-order extension of rods when a cross section does not remain planar during extension. This happens when the rod is not very thin or, in dynamic problems, when the extensional wave length is not much larger than the characteristic dimension of the cross section of the rod. To exhibit flexoelectric couplings in such deformations or motions, a system of approximate, one-dimensional equations is derived from the three-dimensional theory of flexoelectricity for a rod of a rectangular cross section. The equations take into account extensional, thickness-stretch and symmetric thickness-shear deformations. They are used to analyze a few static and dynamic problems, showing that flexoelectric coupling is accompanying second-order extension through symmetric thickness shear where the cross section is no longer planar.

中文翻译：

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杆的二阶延伸中的挠曲电效应

摘要 我们研究了当横截面在拉伸过程中不保持平面时棒的二阶拉伸中的挠曲电耦合。当杆不是很薄时，或者在动态问题中，当延伸波长不大于杆横截面的特征尺寸时，就会发生这种情况。为了在这种变形或运动中表现出挠曲电耦合，从矩形截面棒的挠曲电的三维理论中推导出了一个近似的一维方程组。这些方程考虑了拉伸变形、厚度拉伸变形和对称厚度剪切变形。它们用于分析一些静态和动态问题，