具有圆柱形空腔的柔性电固体的分析

IF 2.6 4区 工程技术 Q2 MECHANICS Journal of Applied Mechanics-Transactions of the Asme Pub Date : 2023-08-10 DOI:10.1115/1.4063145
Jinchen Xie, C. Linder
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引用次数: 0

摘要

柔性电是一种显著的尺寸相关效应,意味着应变梯度可以引起电极化。这种效应在存在大应变梯度的柔性电固体内的缺陷附近特别明显。深入了解柔性电子器件的内部缺陷及其周围的多物理场对于理解其损伤和失效机制至关重要。基于此,利用应变梯度弹性理论研究了具有圆柱形空腔的柔性电固体在双轴拉伸下的力学和电学行为。在平面应变和不透水缺陷的假设下,得到了闭合形式的解。特别是,本研究首次将经典弹性理论的Kirsch问题扩展到高阶电弹性的理论框架中。我们的研究表明,应变梯度和双向加载比的不同长度尺度参数显著影响柔性电固体内圆柱腔附近的环向应力场、径向极化场和电势场。此外,我们使用混合有限元通过数值验证来验证我们的解析解。这两种方法的一致性证实了我们的分析解的准确性。本文的研究结果为柔性电材料的内部缺陷提供了更深入的见解,并可为研究柔性电固体中更复杂的缺陷奠定基础。
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Analysis of Flexoelectric Solids with a Cylindrical Cavity
Flexoelectricity, a remarkable size-dependent effect, means that strain gradients can give rise to electric polarization. This effect is particularly pronounced near defects within flexoelectric solids, where large strain gradients exist. A thorough understanding of the internal defects of flexoelectric devices and their surrounding multiphysics fields is crucial to comprehend their damage and failure mechanisms. Motivated by this, strain gradient elasticity theory is utilized to investigate the mechanical and electrical behaviors of flexoelectric solids with cylindrical cavities under biaxial tension. Closed-form solutions are obtained under the assumptions of plane strain and electrically impermeable defects. In particular, this study extends the Kirsch problem of classical elasticity theory to the theoretical framework of higher-order electroelasticity for the first time. Our research reveals that different length scale parameters of the strain gradient and bidirectional loading ratios significantly affect the hoop stress field, radial electric polarization field, and electric potential field near the inner cylindrical cavity of the flexoelectric solid. Furthermore, we validate our analytical solution by numerical verification using mixed finite elements. The congruence between the two methods confirms our analytical solution's accuracy. The findings presented in this paper provide deeper insights into the internal defects of flexoelectric materials and can serve as a foundation for studying more complex defects in flexoelectric solids.
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来源期刊
CiteScore
4.80
自引率
3.80%
发文量
95
审稿时长
5.8 months
期刊介绍: All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation
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