Interaction Between Flexoelectric Fields Associated With Microholes in Solids
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摘要: 该文研究了固体材料中常见缺陷微孔洞间挠曲电场的相互作用. 通过配点混合有限元法模拟并对比了单孔和双孔模型中孔洞附近的应力、应变梯度以及挠曲电场的分布情况. 数值模拟结果表明，当两个孔洞间的距离逐渐减小时，两孔附近的挠曲电场开始发生相互作用. 此外，进一步探讨了微孔洞间挠曲电场的相互作用随孔间距离和孔洞尺寸的变化规律. 结果表明，当孔间距离越近，尺寸越小时，孔间挠曲电场的相互作用越强.Abstract: The flexoelectric fields' interactions between microholes of common defects in solid materials are studied. With the collocation mixed finite element method, the distributions of the stress, the strain gradient, and the flexoelectric field around the hole of the single hole and the double holes, respectively, are compared. The numerical simulation results indicate that, the flexoelectric fields' interaction around the double holes emerges with the gradual decrease of the distance between the double holes. In addition, the effects of the distance between holes and the size of holes on the flexoelectric fields' interaction between microholes are explored. The results show that, reducing the distance between double holes and shrinking the size of holes will induce to an enhanced interaction of the flexoelectric field between double holes.
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图 1 考虑正、逆挠曲电效应的中心对称电介质的边界条件
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 1. Boundary conditions for centrosymmetric dielectrics considering direct and converse flexoelectric effects
图 2 圆形孔洞问题的直角坐标系及示意图
Figure 2. The Cartesian coordinate system and the circular hole problem
图 4 含单孔和双孔的方形板的应力分量σ22、应变梯度分量η221、电场分量E1和极化分量P1云图
Figure 4. Contours of stress component σ22, strain gradient component η221, electric field component E1 and polarization component P1 of square plates with 1 hole and 2 holes, respectively
图 5 含单孔和双孔的方形板中应力分量σ22、应变梯度分量η221、电场分量E1和极化分量P1沿x轴的变化(虚线表示孔洞边界)
Figure 5. The variations of stress component σ22, strain gradient component η221, electric field component E1 and polarization component P1 along the x-axis in square plates with 1 hole and 2 holes, respectively (with dashed lines representing the boundaries of holes)
图 6 不同孔间距离下方形板的应力分量σ22、应变梯度分量η221、电场分量E1和极化分量P1云图
Figure 6. Contours of stress component σ22, strain gradient component η221, electric field component E1 and polarization component P1 of square plates with different distances between 2 holes
图 7 不同孔间距离下方形板中应力分量σ22、应变梯度分量η221、电场分量E1和极化分量P1沿韧带的变化(虚线表示孔洞边界)
Figure 7. The variations of stress component σ22, strain gradient component η221, electric field component E1, and polarization component P1 along the ligament in square plates with different distances between 2 holes (with dashed lines representing the boundaries of holes)
图 8 不同孔洞半径下方形板的应力分量σ22、应变梯度分量η221、电场分量E1和极化分量P1云图
Figure 8. Contours of stress component σ22, strain gradient component η221, electric field component E1 and polarization component P1 of shaped plates with different hole radii
图 9 单孔和双孔模型在不同孔洞半径下方形板中应变梯度分量η221和电场分量E1沿韧带的变化(虚线表示孔洞边界)
Figure 9. The variations of strain gradient component η221 and electric field component E1 along the ligament in square plates of 1-hole and 2-hole models with different hole radii (with dashed lines representing the boundaries of holes)
elastic constant internal material length
l/mc11/Pa c12/Pa c22/Pa c44/Pa 1.26×1011 5.3×1010 1.17×1011 3.53×1010 2×10－9 permittivity flexoelectric coefficient a11/(C2/(N·m2)) a22/(C2/(N·m2)) f1/(C/m) f2/(C/m) 1.51×10－8 1.30×10－8 1×10－7 0 
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[1] YUDIN P V, TAGANTSEV A K. Fundamentals offlexoelectricity in solids[J]. Nanotechnology, 2013, 24 (43): 432001. doi: 10.1088/0957-4484/24/43/432001 [2] WANG B, GU Y, ZHANG S, et al. Flexoelectricity in solids: progress, challenges, and perspectives[J]. Progress in Materials Science, 2019, 106 : 100570. doi: 10.1016/j.pmatsci.2019.05.003 [3] DENG Q, LV S H, LI Z Q, et al. The impact of flexoelectricity on materials, devices, and physics[J]. Journal of Applied Physics, 2020, 128 (8): 080902. doi: 10.1063/5.0015987 [4] NGUYEN T D, MAO S, YEH Y W, et al. Nanoscale flexoelectricity[J]. Advanced Materials, 2013, 25 (7): 946-974. doi: 10.1002/adma.201203852 [5] JIANG X N, HUANG W B, ZHANG S J. Flexoelectric nano-generator: materials, structures and devices[J]. Nano Energy, 2013, 2 (6): 1079-1092. doi: 10.1016/j.nanoen.2013.09.001 [6] ASKAR A, LEE P C Y, CAKMAK A S. The effect of surface curvature and discontinuity on the surface energy density and other induced fields in elastic dielectrics with polarization gradient[J]. International Journal of Solids and Structures, 1971, 7 (5): 523-537. doi: 10.1016/0020-7683(71)90103-X [7] MARANGANTI R, SHARMA N D, SHARMA P. Electromechanical coupling innonpiezoelectric materials due to nanoscale nonlocal size effects: Green's function solutions and embedded inclusions[J]. Physical Review B, 2006, 74 : 014110. doi: 10.1103/PhysRevB.74.014110 [8] MAO S, PUROHIT P K. Defects in flexoelectric solids[J]. Journal of the Mechanics and Physics of Solids, 2015, 84 : 95-115. doi: 10.1016/j.jmps.2015.07.013 [9] TIAN X P, XU M K, ZHOU H Y, et al. Analytical studies on mode Ⅲ fracture in flexoelectric solids[J]. Journal of Applied Mechanics, 2022, 89 (4): 041006. doi: 10.1115/1.4053268 [10] XU M K, TIAN X P, DENG Q, et al. Modeling the interaction between inclusions and nanocracks in flexoelectric solids[J]. Journal of Applied Mechanics, 2023, 90 (10): 101005. doi: 10.1115/1.4062659 [11] XIE J C, LINDER C. Analysis offlexoelectric solids with a cylindrical cavity[J]. Journal of Applied Mechanics, 2024, 91 (1): 011007. doi: 10.1115/1.4063145 [12] 周承芳, 关长文. 无限大板包含任意排列多个椭圆孔洞的应力集中和多裂纹的应力强度因子计算[J]. 应用数学和力学, 1983, 4 (6): 789-800. http://www.applmathmech.cn/article/id/4263ZHOU Chengfang, GUAN Changwen. Stress concentration and stress intensity factors for an infinite plane with several rows of elliptic holes and cracks[J]. Applied Mathematics and Mechanics, 1983, 4 (6): 789-800. (in Chinese) http://www.applmathmech.cn/article/id/4263 [13] 刘文辉, 何圳涛, 胡忠举. 表面微空洞长大和相互作用的晶体有限元分析[J]. 固体力学学报, 2012, 33 (4): 437-443.LIU Wenhui, HE Zhentao, HU Zhongju. CPFEM analysis on growth and interaction behaviors of surface voids[J]. Chinese Journal of Solid Mechanics, 2012, 33 (4): 437-443. (in Chinese) [14] SOUTIS C, FLECK N A, CURTIS P T. Hole-hole interaction in carbon fibre/epoxy laminates under uniaxial compression[J]. Composites, 1991, 22 (1): 31-38. doi: 10.1016/0010-4361(91)90100-U [15] MINDLIN R D. Polarization gradient in elastic dielectrics[J]. International Journal of Solids and Structures, 1968, 4 (6): 637-642. doi: 10.1016/0020-7683(68)90079-6 [16] SHEN S P, HU S L. A theory of flexoelectricity with surface effect for elastic dielectrics[J]. Journal of the Mechanics and Physics of Solids, 2010, 58 (5): 665-677. doi: 10.1016/j.jmps.2010.03.001 [17] SLADEK J, SLADEK V, HRYTSYNA M, et al. Application of the gradient theory to interface crack between two dissimilar dielectric materials[J]. Engineering Fracture Mechanics, 2022, 276 : 108895. doi: 10.1016/j.engfracmech.2022.108895 [18] WANG S, SU H C, YI M, et al. Strain gradient finite element formulation of flexoelectricity in ferroelectric material based on phase-field method[J]. Acta Mechanica Solida Sinica, 2024, 37 (4): 570-579. doi: 10.1007/s10338-024-00485-5 [19] BAO A W, LI X B, PU Y X, et al. Surface elastic effects on electromechanical responses of a piezoelectric semiconducting nanobeam[J]. Acta Mechanica Solida Sinica, 2024, 37 (4): 598-612. doi: 10.1007/s10338-023-00459-z [20] TIAN X P, SLADEK J, SLADEK V, et al. A collocation mixed finite element method for the analysis of flexoelectric solids[J]. International Journal of Solids and Structures, 2021, 217 : 27-39. [21] TIAN X P, XU M K, ZHOU H Y, et al. Modeling the flexoelectric effect around the tip of nano-cracks using a collocation MFEM[J]. Engineering Fracture Mechanics, 2023, 289 : 109452. doi: 10.1016/j.engfracmech.2023.109452 [22] TIAN X P, ZHOU H Y, DENG Q, et al. Modeling the flexoelectric effect in semiconductors via a second-order collocation MFEM[J]. International Journal of Mechanical Sciences, 2024, 264 : 108837. doi: 10.1016/j.ijmecsci.2023.108837 -
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