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随着微纳声学器件的快速发展,其核心声学结构已进入纳米尺度范畴,表面效应对薄膜材料性能的影响日益凸显,经典弹性理论面临挑战。本文基于表面弹性理论,引入表面能密度研究纳米尺度下的表面效应,采用傅里叶积分变换法推导出纳米尺度SiO2/Si异质结构薄膜表面牵引力下应力场与位移场的解析表达式。研究结果显示,若以表面应力分布与经典理论相差3%作为判断标准,在激励区域宽度2a的5倍范围内,材料的微观特性彰显主导地位。随着激励区域不断减小,在激励区域内及边界附近表面应力分布较经典理论更加集中,剪切应力于边界处有极大值,材料表面刚度与抗变形能力增加,横向与纵向位移较经典理论减小。纳米尺度异质结构存在显著表面效应,导致应力和位移分布明显偏离弹性理论,经典弹性假设在相应纳米尺度范围不再适用。以上结果表明,在纳米尺度固体表面中,超高频纳米波长声波传播将明显受到尺度效应影响,经典弹性波理论在纳米尺度存在失效现象,这对纳米声学理论研究具有参考价值。Due to the rapid development of micro-nano acoustic devices, their core acoustic structures have entered the nanoscale category. The influence of surface effects on the mechanical properties of thin-film materials at the nanoscale becomes increasingly prominent, and the classical elasticity theory struggles to describe mechanical behavior at this scale. In this paper, a mechanical model of nano-SiO2/Si heterostructured thin films considering surface effects is established based on surface elasticity theory by introducing the key parameter of surface energy density. In this paper, a mechanical model of heterostructured nano-SiO2/Si films is created based on the surface elasticity theory, taking into account surface effects by introducing the key parameter of surface energy density. Using the Fourier integral transform method, analytical expressions for stress and displacement fields under surface traction are systematically derived, revealing the influence of surface effects on the mechanical behavior of materials at the nanoscale by comparing the analytical solution with the classical theory. The results show that when the surface stress distribution differs by 3% from that predicted by the classical theory, the microscopic properties of the material are dominant and the surface effect cannot be neglected within a range of 5 times the width of the excitation region 2a. As the size of the excitation region decreases, the surface effect is significantly enhanced and the stress distribution within the excitation region and near the boundary becomes more concentrated than in the classical theory. The shear stress is no longer zero, and an extreme value is observed at the boundary, which differs significantly from that predicted by the classical theory of elasticity. The transverse and longitudinal displacements are reduced compared with the classical theory, and the surface stiffness and deformation resistance of the material are greatly improved. Significant surface effects occur on nanoscale heterostructured thin films, leading to large deviations in stress and displacement distributions from elasticity theory. Therefore, the classical elasticity assumptions are no longer applicable within the corresponding nanoscale range. The results demonstrate that the propagation of ultrahigh frequency nano length acoustic waves in nanoscale solid film surfaces is significantly affected by the scale effect. The failure of the classical elastic wave theory at the nanoscale is valuable for the study of nanoscale acoustic theory. Furthermore, these findings provide a theoretical basis for the subsequent development of a more precise model of interfacial effects and a more detailed investigation of the influence of the film-substrate modulus ratio.
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Keywords:
- Surface elasticity theory /
- Nanoscale /
- Surface effects /
- Failure phenomenon
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[1] Hui X P 2024 Acta Mech. Solida Sin. 37 371-384
[2] Farajpour A, Ghayesh H M, Farokhi H 2018 Int. J. Eng. Sci. 133 231-263
[3] Peddieson J, Buchanan R G, McNitt P R 2003 Int. J. Eng. Sci. 41 305-312
[4] Eringen A C 1967 NY.
[5] Toupin R A 1964 Arch. Ration. Mech. Anal. 17 85-112
[6] Gibbs J W 1879 Trans. Conn. Acad. 2 300-320
[7] Gurtin M E, Murdoch A I 1975 Arch. Ration. Mech. Anal. 59 389-390
[8] Miller R E, Shenoy V B 2000 Nanotechnology 11 139-147
[9] He J, Lilley C M 2008 Nano Lett. 8 1798-1802
[10] Tong L H, Lin F, Xiang Y, Shen H S, Lim C W 2021 Compos. Struct. 265 113708
[11] Zhang S Y, Tang X Y, Ruan H H, Zhu L L 2019 Appl. Phys. A 125 1-14
[12] Chen S, Yao Y 2014 Appl. Mech. 81 121002
[13] Zhang Y Y, Wang Y X, Zhang X,Shen H M, She G L 2021 Steel Compos. Struct. 38 293-304
[14] Wang L Y, Wu H M, Ou Z Y 2024 Math. Mech. Solids 29 401-417
[15] George V, Mohammadreza Y 2017 Crystals 7 321-349
[16] Saffari S, Hashemian M, Toghraie D 2017 Physica B 520 97-105
[17] Chen D Q, Sun D L, Li X F 2017 Compos. Struct. 173 116-126
[18] Ye G J, Yin C, Li S Y, Wang X P, Wu J 2023 Acta Phys. Sin. 72 104201 (in Chinese)[叶高杰, 殷澄, 黎思瑜, 俞强, 王贤平, 吴坚 2023 物理学报 72 104201]
[19] Shang S P, Lu Y J, Wang F H 2022 Acta Phys. Sin. 71 033101 (in Chinese)[尚 帅朋, 陆勇俊, 王峰会 2022 物理学报 71 033101]
[20] Tian X G, Tao L Q, Liu B, Zhou C J, Ren T L 2016 IEEE Electron Device Lett. 37 1063-1066.
[21] Shen B, Huang Z W, Ji Z, Lin Q, Chen S L,Cui D J, Zhang Z N 2019 Surf. Coat. Technol. 380 125061
[22] Selvadurai A P S 2000 Partial Differential Equations in Mechanics (Berlin: Springer)
[23] OuYang G, Wang C X, Yang G W 2009 Chem. Rev. 109 4221-4247
[24] Zhang C, Yao Y, Chen S H 2014 Comput. Mater. Sci. 82 372-377
[25] Yao Y, Chen S 2016 Acta Mech. 227 1799-1811
[26] Gao X, Hao F, Fang D, Huang Z 2013 Int. J. Solids Struct. 50 2620-2630
[27] Wang L Y 2020 Int. J. Mech. Mater. Des. 16 633-645
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