Abstract
Nanomaterials have garnered recognition for their notable surface effects and demonstration of superior mechanical properties. Previous studies on the surface effects of nanomaterials, employing the finite element method, often relied on simplified two-dimensional models due to theoretical complexities. Consequently, these simplified models inadequately represent the mechanical properties of nanomaterials and fail to capture the substantial impact of surface effects, particularly the curvature dependence of nanosurfaces. This study applies the principle of minimum energy and leverages the Steigmann-Ogden surface theory of nanomaterials to formulate a novel finite element surface element that comprehensively accounts for surface effects. We conducted an analysis of the stress distribution and deformation characteristics of four typical 2D and 3D nanomaterial models. The accuracy of the developed surface element and finite element calculation method was verified through comparison with established references. The resulting finite element model provides a robust and compelling scientific approach for accurately predicting the mechanical performance of nanomaterials.
摘要
纳米材料以其显著的表面效应和优异的力学性能而备受关注. 由于理论复杂性, 以往采用有限元方法对纳米材料表面效应研究 常简化为较为简单的二维模型, 因此, 不能很好地反映纳米材料的力学性能, 也不能反映表面效应的实质影响, 特别是纳米表面曲率依 赖性. 本研究应用最小能量原理, 利用纳米材料Steigmann-Ogden表面理论, 提出了一种综合考虑表面效应的新型有限元表面单, 在此基 础上分析了四种典型二维和三维纳米材料模型的应力分布和变形特征. 通过与已有文献的对比, 验证了所提出有限元计算方法的准确 性. 所得到的有限元计算方法为精确预测纳米材料力学性能提供了一种可靠和令人信服的科学方法.
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Acknowledgements
This work was supported by the Jiangsu Funding Program for Excellent Postdoctoral Talent (Grant No. 2023ZB397), and the Project funded by China Postdoctoral Science Foundation (Grant No. 2023M732986).
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Author contributions Yongchao Zhang: Conceptualization, Methodology, Model and Writing – original draft. Lian Wang: Model and Methodology. Fangxin Wang: Model and Review. Bin Li: Code and Example. Xiaofan Gou: Laboratory Management, Supervision and Edit.
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Zhang, Y., Wang, L., Wang, F. et al. Surface element design of nanomaterials considering surface curvature dependence. Acta Mech. Sin. 41, 124096 (2025). https://doi.org/10.1007/s10409-024-24096-x
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DOI: https://doi.org/10.1007/s10409-024-24096-x