MD- and ML-based size-parameter calibration for the non-classical continuum theories

IF 7.1 1区 工程技术 Q1 ENGINEERING, MECHANICAL
Cancan Liu , Jiangong Yu , Longtao Xie , Chaofeng Lü , Vladimir Babeshko , Chuanzeng Zhang
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Abstract

The accurate determination of the size-parameters is crucial for the application of the non-classical continuum theory to characterize the size-effects. This study takes into account of the size-effects and multiple influencing factors and utilizes the molecular dynamics (MD) simulations in conjunction with the machine learning (ML) technique for the precise calibration of the size-parameters required in the non-classical continuum theories. Firstly, theoretical solutions for the elastic wave dispersion relations within the frameworks of the nonlocal elasticity and nonlocal strain-gradient models are derived using the analytical integral Legendre polynomial method. Subsequently, MD simulations are performed to determine the group velocity dispersion relations of the Lamb and SH waves in aluminum plates of varying thickness. Finally, the nonlinear relationships between the guided wave group velocities and the size-parameters are established by the ML technique based on the neural network model. The present study reveals that the size-effects of the elastic wave propagation are closely related to the wavelength, the guided wave mode, and the thickness of the plates. The calibrated nonlocal elasticity theory can predict the guided wave group velocity only within a limited range of the nanoplate thickness. In contrast, the calibrated nonlocal strain-gradient theory demonstrates an excellent performance across all ranges of the nanoplate thickness.
非经典连续介质理论中基于MD和ml的尺寸参数标定
尺寸参数的准确确定是应用非经典连续介质理论表征尺寸效应的关键。本研究考虑了尺寸效应和多种影响因素,利用分子动力学(MD)模拟结合机器学习(ML)技术对非经典连续介质理论所需的尺寸参数进行了精确标定。首先,利用解析积分勒让德多项式方法推导了非局部弹性和非局部应变梯度模型框架下弹性波色散关系的理论解;在此基础上,进行了MD模拟,确定了Lamb波和SH波在不同厚度铝板中的群速频散关系。最后,利用基于神经网络模型的机器学习技术建立了导波群速度与尺寸参数之间的非线性关系。研究表明,弹性波传播的尺寸效应与导波波长、导波模式和导波板厚度密切相关。校正后的非局部弹性理论只能在有限的纳米板厚度范围内预测导波群速度。相比之下,校准的非局部应变梯度理论在纳米板厚度的所有范围内都表现出优异的性能。
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来源期刊
International Journal of Mechanical Sciences
International Journal of Mechanical Sciences 工程技术-工程:机械
CiteScore
12.80
自引率
17.80%
发文量
769
审稿时长
19 days
期刊介绍: The International Journal of Mechanical Sciences (IJMS) serves as a global platform for the publication and dissemination of original research that contributes to a deeper scientific understanding of the fundamental disciplines within mechanical, civil, and material engineering. The primary focus of IJMS is to showcase innovative and ground-breaking work that utilizes analytical and computational modeling techniques, such as Finite Element Method (FEM), Boundary Element Method (BEM), and mesh-free methods, among others. These modeling methods are applied to diverse fields including rigid-body mechanics (e.g., dynamics, vibration, stability), structural mechanics, metal forming, advanced materials (e.g., metals, composites, cellular, smart) behavior and applications, impact mechanics, strain localization, and other nonlinear effects (e.g., large deflections, plasticity, fracture). Additionally, IJMS covers the realms of fluid mechanics (both external and internal flows), tribology, thermodynamics, and materials processing. These subjects collectively form the core of the journal's content. In summary, IJMS provides a prestigious platform for researchers to present their original contributions, shedding light on analytical and computational modeling methods in various areas of mechanical engineering, as well as exploring the behavior and application of advanced materials, fluid mechanics, thermodynamics, and materials processing.
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