The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes

Q Wang; C M Wang

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The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes

机译：碳纳米管非局部连续力学的本构关系和小尺度参数。

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In this paper, the constitutive relations of nonlocal elasticity theory are presented for application in the analysis of carbon nanotubes (CNTs) when modelled as Euler-Bernoulli beams, Timoshenko beams or as cylindrical shells. In particular, the shear stress and strain relation for the nonlocal Timoshenko beam theory is discussed in great detail due to a misconception by some researchers that the nonlocal effect should appear in this constitutive relation. Different theories for proposing the value of the small scale parameter are also introduced and a recommendation for the value from the standpoint of wave propagation of CNTs is given.

机译：本文提出了非局部弹性理论的本构关系，用于建模为欧拉-伯努利梁，蒂莫申科梁或圆柱壳的碳纳米管（CNT）分析。特别是，由于一些研究人员错误地认为非局部效应应在这种本构关系中出现，因此对非局部Timoshenko梁理论的剪应力和应变关系进行了详细讨论。还介绍了提出小规模参数值的不同理论，并从CNT的波传播角度给出了建议值。

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《Nanotechnology》 |2007年第7期|共4页
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Q Wang; C M Wang;
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1. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes [J] . Q Wang, C M Wang Nanotechnology . 2007,第7期

机译：碳纳米管非局部连续力学的本构关系和小尺度参数。
2. Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation [J] . S. Narendar, D. Roy Mahapatra, S. Gopalakrishnan International Journal of Engineering Science . 2011,第6期

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3. Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics [J] . Narendar S., Gopalakrishnan S. Physica, E. Low-dimensional systems & nanostructures . 2011,第6期

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4. Scale Coefficient, Length, Mode and Radius Effect on Critical Axial Compressed Buckling Load of Carbon Nanotubes via Nonlocal Continuum Model [C] . Hongliang Tian International Conference on Materials Science and Information Technology . 2013

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5. Carbon nanotube mechanics: Continuum model development from molecular mechanics virtual experiments. [D] . Sears, Aaron T. 2007

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8. Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams [R] . Harik, V. M. 2001

机译：碳纳米管本构分析中连续梁模型的适用范围：纳米管或纳米梁

The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes

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