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First strain gradient elasticity solution for nanotube-reinforced matrix problem

机译：纳米管增强基质问题的第一个应变梯度弹性解

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摘要

In the current paper, a rigorous proof of an important theorem which has been used frequently for derivation of field equations of first gradient elasticity is given for the first time. After that, due to the wide use of nanoparticles as reinforcements to different types of matrices, the nanotube-reinforced matrix problem is investigated in cylindrical coordinates. Then, using the most general model for an isotropic gradient elastic material, the displacement formulation is employed to solve the governing equations of the nanotube-reinforced matrix problem. For this purpose, the generalized perfect interface conditions for the nonhomogeneous representative volume element (RVE) are introduced and used to derive the solution. Numerical results reveal that as the matrix characteristic length parameter becomes larger in comparison to that of nanotube, the difference between the results of the classical theory and the strain gradient theory will increase and classical theory cannot accurately predict the mechanical response of the RVE; In addition, increasing the nanotube's volume fraction results in reduction of the maximum compressive stress and a rise in the overall stiffness of RVE.
机译：在本文中，首次给出了重要定理的严格证明，该定理经常被用于推导第一梯度弹性场方程。此后，由于纳米粒子被广泛用作不同类型基质的增强剂，因此在圆柱坐标系中研究了纳米管增强基质的问题。然后，使用各向同性梯度弹性材料的最通用模型，采用位移公式来求解纳米管增强基质问题的控制方程。为此，介绍了非均匀代表性体积元素（RVE）的广义理想界面条件，并将其用于导出解决方案。数值结果表明，与纳米管相比，随着基体特征长度参数的增大，经典理论与应变梯度理论的结果之间的差异将会增大，经典理论无法准确地预测RVE的机械响应。另外，增加纳米管的体积分数导致最大压应力的降低和RVE的整体刚度的提高。

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  • 来源
    《Composite Structures》 |2014年第6期|273-282|共10页
  • 作者

    I. Zibaei; H. Rahnama; F. Taheri-Behrooz; M.M. Shokrieh;

  • 作者单位

    Composites Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran;

    Composites Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran;

    Composites Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran;

    Composites Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Elasticity; Strain gradient theory; Nanotube; Representative volume element; Size effect;

    机译：弹性;应变梯度理论;纳米管代表性的体积要素;尺寸效果;

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