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A unified analysis of a micro-beam, droplet and CNT ring adhered on a substrate: Calculation of variation with movable boundaries

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Abstract

In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube (CNT) ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thoroughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materials, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.

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Authors and Affiliations

  1. School of Pipeline and Civil Engineering, China University of Petroleum, 266580, Qingdao, China

    Jian-Lin Liu

  2. School of Power and Mechanical Engineering, Wuhan University, 430072, Wuhan, China

    Re Xia

Authors
  1. Jian-Lin Liu
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  2. Re Xia
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Corresponding authors

Correspondence to Jian-Lin Liu or Re Xia.

Additional information

The project was supported by the National Natural Science Foundation of China (11272357 and 11102140), Doctoral Fund of Ministry of Education of China (200804251520 and 20110141120024) and Natural Science Foundation of Shandong Province (ZR2009AQ006).

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Liu, JL., Xia, R. A unified analysis of a micro-beam, droplet and CNT ring adhered on a substrate: Calculation of variation with movable boundaries. Acta Mech Sin 29, 62–72 (2013). https://doi.org/10.1007/s10409-012-0202-8

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  • DOI: https://doi.org/10.1007/s10409-012-0202-8

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