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Structural and Micropolar Beam Models of Nanocrystalline Materials (One-Dimensional Case)

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Nonlinear Wave Dynamics of Materials and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 122))

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Abstract

In the present paper, linear atomic chain is studied. It is assumed that there is a non-central force and moment interaction between the atoms of the chain. The discrete model of the chain is constructed with the main equations and Hamilton principle. Further, the limit procedure to the continual (beam) model is performed. It is shown that the continual (beam) model of the linear chain of atoms is identical to the applied beam model, which is constructed based on the moment (micropolar) theory of elasticity. Elastic constants of the micropolar beam are determined through the elastic parameters of the discrete model of the linear chain of atoms.

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Author information

Authors and Affiliations

  1. Shirak State University, Gyumri, Armenia

    Samvel H. Sargsyan

Authors
  1. Samvel H. Sargsyan
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Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  3. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    Igor S. Pavlov

  4. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg, Russia

    Alexey V. Porubov

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Sargsyan, S.H. (2020). Structural and Micropolar Beam Models of Nanocrystalline Materials (One-Dimensional Case). In: Altenbach, H., Eremeyev, V., Pavlov, I., Porubov, A. (eds) Nonlinear Wave Dynamics of Materials and Structures. Advanced Structured Materials, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-030-38708-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-38708-2_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38707-5

  • Online ISBN: 978-3-030-38708-2

  • eBook Packages: EngineeringEngineering (R0)

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