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Length scale effect on the buckling behavior of a graphene sheets using modified couple stress theory and molecular dynamics method

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Abstract

In this paper, the dependence of the length scale parameter on the dimensions of a graphene sheet is investigated. Then, the buckling and elastic properties of the graphene sheet are estimated. To incorporate the size effect in the buckling behavior of graphene sheets, a theoretical framework of non-classical continuous mechanics has been applied using the modified couple stress (MCS) theory in classical plate equations. To get an accurate estimate of the elastic properties and buckling behavior of the graphene plate, we tried to rewrite the finite element (FE) method expression of the Kirchhoff plate equations by adding the modified couple stress theory equations. In this way, this paper includes the dependence of the length scale parameter to the dimensions of the graphene sheet due to the size effect. The length scale parameter for each sheet was estimated by calculation of the bending rigidity with the molecular dynamics (MD) and the equations of elastic properties methods. The calculations show that understanding the buckling behavior of nanostructures requires estimating size dependence parameters such as length scale and mechanical properties to achieve acceptable results for buckling forces. In addition, the results show that the buckling instability of graphene sheets depends significantly on their size.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Urmia University, Urmia, Iran

    Farzin Sha’bani & Samrand Rash-Ahmadi

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  1. Farzin Sha’bani
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  2. Samrand Rash-Ahmadi
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Correspondence to Samrand Rash-Ahmadi.

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Sha’bani, F., Rash-Ahmadi, S. Length scale effect on the buckling behavior of a graphene sheets using modified couple stress theory and molecular dynamics method. Acta Mech 233, 943–960 (2022). https://doi.org/10.1007/s00707-022-03156-z

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  • DOI: https://doi.org/10.1007/s00707-022-03156-z

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