, Volume 54, Issue 1–2, pp 299–310 | Cite as

Prediction of in-plane elastic properties of graphene in the framework of first strain gradient theory

  • Saba Hassanpour
  • Fahimeh Mehralian
  • R. D. Firouz-AbadiEmail author
  • M. R. Borhan-Panah
  • Mohammad Rahmanian


In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner–Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is implemented.


Elastic stiffness coefficients Graphene First strain gradient theory Molecular mechanics model In-plane free vibration 


Compliance with ethical standards

Conflict of interest

There is no conflict of interest regarding the publication of this article.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringSharif University of TechnologyTehranIran
  2. 2.Department of Mechanical EngineeringJahrom UniversityJahromIran

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