Continuum mechanics model of graphene as a doubly-periodic perforated thin elastic plate Continuum mechanics model of graphene

In this paper, a continuum mechanics model of graphene is proposed, and its analytical solution is derived. Graphene is modeled as a doubly-periodic thin elastic plate with a hexagonal cell having a circular hole at the hexagon center. Graphene is characterized by a general chiral vector and is subj...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 76; no. 4
Main Author Antipov, Yuri A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 29.07.2025
Subjects
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Doubly-periodic structures
74K20
31B30
Graphene
Plane elasticity
35B10
Weierstrass elliptic function
Elastic moduli of the bonds
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Summary:In this paper, a continuum mechanics model of graphene is proposed, and its analytical solution is derived. Graphene is modeled as a doubly-periodic thin elastic plate with a hexagonal cell having a circular hole at the hexagon center. Graphene is characterized by a general chiral vector and is subject to remote tension. For the solution, the Filshtinskii solution obtained for the symmetric case is generalized for any chirality. The method uses the doubly-periodic Kolosov–Muskhelishvili complex potentials, the theory of the elliptic Weierstrass function and quasi-doubly-periodic meromorphic functions and reduces the model to an infinite system of linear algebraic equations with complex coefficients. Analytical expressions and numerical values for the stresses and displacements are obtained and discussed. The displacements expressions possess the Young modulus and Poisson ratio of the graphene bonds. They are derived as functions of the effective graphene moduli available in the literature.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-025-02548-0