Continuum mechanics model of graphene as a doubly-periodic perforated thin elastic plate
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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| Published in | Zeitschrift für angewandte Mathematik und Physik Vol. 76; no. 4 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.08.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0044-2275 1420-9039 |
| DOI | 10.1007/s00033-025-02548-0 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 169 |
| Author | Antipov, Yuri A. |
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| Cites_doi | 10.1142/p080 10.1177/1081286507086898 10.1016/j.ijengsci.2014.08.007 10.1016/j.ijnonlinmec.2014.09.005 10.1016/j.ijsolstr.2017.11.008 10.1016/j.ijsolstr.2015.03.030 10.1007/s11012-016-0503-2 10.1016/S0020-7683(00)00126-8 10.1016/S0009-2614(00)00764-8 10.1007/s00707-011-0528-5 10.1016/j.spmi.2015.06.001 10.1016/0021-8928(64)90095-4 10.1016/j.physe.2018.11.025 10.1103/PhysRevLett.102.235502 |
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| References | E Cadelano (2548_CR2) 2009; 102 IV Lebedeva (2548_CR11) 2019; 108 GV Lier (2548_CR12) 2000; 326 HM Shodja (2548_CR22) 2011; 222 2548_CR16 R Ghaffari (2548_CR8) 2018; 135 G Cao (2548_CR3) 2024; 146 M Pitteri (2548_CR18) 2003 D Sfyris (2548_CR20) 2014; 67 A Favata (2548_CR6) 2017; 52 D Sfyris (2548_CR19) 2014; 85 JL Ericksen (2548_CR5) 2008; 13 F Liu (2548_CR13) 2007; 76 D Sfyris (2548_CR21) 2015; 66 EG Kirsch (2548_CR10) 1898; 42 G Zhang (2548_CR23) 2022; 169 LA Filshtinskii (2548_CR7) 1964; 28 NI Muskhelishvili (2548_CR15) 1963 AH England (2548_CR4) 1971 R Saito (2548_CR17) 1998 YA Antipov (2548_CR1) 2001; 38 H Hancock (2548_CR9) 1958 F Memarian (2548_CR14) 2015; 85 |
| References_xml | – volume-title: Complex Variable Methods in Elasticity year: 1971 ident: 2548_CR4 – volume-title: Physical Properties of Carbon Nanotubes year: 1998 ident: 2548_CR17 doi: 10.1142/p080 – volume: 13 start-page: 199 year: 2008 ident: 2548_CR5 publication-title: Math. Mech. Solids doi: 10.1177/1081286507086898 – volume: 76 year: 2007 ident: 2548_CR13 publication-title: Phys. Rev. B – volume: 85 start-page: 224 year: 2014 ident: 2548_CR19 publication-title: Int. J. Eng. Sci. doi: 10.1016/j.ijengsci.2014.08.007 – volume: 67 start-page: 186 year: 2014 ident: 2548_CR20 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2014.09.005 – volume: 146 year: 2024 ident: 2548_CR3 publication-title: Diamond Relat. Mater. – volume: 135 start-page: 37 year: 2018 ident: 2548_CR8 publication-title: Int. J. Solids Struct. doi: 10.1016/j.ijsolstr.2017.11.008 – volume-title: Continuum Models for Phase Transitions and Twinning in Crystals year: 2003 ident: 2548_CR18 – volume: 66 start-page: 98 year: 2015 ident: 2548_CR21 publication-title: Int. J. Solids Struct. doi: 10.1016/j.ijsolstr.2015.03.030 – volume: 42 start-page: 797 year: 1898 ident: 2548_CR10 publication-title: Zeitschrift des Vereines deutscher Ingenieure – volume: 52 start-page: 1601 year: 2017 ident: 2548_CR6 publication-title: Meccanica doi: 10.1007/s11012-016-0503-2 – volume: 38 start-page: 1659 year: 2001 ident: 2548_CR1 publication-title: Int. J. Solids Struct. doi: 10.1016/S0020-7683(00)00126-8 – volume: 326 start-page: 181 year: 2000 ident: 2548_CR12 publication-title: Chem. Phys. Let. doi: 10.1016/S0009-2614(00)00764-8 – volume-title: Lectures on the Theory of Elliptic Functions year: 1958 ident: 2548_CR9 – ident: 2548_CR16 – volume-title: Some Basic Problems of the Mathematical Theory of Elasticity year: 1963 ident: 2548_CR15 – volume: 222 start-page: 91 year: 2011 ident: 2548_CR22 publication-title: Acta Mech. doi: 10.1007/s00707-011-0528-5 – volume: 85 start-page: 348 year: 2015 ident: 2548_CR14 publication-title: Superlattices Microstruct. doi: 10.1016/j.spmi.2015.06.001 – volume: 28 start-page: 530 year: 1964 ident: 2548_CR7 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(64)90095-4 – volume: 108 start-page: 326 year: 2019 ident: 2548_CR11 publication-title: Physica E: Low-dimen. Syst. Nanostruct. doi: 10.1016/j.physe.2018.11.025 – volume: 169 year: 2022 ident: 2548_CR23 publication-title: J. Mech. Phys. Solids – volume: 102 year: 2009 ident: 2548_CR2 publication-title: Phys. Rev. Let. doi: 10.1103/PhysRevLett.102.235502 |
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| SubjectTerms | Chirality Continuum mechanics Elastic plates Exact solutions Graphene Hexagonal cells Linear algebra Mathematical analysis Meromorphic functions Poisson's ratio |
| Title | Continuum mechanics model of graphene as a doubly-periodic perforated thin elastic plate |
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