Determination of Orthotropic Elastic Properties and Study of Size Effect of Single-Layer and Double-Layer Graphene Nanoplates Using Atomic Finite Element Method

Document Type : Original Article

Authors
Akbar Jafari 1
Karim Aliakbari 1
Mina Amiri 2
Saeed Rouhi 3
1 Associate professor, Department of Mechanical Engineering, Technical and Vocational University (TVU), Tehran, Iran.
2 Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran.
3 Department of Mechanical Engineering, Langaroud Branch, Islamic Azad University, Langaroud, Iran.
10.22034/stme.2025.495533.1092
Abstract
This study examines the effect of size on the elastic properties of single-layer and double-layer armchair-type graphene nanoplates. To maintain the discrete nature of the nanoplates, they were modeled using equivalent spatial frame structures, with the finite element method employed to predict their elastic properties. The results were then validated by comparison with previous studies. Based on the findings, the mechanical properties of the double-layer nanoplates exhibited a slight difference in size dependence compared to the single-layer sheets. It was also observed that, for both single-layer and double-layer nanoplates, the elastic properties at smaller sizes were direction-dependent. However, as the size increased, the properties transitioned toward orthotropy, and with further enlargement, the dependence diminished, eventually approaching isotropy. Specifically, the results showed that for small nanoplates (30 Å), the Young’s moduli in two directions differed by about 6%. At a larger size (100 Å), this difference decreased to around 2%, and at 300 Å, it dropped to approximately 0.7%. Additionally, Poisson’s ratios in the two orthogonal directions for single-layer square nanoplates at smaller sizes (10 Å) exhibited a notable difference of 19%. As the size increased to (100 Å), this difference reduced to about 8%, and at 300 Å, it significantly decreased to about 1.5%. These findings suggest that the convergence to isotropy occurs more rapidly for the Young’s modulus compared to Poisson’s ratio.
Keywords
Ggraphene nanoplate
Layers
Elastic properties
Atomic finite element model
Subjects

  1. [1] S. Iijima, “Helical microtubules of graphitic carbon,” Nature, vol. 354, pp. 56–58, 1991. [Online]. doi: 10.1038/354056a0

    [2] M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, “Unusual properties and structure of carbon nanotubes,” Annual Review of Materials Research, vol. 34, pp. 247–278, 2004. [Online]. doi: 10.1146/annurev.matsci.34.040203.112300

    [3] A. Alizadeh, M. Heydari Beni, and R. Soltani Bidar, “Fabrication and Investigation of Mechanical Properties of Copper Alloy Matrix Composite Reinforced with Micron Diamond Particles,” Scientific and Technological Mechanical Engineering, vol. 3, pp. 117–132, 2024. [Online]. doi:10.22034/STME.2024.471009.1068 (in Persian)

    [4] A. Alizadeh, M. Lotfian, and M. Heydari Beni, “Preparation of Al-B4C Composite by Mechanical Alloying Method and Investigation of Its Thermomechanical Properties,” Scientific and Technological Mechanical Engineering, vol. 3, pp. 163–183, 2024. [Online]. doi: 10.22034/STME.2024.471431.1070 (in Persian)

    [5] C. Q. Ru, “Axially compressed buckling of a double-walled carbon nanotube embedded in an elastic medium,” Journal of the Mechanics and Physics of Solids, vol. 49, pp. 1265–1279, 2001.

    [6] M. M. Shokrieh, Z. Shokrieh, and S. M. Hashemianzadeh, “Effective parameters in modeling of graphene sheet Young’s modulus,” Modares Mechanical Engineering, vol. 12, pp. 147–155, 2012. (in Persian)

    [7] C. Li and T.-W. Chou, “A structural mechanics approach for the analysis of carbon nanotubes,” International Journal of Solids and Structures, vol. 40, pp. 2487–2499, 2003.

    [8] K. I. Tserpes and I. Vatistas, “Buckling analysis of pristine and defected graphene,” Mechanics Research Communications, vol. 64, pp. 50–56, 2015.

    [9] L. Wang and Q. Zhang, “Elastic behavior of bilayer graphene under in-plane loadings,” Current Applied Physics, vol. 12, pp. 1173–1177, 2012.

    [10] A. Jafari, S. S. Shah-enayati, and A. A. Atai, “Size dependency in vibration analysis of nano plates; one problem, different answers,” European Journal of Mechanics, vol. 59, pp. 124–139, 2016.

    [11] S. F. A. Namin and R. Pilafkan, “Vibration analysis of defective graphene sheets using nonlocal elasticity theory,” Physica E: Low-dimensional Systems and Nanostructures, vol. 93, pp. 257–264, 2017.

    [12] B. Liu, Z. Zhang, and Y. Chen, “Atomistic statics approaches—Molecular mechanics, finite element method and continuum analysis,” Journal of Computational and Theoretical Nanoscience, vol. 5, pp. 1891–1913, 2008.

    [13] B. Liu, Y. Huang, H. Jiang, S. Qu, and K. C. Hwang, “The atomic-scale finite element method,” Computational Methods in Applied Mechanics and Engineering, vol. 193, pp. 1849–1864, 2004.

    [14] B. Liu, H. Jiang, Y. Huang, S. Qu, M.-F. Yu, and K. C. Hwang, “Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes,” Physical Review B, vol. 72, p. 035435, 2005.

    [15] M. Malakouti and A. Montazeri, “Nanomechanics analysis of perfect and defected graphene sheets via a novel atomic-scale finite element method,” Superlattices and Microstructures, vol. 94, pp. 1–12, 2016.

    [16] A. Jafari, A. A. Khatibi, and M. M. Mashhadi, “Evaluation of mechanical and piezoelectric properties of boron nitride nanotube: a novel electrostructural analogy approach,” Journal of Computational and Theoretical Nanoscience, vol. 9, pp. 461–468, 2012.

    [17] A. Sakhaee-Pour, M. T. Ahmadian, and A. Vafai, “Potential application of single-layered graphene sheet as strain sensor,” Solid State Communications, vol. 147, pp. 336–340, 2008.

    [18] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science, vol. 321, pp. 385–388, 2008.

    [19] Y. Zhang and C. Pan, “Measurements of mechanical properties and number of layers of graphene from nano-indentation,” Diamond and Related Materials, vol. 24, pp. 1–5, 2012.

    [20] K. Esfarjani, N. Gorjizadeh, and Z. Nasrollahi, “Molecular dynamics of single wall carbon nanotube growth on nickel surface,” Computational Materials Science, vol. 36, pp. 117–120, 2006.

    [21] T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff, “Atomistic simulations of nanotube fracture,” Physical Review B, vol. 65, p. 235430, 2002.

    [22] K. M. Liew, B. J. Chen, and Z. M. Xiao, “Analysis of fracture nucleation in carbon nanotubes through atomistic-based continuum theory,” Physical Review B, vol. 71, p. 235424, 2005.

    1. Sun and W. Zhao, “Prediction of stiffness and strength of single-walled carbon nanotubes by molecular-mechanics based finite element approach,” Materials Science and Engineering: A, vol. 390, pp. 366–371, 2005.

    [24] J. R. Xiao, J. Staniszewski, and J. W. Gillespie Jr, “Fracture and progressive failure of defective graphene sheets and carbon nanotubes,” Composite Structures, vol. 88, pp. 602–609, 2009.

    [25] T. Natsuki and M. Endo, “Structural dependence of nonlinear elastic properties for carbon nanotubes using a continuum analysis,” Applied Physics A, vol. 80, pp. 1463–1468, 2005.

    [26] G. J. Huguet Rodríguez, “Comparison of finite element buckling solutions for flat plates under complex combined loading to analytical methods,” M.S. thesis, 2015.

    [27] B. R. Gelin, Molecular Modeling of Polymer Structures and Properties, Hanser-Gardner Publications, 1994.

    [28] K. I. Tserpes and P. Papanikos, “Finite element modeling of single-walled carbon nanotubes,” Composites Part B: Engineering, vol. 36, pp. 468–477, 2005. [Online].: doi:10.1016/j.compositesb.2004.10.003

    [29] S. Singh and V. Dutt, “A reduced form for fundamental transverse modal frequency of carbon nanotubes,” Materials Today Communications, vol. 25, p. 101404, 2020. [Online]. doi:10.1016/j.mtcomm.2020.101404

    [30] S. K. Georgantzinos and N. K. Anifantis, “Vibration analysis of multi-walled carbon nanotubes using a spring–mass based finite element model,” Computational Materials Science, vol. 47, pp. 168–177, 2009.

    [31] D. Sánchez-Portal, E. Artacho, J. M. Soler, A. Rubio, and P. Ordejón, “Ab initio structural, elastic, and vibrational properties of carbon nanotubes,” Physical Review B, vol. 59, p. 12678, 1999.

    [32] F. Liu, P. Ming, and J. Li, “Ab initio calculation of ideal strength and phonon instability of graphene under tension,” Physical Review B - Condensed Matter and Materials Physics, vol. 76, p. 064120, 2007.

    [33] B. WenXing, Z. ChangChun, and C. WanZhao, “Simulation of Young’s modulus of single-walled carbon nanotubes by molecular dynamics,” Physica B: Condensed Matter, vol. 352, pp. 156–163, 2004.

    [34] J.-L. Tsai and J.-F. Tu, “Characterizing mechanical properties of graphite using molecular dynamics simulation,” Materials & Design, vol. 31, pp. 194–199, 2010.

    [35] S. K. Georgantzinos, G. I. Giannopoulos, and N. K. Anifantis, “Numerical investigation of elastic mechanical properties of graphene structures,” Materials & Design, vol. 31, pp. 4646–4654, 2010.

    [36] G. I. Giannopoulos, I. A. Liosatos, and A. K. Moukanidis, “Parametric study of elastic mechanical properties of graphene nanoribbons by a new structural mechanics approach,” Physica E: Low-Dimensional Systems and Nanostructures, vol. 44, pp. 124–134, 2011

     

     

Science and Technology in Mechanical Engineering
Volume 3, Issue 2 - Serial Number 5
January 2025
Pages 99-117

  • Receive Date 23 December 2024
  • Revise Date 18 February 2025
  • Accept Date 16 March 2025
  • First Publish Date 16 March 2025
  • Publish Date 16 March 2025