Skip to main content
SpringerLink
Log in

An atomistic-based finite element progressive fracture model for silicene nanosheets

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A progressive finite element method is proposed herein to investigate the fracture of silicene nanosheets. By treating a silicene nanosheet as a buckled frame structure, its mechanical behavior is simulated using the modified Morse potential function. The interatomic force per atom is calculated for all atoms as a set of inharmonic oscillator networks, which are described by the modified Morse potential function, while the nonlinear behavior is defined by these interatomic forces with an iterative solution procedure as strain increases. The nonlinear stress–strain relationships of the armchair and zigzag silicene nanosheets are also obtained for pristine and defective cases including the tensile strength and ultimate strain. For the silicene with both configurations, i.e., armchair and zigzag, a sudden drop is seen in the stress–strain diagram, showing that both of them represent the brittle behavior. Moreover, it is concluded that the tensile strength and ultimate strain of the armchair silicenes are slightly larger than those of the zigzag one. It is also seen that the mechanical properties of the silicene are significantly affected by the single-vacancy and Stone–Wales defects. The computed results reveal that single-vacancy defects can reduce the ultimate strain of silicene by approximately 7.3% with respect to that of pristine silicene, whereas the effect of Stone–Wales defects is less significant.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Jose, D., Datta, A.: Structures and chemical properties of silicene: unlike graphene. Acc. Chem. Res. 47, 593–602 (2013)

    Google Scholar 

  2. Xu, M., Liang, T., Shi, M., Chen, H.: Graphene-like two-dimensional materials. Chem. Rev. 113, 3766–3798 (2013)

    Google Scholar 

  3. Grazianetti, C., Cinquanta, E., Molle, A.: Two-dimensional silicon: the advent of silicene. 2D Mater. 3, 012001 (2016)

    Google Scholar 

  4. Şahin, H., Cahangirov, S., Topsakal, M., Bekaroglu, E., Akturk, E., Senger, R.T., Ciraci, S.: Monolayer honeycomb structures of group-IV elements and III–V binary compounds: first-principles calculations. Phys. Rev. B 80, 155453 (2009)

    Google Scholar 

  5. Li, X., Wu, S., Zhou, S., Zhu, Z.: Structural and electronic properties of germanene/MoS2 monolayer and silicene/MoS2 monolayer superlattices. Nanoscale Res. Lett. 9, 110 (2014)

    Google Scholar 

  6. Pizzochero, M., Bonfanti, M., Martinazzo, R.: Hydrogen on silicene: like or unlike graphene? Phys. Chem. Chem. Phys. 18, 15654–15666 (2016)

    Google Scholar 

  7. Vogt, P., De Padova, P., Quaresima, C., Avila, J., Frantzeskakis, E., Asensio, M.C., Resta, A., Ealet, B., Le Lay, G.: Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys. Rev. Lett. 108, 155501 (2012)

    Google Scholar 

  8. Chiappe, D., Grazianetti, C., Tallarida, G., Fanciulli, M., Molle, A.: Local electronic properties of corrugated silicene phases. Adv. Mater. 24, 5088–5093 (2012)

    Google Scholar 

  9. Feng, B., Ding, Z., Meng, S., Yao, Y., He, X., Cheng, P., Chen, L., Wu, K.: Evidence of silicene in honeycomb structures of silicon on Ag (111). Nano Lett. 12, 3507–3511 (2012)

    Google Scholar 

  10. Fleurence, A., Friedlein, R., Ozaki, T., Kawai, H., Wang, Y., Yamada-Takamura, Y.: Experimental evidence for epitaxial silicene on diboride thin films. Phys. Rev. Lett. 108, 245501 (2012)

    Google Scholar 

  11. Gao, J., Zhao, J.: Initial geometries, interaction mechanism and high stability of silicene on Ag (111) surface. Sci. Rep. 2, 861 (2012)

    Google Scholar 

  12. Meng, L., Wang, Y., Zhang, L., Du, S., Wu, R., Li, L., Zhang, Y., Li, G., Zhou, H., Hofer, W.A.: Buckled silicene formation on Ir (111). Nano Lett. 13, 685–690 (2013)

    Google Scholar 

  13. Drummond, N.D., Zólyomi, V., Fal’ko, V.I.: Electrically tunable band gap in silicene. Phys. Rev. B 85, 075423 (2012)

    Google Scholar 

  14. Tritsaris, G.A., Kaxiras, E., Meng, S., Wang, E.: Adsorption and diffusion of lithium on layered silicon for Li-ion storage. Nano Lett. 13, 2258–2263 (2013)

    Google Scholar 

  15. Feng, J.-W., Liu, Y.-J., Wang, H.-X., Zhao, J.-X., Cai, Q.-H., Wang, X.-Z.: Gas adsorption on silicene: a theoretical study. Comput. Mater. Sci. 87, 218–226 (2014)

    Google Scholar 

  16. Yang, K., Cahangirov, S., Cantarero, A., Rubio, A., D’Agosta, R.: Thermoelectric properties of atomically thin silicene and germanene nanostructures. Phys. Rev. B 89, 125403 (2014)

    Google Scholar 

  17. Pei, Q.-X., Sha, Z.-D., Zhang, Y.-Y., Zhang, Y.-W.: Effects of temperature and strain rate on the mechanical properties of silicene. J. Appl. Phys. 115, 023519 (2014)

    Google Scholar 

  18. Ding, N., Wang, H., Chen, X., Wu, C.-M.L.: Defect-sensitive performance of silicene sheets under uniaxial tension: mechanical properties, electronic structures and failure behavior. RSC Adv. 7, 10306–10315 (2017)

    Google Scholar 

  19. Roman, R.E., Cranford, S.W.: Mechanical properties of silicene. Comput. Mater. Sci. 82, 50–55 (2014)

    Google Scholar 

  20. Zhao, H.: Strain and chirality effects on the mechanical and electronic properties of silicene and silicane under uniaxial tension. Phys. Lett. A 376, 3546–3550 (2012)

    Google Scholar 

  21. Mortazavi, B., Rahaman, O., Makaremi, M., Dianat, A., Cuniberti, G., Rabczuk, T.: First-principles investigation of mechanical properties of silicene, germanene and stanene. Phys. E 87, 228–232 (2017)

    Google Scholar 

  22. Alian, A., Meguid, S., Kundalwal, S.: Unraveling the influence of grain boundaries on the mechanical properties of polycrystalline carbon nanotubes. Carbon 125, 180–188 (2017)

    Google Scholar 

  23. Kundalwal, S., Meguid, S., Weng, G.: Strain gradient polarization in graphene. Carbon 117, 462–472 (2017)

    Google Scholar 

  24. Belytschko, T., Xiao, S., Schatz, G.C., Ruoff, R.: Atomistic simulations of nanotube fracture. Phys. Rev. B 65, 235430 (2002)

    Google Scholar 

  25. Xiao, J., Staniszewski, J., Gillespie Jr., J.: Fracture and progressive failure of defective graphene sheets and carbon nanotubes. Compos. Struct. 88, 602–609 (2009)

    Google Scholar 

  26. Tserpes, K.I.: Strength of graphenes containing randomly dispersed vacancies. Acta Mech. 223, 669–678 (2012)

    MATH  Google Scholar 

  27. Fan, N., Ren, Z., Jing, G., Guo, J., Peng, B., Jiang, H.: Numerical investigation of the fracture mechanism of defective graphene sheets. Materials 10, 164 (2017)

    Google Scholar 

  28. Wernik, J.M., Meguid, S.A.: Atomistic-based continuum modeling of the nonlinear behavior of carbon nanotubes. Acta Mech. 212, 167–179 (2010)

    MATH  Google Scholar 

  29. Baykasoglu, C., Mugan, A.: Nonlinear fracture analysis of single-layer graphene sheets. Eng. Fract. Mech. 96, 241–250 (2012)

    Google Scholar 

  30. Baykasoglu, C., Mugan, A.: Coupled molecular/continuum mechanical modeling of graphene sheets. Phys. E 45, 151–161 (2012)

    Google Scholar 

  31. Baykasoglu, C., Kirca, M., Mugan, A.: Nonlinear failure analysis of carbon nanotubes by using molecular-mechanics based models. Compos. B Eng. 50, 150–157 (2013)

    Google Scholar 

  32. Baykasoglu, C., Mugan, A.: Failure analysis of graphene sheets with multiple Stone–Thrower–Wales defects using molecular mechanics based nonlinear finite element models. Hittite J. Sci. Eng. 5(1), 19–24 (2018)

    Google Scholar 

  33. Mohammadpour, E., Awang, M.: Nonlinear finite-element modeling of graphene and single-and multi-walled carbon nanotubes under axial tension. Appl. Phys. A 106, 581–588 (2012)

    Google Scholar 

  34. Mohammadpour, E., Awang, M.: A finite element model to investigate the stress–strain behavior of single walled carbon nanotube. In: Öchsner, A., da Silva, L.F.M., Altenbach, H. (eds.) Materials with Complex Behaviour II, pp. 369–381. Springer, Berlin (2012)

  35. Tserpes, K., Papanikos, P., Tsirkas, S.: A progressive fracture model for carbon nanotubes. Compos. B Eng. 37, 662–669 (2006)

    Google Scholar 

  36. Tserpes, K., Papanikos, P.: The effect of Stone–Wales defect on the tensile behavior and fracture of single-walled carbon nanotubes. Compos. Struct. 79, 581–589 (2007)

    Google Scholar 

  37. Tserpes, K.I., Papanikos, P.: Finite element modeling of the tensile behavior of carbon nanotubes, graphene and their composites. In: Tserpes, K.I., Silvestre, N. (eds.) Modeling of Carbon Nanotubes, Graphene and their Composites, pp. 303–329. Springer, Berlin (2014)

  38. Nickabadi, S., Ansari, R., Rouhi, S.: Evaluation of the Morse potential function coefficients for germanene by the first principles approach. J. Mol. Graph. Model. 98, 107589 (2020)

    Google Scholar 

  39. Hu, M., Zhang, X., Poulikakos, D.: Anomalous thermal response of silicene to uniaxial stretching. Phys. Rev. B 87, 195417 (2013)

    Google Scholar 

  40. Zhang, X., Xie, H., Hu, M., Bao, H., Yue, S., Qin, G., Su, G.: Thermal conductivity of silicene calculated using an optimized Stillinger–Weber potential. Phys. Rev. B 89, 054310 (2014)

    Google Scholar 

  41. Rouhi, S., Ansari, R., Nickabadi, S.: Modal analysis of double-walled carbon nanocones using the finite element method. Int. J. Mod. Phys. B 31, 1750262 (2017)

    Google Scholar 

  42. Ansari, R., Motevalli, B., Montazeri, A., Ajori, S.: Fracture analysis of monolayer graphene sheets with double vacancy defects via MD simulation. Solid State Commun. 151, 1141–1146 (2011)

    Google Scholar 

  43. Rakib, T., Mojumder, S., Das, S., Saha, S., Motalab, M.: Graphene and its elemental analogue: a molecular dynamics view of fracture phenomenon. Phys. B 515, 67–74 (2017)

    Google Scholar 

  44. Rouhi, S.: Fracture behavior of hydrogen-functionalized silicene nanosheets by molecular dynamics simulations. Comput. Mater. Sci. 131, 275–285 (2017)

    Google Scholar 

  45. Jing, Y., Sun, Y., Niu, H., Shen, J.: Atomistic simulations on the mechanical properties of silicene nanoribbons under uniaxial tension. Phys. Status Solidi (b) 250, 1505–1509 (2013)

    Google Scholar 

  46. Li, C., Chou, T.-W.: Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach. Mech. Mater. 36, 1047–1055 (2004)

    Google Scholar 

  47. Trivedi, S., Srivastava, A., Kurchania, R.: Silicene and Germanene: a first principle study of electronic structure and effect of hydrogenation–passivation. J. Comput. Theor. Nanosci. 11, 781–788 (2014)

    Google Scholar 

  48. Nickabadi, S., Ansari, R., Rouhi, S.: On the derivation of the coefficient of Morse Potential function for the silicene: a DFT investigation J. Mol. Graph. Model. 98, 107589 (2020)

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, University Campus 2, University of Guilan, Rasht, Iran

    S. Nickabadi

  2. Faculty of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

    R. Ansari

  3. Department of Mechanical Engineering, Langarud Branch, Islamic Azad University, Langarud, Iran

    S. Rouhi

Authors
  1. S. Nickabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Ansari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Rouhi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Ansari.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nickabadi, S., Ansari, R. & Rouhi, S. An atomistic-based finite element progressive fracture model for silicene nanosheets. Acta Mech 231, 4351–4363 (2020). https://doi.org/10.1007/s00707-020-02757-w

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02757-w

Search

Navigation