Fracture analysis of pre-cracked graphene layer sheets using peridynamic theory
Source abstract
Abstract
The peridynamic (PD) theory is a nonlocal reformulation of mechanics with various advantages over common approaches, mainly local continuum mechanics and molecular dynamics (MD). PD theory can capture phenomena at different dimensions, including nanoscale. However, limited studies have been performed by this theory in nanoscale, which have generally focused on the feasibility and accuracy of using PD in atomic-scale modeling. In the present study, based on the ordinary state-based peridynamic method, we investigate the fracture of pre-cracked single layer graphene sheets (SLGSs) under uniaxial tension. By simulating the exact atomic model of graphene, the failure strain and crack growth pattern in the zigzag and armchair directions in PD are compared with MD. We show that by considering some restrictions, these two methods have a good consistency with each other. Afterward, we study two different coarse-grained PD models and demonstrate this method can simulate the failure of graphene with acceptable accuracy. A significant reduction in simulation cost is an excellent point of the PD compared to the MD simulation model. Under these conditions, a massive atomic model with several million atoms can be easily simulated.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Electromagnetic Simulation and Numerical Methods · Geophysical Methods and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (75)
Show source-provided references
1. Ahadi A, Melin S (2018) Capturing nanoscale effects by peridynamics. Mech Adv Mater Struct 25(13):1115–112010.1080/15376494.2017.1365985 ↗
2. Ahadi A, Hansson P, Melin S (2016) Indentation of thin copper film using molecular dynamics and peridynamics. Procedia Struct Integr 2:1343–135010.1016/j.prostr.2016.06.171 ↗
3. Allen BL, Kichambare PD, Star A (2007) Carbon nanotube field-effect-transistor-based biosensors. Adv. Mater. 19(11):1439–145110.1002/adma.200602043 ↗
4. Arroyo M, Belytschko T (2004) Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-born rule. Phys Rev B 69(11):11541510.1103/PhysRevB.69.115415 ↗
5. Behzadinasab M, Vogler TJ, Peterson AM, Rahman R, Foster JT (2018) Peridynamics modeling of a shock wave perturbation decay experiment in granular materials with intra-granular fracture. J Dyn Behav Mater 4(4):529–54210.1007/s40870-018-0174-2 ↗
6. Bie Y, Cui X, Li Z (2018) A coupling approach of state-based peridynamics with node-based smoothed finite element method. Comput Methods Appl Mech Eng 331:675–70010.1016/j.cma.2017.11.022 ↗
7. Bobaru F (2007) Influence of van der waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach. Model Simul Mater Sci Eng 15(5):39710.1088/0965-0393/15/5/002 ↗
8. Bobaru F, Duangpanya M (2010) The peridynamic formulation for transient heat conduction. Int J Heat Mass Transf 53(19–20):4047–405910.1016/j.ijheatmasstransfer.2010.05.024 ↗
9. Bobaru F, Hu W (2012) The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials. Int J Fract 176(2):215–22210.1007/s10704-012-9725-z ↗
10. Bobaru F, Silling SA, Jiang H (2005) Peridynamic fracture and damage modeling of membranes and nanofiber networks. In: Proceedings of the XI international conference on fracture, vol 5748, pp 1–6
11. Bowden F, Brunton J, Field J, Heyes A (1967) Controlled fracture of brittle solids and interruption of electrical current. Nature 216(5110):38–4210.1038/216038a0 ↗
12. Cao G (2014) Atomistic studies of mechanical properties of graphene. Polymers 6(9):2404–243210.3390/polym6092404 ↗
13. der Merwe V, Wagener C (2014) A peridynamic model for sleeved hydraulic fracture, Ph.D. thesis, Stellenbosch University, Stellenbosch
14. Dewapriya M, Rajapakse R (2018) Atomistic and continuum modelling of stress field at an inhomogeneity in graphene. Mater Des 160:718–73010.1016/j.matdes.2018.10.006 ↗
15. Dipasquale D, Zaccariotto M, Galvanetto U (2014) Crack propagation with adaptive grid refinement in 2d peridynamics. Int J Fract 190:1–2210.1007/s10704-014-9970-4 ↗
16. Dipasquale D, Sarego G, Zaccariotto M, Galvanetto U (2016) Dependence of crack paths on the orientation of regular 2d peridynamic grids. Eng Fract Mech 160:248–26310.1016/j.engfracmech.2016.03.022 ↗
17. Diyaroglu C, Behera D, Madenci E, Kaya Y, Kedziora G, Nepal D (2019) Peridynamic modeling of wrinkling in a graphene layer. In: AIAA Scitech 2019 forum, p 104010.2514/6.2019-1040 ↗
18. Eringen A (1972) Nonlocal polar elastic continua. Int J Eng Sci 10(1):1–1610.1016/0020-7225(72)90070-5 ↗
19. Eringen A (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–471010.1063/1.332803 ↗
20. Eringen A (2002) Nonlocal continuum field theories. Springer, New York
21. Gerstle W, Sau N, Silling S (2005) Peridynamic modeling of plain and reinforced concrete structures
22. Gu X, Zhang Q, Huang D, Yv Y (2016) Wave dispersion analysis and simulation method for concrete shpb test in peridynamics. Eng Fract Mech 160:124–13710.1016/j.engfracmech.2016.04.005 ↗
23. Gu X, Madenci E, Zhang Q (2018) Revisit of non-ordinary state-based peridynamics. Eng Fract Mech 190:31–5210.1016/j.engfracmech.2017.11.039 ↗
24. Guerriero E, Polloni L, Bianchi M, Behnam A, Carrion E, Rizzi LG, Pop E, Sordan R (2013) Gigahertz integrated graphene ring oscillators. ACS Nano 7(6):5588–559410.1021/nn401933v ↗
25. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1):229–244
26. Hou J, Deng B, Zhu H, Lan Y, Shi Y, De S, Liu L, Chakraborty P, Gao F, Peng Q (2019) Magic auxeticity angle of graphene. Carbon 149:350–35410.1016/j.carbon.2019.04.057 ↗
27. Jafarzadeh S, Chen Z, Zhao J, Bobaru F (2019) Pitting, lacy covers, and pit merger in stainless steel: 3d peridynamic models. Corros Sci 150:17–3110.1016/j.corsci.2019.01.006 ↗
28. Jafarzadeh S, Larios A, Bobaru F (2020) Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods. J Peridyn Nonlocal Model 2:85–11010.1007/s42102-019-00026-6 ↗
29. Jafarzadeh S, Wang L, Larios A, Bobaru F (2021) A fast convolution-based method for peridynamic transient diffusion in arbitrary domains. Comput Methods Appl Mech Eng 375:11363310.1016/j.cma.2020.113633 ↗
30. Jafarzadeh S, Mousavi F, Larios A, Bobaru F (2022) A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture. Comput Methods Appl Mech Eng 392:11466610.1016/j.cma.2022.114666 ↗
31. Javili A, Morasata R, Oterkus E, Oterkus S (2019) Peridynamics review. Math Mech Solids 24(11):3714–373910.1177/1081286518803411 ↗
32. Khare R, Mielke SL, Paci JT, Zhang S, Ballarini R, Schatz GC, Belytschko T (2007) Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys Rev B 75(7):07541210.1103/PhysRevB.75.075412 ↗
33. Kunin IA (1982) Elastic media with microstructure i: one-dimensional models. In: Springer series in solid-state sciences, vol 26. Springer, Berlin. https://doi.org/10.1007/978-3-642-81748-910.1007/978-3-642-81748-9 ↗
34. Kunin IA (1983) Elastic media with microstructure ii: three-dimensional model. In: Springer series in solid-state sciences, vol 44. Springer, Berlin. https://doi.org/10.1007/978-3-642-81960-510.1007/978-3-642-81960-5 ↗
35. Le QV, Bobaru F (2018) Surface corrections for peridynamic models in elasticity and fracture. Comput Mech 61(4):499–518. https://doi.org/10.1007/s00466-017-1469-110.1007/s00466-017-1469-1 ↗
36. Le QV, Chan WK, Schwartz J (2014) A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int J Numer Methods Eng 98(8):547–561. https://doi.org/10.1002/nme.464210.1002/nme.4642 ↗
37. Li M, Deng T, Zheng B, Zhang Y, Liao Y, Zhou H (2019) Effect of defects on the mechanical and thermal properties of graphene. Nanomaterials 9(3):34710.3390/nano9030347 ↗
38. Liu X, He X, Wang J, Sun L, Oterkus E (2018) An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets. Proc R Soc A 474(2217):2018001910.1098/rspa.2018.0019 ↗
39. Liu X, He X, Sun L, Wang J, Yang D, Shi X (2020) A chirality-dependent peridynamic model for the fracture analysis of graphene sheets. Mech Mater 149:10353510.1016/j.mechmat.2020.103535 ↗
40. Madenci E, Oterkus E (2014) Peridynamic theory. In: Peridynamic theory and its applications, Springer, pp 19–4310.1007/978-1-4614-8465-3_2 ↗
41. Martowicz A, Staszewski W, Ruzzene M, Uhl T (2015) Peridynamics as an analysis tool for wave propagation in graphene nanoribbons. In: Sensors and smart structures technologies for civil, mechanical, and aerospace systems 2015, vol 9435. International Society for Optics and Photonics, p 94350I10.1117/12.2084312 ↗
42. Mousavi F, Jafarzadeh S, Bobaru F (2021) An ordinary state-based peridynamic elastoplastic 2d model consistent with j2 plasticity. Int J Solids Struct 229:11114610.1016/j.ijsolstr.2021.111146 ↗
43. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306(5696):666–66910.1126/science.1102896 ↗
44. Oterkus S, Madenci E, Agwai A (2014) Fully coupled peridynamic thermomechanics. J Mech Phys Solids 64:1–2310.1016/j.jmps.2013.10.011 ↗
45. Oterkus E, Diyaroglu C, Zhu N, Oterkus S, Madenci E (2015) Utilization of peridynamic theory for modeling at the nano-scale. In: Nanopackaging: from nanomaterials to the atomic scale. Springer, New York, pp 1–1610.1007/978-3-319-21194-7_1 ↗
46. Parks ML, Lehoucq RB, Plimpton SJ, Silling SA (2008) Implementing peridynamics within a molecular dynamics code. Comput Phys Commun 179(11):777–78310.1016/j.cpc.2008.06.011 ↗
47. Rahman R, Foster J (2015) Peridynamic theory of solids from the perspective of classical statistical mechanics. Physica A 437:162–18310.1016/j.physa.2015.05.099 ↗
48. Rajasekaran G, Parashar A (2018) Effect of topological defects on mechanical properties of graphene sheets: a molecular dynamics study. Mater Today Proc 5(2):6780–678810.1016/j.matpr.2017.11.337 ↗
49. Ramulu M, Kobayashi A (1985) Mechanics of crack curving and branching-a dynamic fracture analysis. In: Dynamic fracture. Springer, New York, pp. 61–7510.1007/978-94-009-5123-5_5 ↗
50. Rogula D (1982) Nonlocal theory of material media. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2890-910.1007/978-3-7091-2890-9 ↗
51. Seleson P (2014) Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations. Comput Methods Appl Mech Eng 282:184–21710.1016/j.cma.2014.06.016 ↗
52. Seleson P, Parks ML, Gunzburger M (2014) Peridynamic state-based models and the embedded-atom model. Commun Comput Phys 15(1):179–20510.4208/cicp.081211.300413a ↗
53. Shojaei A, Mudric T, Zaccariotto M, Galvanetto U (2016) A coupled meshless finite point/peridynamic method for 2d dynamic fracture analysis. Int J Mech Sci 119:419–43110.1016/j.ijmecsci.2016.11.003 ↗
54. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–20910.1016/S0022-5096(99)00029-0 ↗
55. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–153510.1016/j.compstruc.2004.11.026 ↗
56. Silling SA, Bobaru F (2005) Peridynamic modeling of membranes and fibers. Int J Non-Linear Mech 40(2–3):395–409. https://doi.org/10.1016/j.ijnonlinmec.2004.08.00410.1016/j.ijnonlinmec.2004.08.004 ↗
57. Silling SA, Fermen-Coker M (2021) Peridynamic model for microballistic perforation of multilayer graphene. Theor Appl Fract Mech 113:10294710.1016/j.tafmec.2021.102947 ↗
58. Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:73–16810.1016/S0065-2156(10)44002-8 ↗
59. Silling SA, Epton MJ, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184. https://doi.org/10.1007/s10659-007-9125-110.1007/s10659-007-9125-1 ↗
60. Silling SA, D’Elia M, Yu Y, You H, Fermen-Coker M (2022) Peridynamic model for single-layer graphene obtained from coarse-grained bond forces. J Peridyn Nonlocal Model 1:1–2210.1007/s42102-019-00009-7 ↗
61. Stuart SJ, Tutein AB, Harrison JA (2000) A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys 112(14):6472–648610.1063/1.481208 ↗
62. Tang C, Guo W, Chen C (2009) Molecular dynamics simulation of tensile elongation of carbon nanotubes: temperature and size effects. Phys Rev B 79(15):15543610.1103/PhysRevB.79.155436 ↗
63. Torkaman-Asadi M, Kouchakzadeh M (2022) Atomistic simulations of mechanical properties and fracture of graphene: a review. Comput Mater Sci 210:11145710.1016/j.commatsci.2022.111457 ↗
64. Trageser J, Seleson P (2020) Bond-based peridynamics: a tale of two Poisson’s ratios. J Peridyn Nonlocal Model 2(3):278–28810.1007/s42102-019-00021-x ↗
65. Tupek MR, Rimoli JJ, Radovitzky R (2013) An approach for incorporating classical continuum damage models in state-based peridynamics. Comput Methods Appl Mech Eng 263:20–2610.1016/j.cma.2013.04.012 ↗
66. Van Le Q, Bobaru F (2018) Objectivity of state-based peridynamic models for elasticity. J Elast 131(1):1–1710.1007/s10659-017-9641-6 ↗
67. Wang MC, Yan C, Galpaya D, Lai ZB, Ma L, Hu N, Yuan Q, Bai RX, Zhou LM (2013) Molecular dynamics simulation of fracture strength and morphology of defective graphene. J Nano Res 23:43–4910.4028/www.scientific.net/JNanoR.23.43 ↗
68. Xu M, Paci JT, Oswald J, Belytschko T (2012) A constitutive equation for graphene based on density functional theory. Int J Solids Struct 49(18):2582–258910.1016/j.ijsolstr.2012.05.019 ↗
69. Xu Z, Zhang G, Chen Z, Bobaru F (2018) Elastic vortices and thermally-driven cracks in brittle materials with peridynamics. Int J Fract 209:203–22210.1007/s10704-017-0256-5 ↗
70. Yao J, Xia Y, Dong S, Yu P, Zhao J (2019) Finite element analysis and molecular dynamics simulations of nanoscale crack-hole interactions in chiral graphene nanoribbons. Eng Fract Mech 218:10657110.1016/j.engfracmech.2019.106571 ↗
71. Yeh Y-K, Hwu C (2017) A modified molecular-continuum model for estimating the strength and fracture toughness of graphene and carbon nanotube. Eng Fract Mech 176:326–34210.1016/j.engfracmech.2017.03.039 ↗
72. You H, Yu Y, Silling S, D’Elia M (2022) A data-driven peridynamic continuum model for upscaling molecular dynamics. Comput Methods Appl Mech Eng 389:11440010.1016/j.cma.2021.114400 ↗
73. Zhang Z, Wang X, Lee JD (2014) An atomistic methodology of energy release rate for graphene at nanoscale. J Appl Phys 115(11):11431410.1063/1.4869207 ↗
74. Zhao H, Min K, Aluru NR (2009) Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension. Nano Lett 9(8):3012–301510.1021/nl901448z ↗
75. Zhou J, Huang R (2008) Internal lattice relaxation of single-layer graphene under in-plane deformation. J Mech Phys Solids 56(4):1609–162310.1016/j.jmps.2007.07.013 ↗