Effect of uncertainty parameters on graphene sheets Young’s modulus prediction

다국어 초록 (Multilingual Abstract)

Software based on molecular structural mechanics approach (MSMA) and using finite element method (FEM) has been developed to predict the Young’s modulus of graphene sheets. Obtained results have been compared to results available in the literature and good agreement has been shown when the same values of uncertainty parameters are used. A sensibility of the models to their uncertainty parameters has been investigated using a stochastic finite element method (SFEM). The different values of the used uncertainty parameters,such as molecular mechanics force field constants r k and kθ , thickness (t) of a graphene sheet and length ( B L ) of a carboncarbon bonds, have been collected from the literature. Strong sensibilities of 91% to the thickness and of 21% to the stretching force ( r k )have been shown. The results justify the great difference between Young’s modulus predicted values of the graphene sheets and their large disagreement with experimental results.

참고문헌 (Reference)

1 A. Krishann, "Young’s modulus of single-walled nanotubes" 58 (58): 14013-14019, 1998

2 R. A. Ibrahim, "Structural dynamics with parameter uncertainties" 2 (2): 309-328, 1987

3 Y. Jin, "Simulation of elastic properties of single-walled carbon nanotubes" 63 : 1507-1515, 2003

4 Zhimin Xi, "Predictive carbon nanotube models using the eigenvector dimension reduction (EDR) method" 대한기계학회 26 (26): 1089-1097, 2012

5 M. M. Shokrieh, "Prediction of young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach" 31 : 790-795, 2010

6 T. Natsuki, "Prediction of elastic properties for single-walled carbon nanotubes" 42 : 39-45, 2004

7 H. F. Ye, "Numerical algorithms for prediction of mechanical properties of singlewalled carbon nanotubes based on molecular mechanics model" 44 : 1089-1097, 2009

8 B. I. Yakobson, "Nanomechanics of carbon nanotubes instability beyond linear response" 76 : 2511-2514, 1996

9 E. W. Wong, "Nanobeam mechanics elasticity strength and toughness of nanorods and nanotubes" 277 : 1971-1975, 1997

10 C. Tang, "Molecular dynamics simulation of tensile elongation of carbon nanotubes: Temperature and size effects" 79 : 155436-, 2009

11 J. P. Salvetat, "Mechanical properties of carbon nanotubes" 69 (69): 255-260, 1999

12 G. V. Lier, "Initio study of the elastic properties of single-walled carbon nanotubes and grapheme" 326 : 181-185, 2000

13 B. I. Yakobson, "High strain rate fracture and C-chain unraveling in carbon nanotubes" 8 : 341-348, 1997

14 K. I. Tserpes, "Finite element modeling of single-walled carbon nanotubes" 36 : 468-477, 2005

15 G. M. Odegard, "Equivalent-continuum modeling of nano-structured materials" 62 : 1869-1880, 2002

16 E. J. Haug, "Design sensitivity analysis of structural systems" Academic Press 1973

17 Sheng Lu, "An inscribed surface model for the elastic properties of armchair carbon nanotube" 대한기계학회 24 (24): 2233-2239, 2010

18 A. Florian, "An efficient sampling scheme: updates Latin Hypercube sampling" 7 : 123-130, 1992

19 C. Li, "A structural mechanics approach for the analysis of carbon nanotubes" 40 : 2487-2499, 2003

20 M. Meo, "A molecular-mechanics based finite element model for strength prediction of single wall carbon nanotubes" 454 (454): 170-177, 2007