Modeling of strains and stresses of material nanostructures

Bulletin of the Polish Academy of Sciences: Technical Sciences

Volumn 57, Issue 1, 2009, Pages 41-46

  Szefer, G ^a   Jasinska D ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Deformation gradients; Molecular dynamics; Strain tensor; Stress tensor

Indexed keywords

CONTINUUM MECHANICS; DEFORMATION; ELASTICITY; MOLECULAR DYNAMICS; STRUCTURAL DESIGN; TENSORS;

ATOMIC INTERACTIONS; CONTINUUM MODELING; DEFORMATION GRADIENTS; MATERIAL NANOSTRUCTURE; STRAIN AND STRESS; STRAIN TENSOR; STRESS AND DEFORMATION; STRESS TENSORS;

STRAIN;

EID: 69249188448     PISSN: 02397528     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10175-010-0103-6     Document Type: Article

References (36)

1. J. Ray, "Molecular dynamics equations of motion for systems varying in shape and size", J. Chem. Phys. 79 (10), 5128-5130 (1983).
2. M. Ribarsky and U. Landman, "Dynamical simulation of stress, strain and finite deformation", Phys. Rev. B 38 (14), 9522-9537 (1988).
3. W.K. Liu, E. Karpow, and H. Park, Nano Mechanics and Materials, Wiley, Chicester, 2006.
4. H. Kitagawa, T. Aihara Jr, and Y. Kawazoe, Mesoscopic Dynamics of Fracture, Springer, Berlin, 1998.
5. D. Raabe, Computational Material Science, Willey, Weinheim, 1998.
6. Ch. Li and T. Chou, "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solids Struct. 40, 2487-2499 (2003).
7. X. Gao and K. Li, "Finite deformation continuum model for single-walled carbon nanotubes", Int. J. Solids Struct. 40, 7329-7373 (2003).
8. A. Pantano, D. Parks, and M. Boyce, "Mechanics of deformation of single- and-multi walled carbon nanotubes", J. Mech. Phys Solids 52, 789-821 (2004).
9. G. Odagard, T. Gates, L. Nicholson, and K. Wise, "Equivalent continuum modeling of nano-structured materials", Comp. Sci. Techn. 62 (14), 1869-1880 (2002).
10. K. Tserpes and P. Papanikos, "Finite element modeling of single walled carbon nanotubes", Composites B 36, 468-477 (2005).
11. R. Phillips, Crystals, Defects, and Microstructures, Cambridge Univ. Press, Cambridge, 2001.
12. M. Parrinello and A. Rahman, "Crystal structure and pair potentials: a molecular dynamics study", Phys. Rev. Lett. 45 (14), 1196-1199 (1980).
13. M. Parrinello and A. Rahman, "Strain fluctuations and elastic constants", J. Chem. Phys. 76 (5), 2662-2666 (1982).
14. P. Mott, A. Argon, and U. Sutter, "The atomic strain tensor", J. Theor. Phys. 101, 140-150 (1992).
15. R. Pyrz and B. Bochenek, "Discrete-continuum transition at interfaces of nanocomposites", Bull. Pol. Ac.: Tech. 55 (2), 251-260 (2007).
16. P. Dłużewski and P. Traczykowski, "Numerical simulation of atomic position in quantum dot by means of molecular statics", Arch. Mech. 55 (5-6), 393-406 (2003).
17. G. Capriz, Introductory remarks to the dynamics of continua with microstructure, Banach Center Publications, vol. 15, PWN, Warsaw, 1986.
18. W. Hoover, Molecular Dynamics (Lecture Notes in Physics), No. 258, Springer, Berlin, 1986.
19. U. Landman, W. Luedtke, and E. Ringer, "Molecular dynamics simulations of adhesive contact formation and friction" in Fundamentals of Friction: Macroscopic and Microscopic Processes, eds. I. Singer and H. Polloc, Kluver Ac. Publ., Dordrecht, 1992.
20. M. Zhou, "A new look at the atomic level virial stress: on continuum-molecular system equivalence", Proc. Roy. Soc. Lond. A 459, 2347-2392 (2003).
21. H. Wu, "Molecular dynamics study of the mechanics of metal nanovires at finite temperature", Europ. J. Mech. A/Solids 25, 370-377 (2006).
22. A. Subramaniyan and C. Sun, "Continuum interpretation of virial stress in molecular simulations", Int. J. Solids Struct. 45, 4340-4346 (2008).
23. R. Sunyk and P. Steinmann, "On higher gradient in continuumatomistic modelling", Int. J. Solids Struct. 40, 6877-6896 (2003).
24. R. Sunyk and P. Steinman, Zur Beschreibung Komplexen Materialverhaltens, Univ. Stuttgart, 2001.
25. R. Sumyk and P. Steinman, "Localization analysis of mixed continuum-atomistic model", J. Phys. IV France 11, 251-258 (2001).
26. T. Belytschko and S. Xiao, "Coupling methods for continuum model with molecular model", Int. J. Multiscale Comput. Engin. 1 (1), 115-126 (2003).
27. T. Delph, "Local stresses and elastic constants at the atomic scale", Proc. R. Soc. A 461, 1869-1888 (2005).
28. S. Iijima, "Helical microtubes of graphitic carbon", Nature 354, 56-58 (1991).
29. M. Chwał, Homogenization of Mechanical Properties of Composite Materials Reinforced by Carbon Nanotubes, PhD Thesis, Cracow Univ. Technology, Krakow, 2007, (in Polish).
30. D. Qian, G. Wagner, W. Liu, M. Yu, and R. Ruoff, "Mechanics of carbon nanotubes", Appl. Mech. Rev. 55 (6), 495-533 (2002).
31. M. Arroyo and T. Belytschko, "A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes", Mech. Mater. 35, 193-215 (2003).
32. M. Arroyo and T. Belytschko, "Finite element methods for the nonlinear mechanics of crystalline sheets and nanotubes", Int. J. Numer. Meth. Eng. 59, 419-456 (2004).
33. T. Belytschko, S. Xiao, G. Schatz, and R. Ruoff, "Atomistic simulations of nanotube fracture", Phys. Rev. B 65 (23), 235430 (2002).
34. D. Qian, G. Wagner, and W. Liu, "A multiscale projection method for the analysis of carbon nanotubes", Comp. Meth. Appl. Mech. Engng. 193, 1603-1632 (2004).
35. K.Chandraseker and S.Mukherjee, "Modification to the Cauchy-Born rule: Applications in the deformation of the single walled carbon nanotubes", Int. J. Solids Struct. 43, 7128-7144 (2006).
36. http://lammps.sandia.gov.