Multiscale methods for graphene based nanocomposites

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Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.

Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.

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  • 1. Multiscale methods for graphene based nanocomposites Nanocomposites for Aerospace Applications Symposium, NSQI, Bristol, 12/02/2013www.bris.ac.uk/composites
  • 2. Acknowledgements Royal Society of London, European Project FP7-NMP-2009- LARGE-3 M-RECT, A4B and WEFO through the WCC and ASTUTE projects S. Adhikari, Y. Chandra, R. Chowdhury, J.Sienz, C. Remillat, L. Boldrin, E. Saavedra- Flores, M. R. Friswell Nanocomposites for Aerospace, KTN
  • 3. ContentRationaleThe hybrid atomistic-FE multiscale approachExamplesEpoxy/graphene nanocomposite modelsDevelopments and conclusions Nanocomposites for Aerospace, KTN
  • 4. Rationale DGEBA/33DDS with (a) a parallel MLG, and (b) a normal MLG, after 400 ps NPT equilibration• MD simulations using Dreiding and COMPASS force models• Composite with DGEBA/33DDS and MLG• 69,120 atoms à large CPU times involved in parallel processor machine (Li et al., 2012. Comp. Part A, 43(8), 1293) Nanocomposites for Aerospace, KTN
  • 5. Rationale • MD and DFT tools are used mainly by the physics and chemistry community à engineers tend to use CAE/FEA tools • MD and DFT methods are very computational expensive for large systems, accurate in predicting mechanical and electronic properties • Continuum mechanics models (like FEA) are used to design compositesCan we bridge between MD/DFT and continuum mechanics? Nanocomposites for Aerospace, KTN
  • 6. Hybrid atomistic – FE in sp2 CC bonds• Atomic bonds are represented by beam elements• Beam properties are obtained by energy balance 1 EA U axial = K axial (ΔL) 2 = (ΔL) 2 Utotal = Ur +Uθ +Uτ 2 2L 1 GJ U torsion = K torsion (Δβ ) 2 = (Δβ ) 2 2L 1 EI 4 + Φ 1 2 1 2 1 Ur = kr ( Δr ) Uθ = kθ ( Δθ ) Uτ = kτ ( Δφ ) 2 U bending = K bending (2α ) 2 = (2α ) 2 2 2 2 2 2L 1+ Φ (Li C, Chou TW, 2003. Int. J. Solid Struct. 40(10), 2487-2499) (Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306) Nanocomposites for Aerospace, KTN
  • 7. Hybrid atomistic – FE in sp2 CC bonds (Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306) Nanocomposites for Aerospace, KTN
  • 8. The structural mechanics approachThe equivalent mechanical properties of the CC-bond beams are input in a FEmodel representing a 3D structural frame [K]{u}= {f } [K] à stiffness matrix {u} à nodal displacement vector {f} à nodal force vector (Li C, Chou TW, 2003. Int. J. Solid Struct. 40(10), 2487-2499) The graphene nanostructure is then represented as a truss assembly either in graphitic or corrugated shape Nanocomposites for Aerospace, KTN
  • 9. Examples – buckling of carbon nanotubes (a) Molecular dynamics (b) Hyperplastic atomistic FE (Ogden strain energy density function )Comparison of bucklingmechanisms in a (5,5)SWCNT with 5.0 nm length. (Flores, E. I. S., Adhikari, S., Friswell, M. I. and Scarpa, F., "Hyperelastic axial buckling of single wall carbon nanotubes", Physica E: Low-dimensional Systems and Nanostructures, 44[2] (2011), pp. 525-529) Nanocomposites for Aerospace, KTN
  • 10. Examples – grapheneCircular SLGS (R = 9: 5 nm)under central loading. Deformation of rectangularDistribution of equivalent SLGS (15.1 x 13.03 nm2)membrane stresses. 8878 under central loading. ~ 7890atoms atoms Scarpa, F., Adhikari, S., Gil, A. J. and Remillat, C., "The bending of single layer graphene sheets: Lattice versus continuum approach", Nanotechnology, 21[12] (2010), pp. 125702:1-9. Nanocomposites for Aerospace, KTN
  • 11. Examples – graphene 35 Lattice R = 2.5 nm 35 Lattice a = 3.88 nm 30 Continuum R = 2.5 nm Continuum a = 3.88 nm Lattice R = 5.0 nm 30 Lattice a = 5.0 nm Continuum R = 5.0 nm Continuum a = 5.0 nm 25 25 Lattice a = 15.1 nm Lattice R = 9.5 nm Continuum a = 15.1 nm 20 Continuum R = 9.5 nm Eq. (18) F a b/Y/d3FR2/Y/d3 20 Eq. (17) 15 15 10 10 5 5 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 w/d w/d circular SLGS rectangular SLGS Scarpa, F., Adhikari, S., Gil, A. J. and Remillat, C., "The bending of single layer graphene sheets: Lattice versus continuum approach", Nanotechnology, 21[12] (2010), pp. 125702:1-9. Nanocomposites for Aerospace, KTN
  • 12. Examples – bilayer graphene • Equivalent to structural “sandwich” beams • C-C bonds in graphene layers represented with classical equivalent beam models • “Core” represented by Lennard-Jones potential interactions: Ef =0.5 TPa (I.W. Frank, D.M. Tanenbaum, A.M. van der Zande, P.L. McEuen, J. Vac. Sci. Technol. B 25 (2007) 2558) Scarpa, F., Adhikari, S. and Chowdhury, R., "The transverse elasticity of bilayer graphene", Physics Letters A, 374[19-20] (2010), pp. 2053-2057. Nanocomposites for Aerospace, KTN
  • 13. Epoxy/SLGS nanocomposite Polymer Matrix Graphene sheet van der Waals interaction 250 Armchair GRP2 Zigzag GRP4 200 150(GHz) 1 100 50 Chandra, Y., Chowdhury, R., Scarpa, F., Adhikari, S. and Seinz, J., 0 "Multiscale modeling on dynamic behaviour of graphene based 0 5 10 15 20 Length (nm) composites", Materials Science and Engineering B, in press. Nanocomposites for Aerospace, KTN
  • 14. Epoxy/SLGS nanocomposite • RVE representing 0.05 wt % of SLGS with epoxy matrix • Epoxy represented by 3D elements with 6 DOFs and Ramberg Osgood approximation (E = 2 GPa) • SLGS with 1318 beam elements max • L J interactions by 21,612 nonlinear spring elements • Short and long (continuous) SLGS inclusions • Full nonlinear loading with activation/deactivation of LJ springs based on cut-off distance • Coded in ABAQUS 6.10Continuous SLGS reinforcement Short SLGS reinforcement • Models with different orientations in space Nanocomposites for Aerospace, KTN
  • 15. Epoxy/SLGS nanocomposite Direction || to loading Direction 45o to loading Nanocomposites for Aerospace, KTN
  • 16. Epoxy/SLGS nanocompositeModel compares well with single/few layer graphene-epoxycomposites existing in open literature in terms of stiffnessand strength enhancement (Chandra Y., Scarpa F. , Chowdhury R. Adhikari S., Sienz J. Multiscale hybrid atomistic-FE approach for the nonlinear tensile behaviour of graphene nanocomposites. Comp. A 46 (2013), 147) Nanocomposites for Aerospace, KTN
  • 17. Developments and conclusions Possibility of coding in any commercial FEA code à can be used by stress engineers and designers Large possibilities of multiphysics loading and material properties – from embedding viscoelasticity, thermal and piezoelectric environment to crack propagation simulation Can be extended to non CC bonds and represent other chemical groups (Example: DNA modelling) Significant potential for multiphysics modelling using FEA and bridging length scales(Adhikari S., E. Saavedra-Flores, Scarpa F. Chowdhury R.,Friswell M. I., 2013. J. Royal Soc. Interface. Submitted) Nanocomposites for Aerospace, KTN
  • 18. Thanks for your kind attention Any question? Nanocomposites for Aerospace, KTN