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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

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