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

1. Multiscale methods for graphene
based nanocomposites
Nanocomposites for Aerospace Applications
Symposium, NSQI, Bristol, 12/02/2013
www.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
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3. Content
Rationale
The hybrid atomistic-FE multiscale approach
Examples
Epoxy/graphene nanocomposite models
Developments and conclusions
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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)
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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 composites
Can we bridge between MD/DFT and continuum mechanics?
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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)
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7. Hybrid atomistic – FE in sp2 CC bonds
(Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306)
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8. The structural mechanics approach
The equivalent mechanical properties of the CC-bond beams are input in a FE
model 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
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9. Examples – buckling of carbon nanotubes
(a) Molecular dynamics
(b) Hyperplastic atomistic FE
(Ogden strain energy density
function )
Comparison of buckling
mechanisms 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)
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10. Examples – graphene
Circular SLGS (R = 9: 5 nm)
under central loading. Deformation of rectangular
Distribution of equivalent SLGS (15.1 x 13.03 nm2)
membrane stresses. 8878 under central loading. ~ 7890
atoms 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.
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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/d3
FR2/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.
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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.
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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.
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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 6.10
Continuous SLGS reinforcement Short SLGS reinforcement • Models with different
orientations in space
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15. Epoxy/SLGS nanocomposite
Direction || to loading
Direction 45o to loading
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16. Epoxy/SLGS nanocomposite
Model compares well with single/few layer graphene-epoxy
composites existing in open literature in terms of stiffness
and 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)
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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)
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18. Thanks for your kind attention
Any question?
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