multiscale methods for graphene based nanocomposites
DESCRIPTION
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.TRANSCRIPT
Multiscale methods for graphene based nanocomposites
Nanocomposites for Aerospace Applications Symposium, NSQI, Bristol, 12/02/2013
www.bris.ac.uk/composites
Acknowledgements
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S. Adhikari, Y. Chandra, R. Chowdhury, J. Sienz, C. Remillat, L. Boldrin, E. Saavedra-
Flores, M. R. Friswell
Royal Society of London, European Project FP7-NMP-2009- LARGE-3 M-
RECT, A4B and WEFO through the WCC and ASTUTE projects
Content
Nanocomposites for Aerospace, KTN
Rationale
The hybrid atomistic-FE multiscale approach
Examples
Epoxy/graphene nanocomposite models
Developments and conclusions
Rationale
Nanocomposites for Aerospace, KTN
DGEBA/33DDS with (a) a parallel MLG, and (b) a normal MLG, after 400 ps NPT equilibration
(Li et al., 2012. Comp. Part A, 43(8), 1293)
• 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
Rationale
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• 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?
Hybrid atomistic – FE in sp2 CC bonds
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• Atomic bonds are represented by beam elements
• Beam properties are obtained by energy balance
Utotal =Ur +Uθ +Uτ
Ur =12kr Δr( )2 Uθ =
12kθ Δθ( )2 Uτ =
12kτ Δφ( )2
Uaxial =12Kaxial (ΔL)
2 =EA2L(ΔL)2
Utorsion =12Ktorsion (Δβ)
2 =GJ2L(Δβ)
Ubending =12Kbending (2α)
2 =EI2L4+Φ1+Φ
(2α)2
(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)
Hybrid atomistic – FE in sp2 CC bonds
Nanocomposites for Aerospace, KTN
(Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306)
The structural mechanics approach
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The equivalent mechanical properties of the CC-bond beams are input in a FE model representing a 3D structural frame
[ ]{ } { }fuK = [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
Examples – buckling of carbon nanotubes
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(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)
Examples – graphene
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Circular SLGS (R = 9: 5 nm) under central loading. Distribution of equivalent membrane stresses. 8878 atoms
Deformation of rectangular SLGS (15.1 x 13.03 nm2) under central loading. ~ 7890 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.
Examples – graphene
Nanocomposites for Aerospace, KTN
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.
0 0.5 1 1.5 2 2.5 30
5
10
15
20
25
30
35
w/d
FR2 /Y/d3
Lattice R = 2.5 nmContinuum R = 2.5 nmLattice R = 5.0 nmContinuum R = 5.0 nmLattice R = 9.5 nmContinuum R = 9.5 nmEq. (17)
0 0.5 1 1.5 20
5
10
15
20
25
30
35
w/d
F a
b/Y/
d3
Lattice a = 3.88 nmContinuum a = 3.88 nmLattice a = 5.0 nmContinuum a = 5.0 nmLattice a = 15.1 nmContinuum a = 15.1 nmEq. (18)
circular SLGS rectangular SLGS
Examples – bilayer graphene
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Scarpa, F., Adhikari, S. and Chowdhury, R., "The transverse elasticity of bilayer graphene", Physics Letters A, 374[19-20] (2010), pp. 2053-2057.
• 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)
Epoxy/SLGS nanocomposite
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Chandra, Y., Chowdhury, R., Scarpa, F., Adhikari, S. and Seinz, J., "Multiscale modeling on dynamic behaviour of graphene based composites", Materials Science and Engineering B, in press.
Polymer Matrix
van der Waals interaction
Graphene sheet
0 5 10 15 200
50
100
150
200
250
t1 (G
Hz)
Length (nm)
ArmchairïGRP2ZigzagïGRP4
Epoxy/SLGS nanocomposite
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Continuous SLGS reinforcement Short SLGS reinforcement
• 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 • LJ 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 • Models with different orientations in space
Epoxy/SLGS nanocomposite
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Direction || to loading
Direction 45o to loading
Epoxy/SLGS nanocomposite
Nanocomposites for Aerospace, KTN
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)
Developments and conclusions
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(Adhikari S., E. Saavedra-Flores, Scarpa F. Chowdhury R., Friswell M. I., 2013. J. Royal Soc. Interface. Submitted)
Significant potential for multiphysics
modelling using FEA and bridging length
scales
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)
Nanocomposites for Aerospace, KTN
Thanks for your kind attention
Any question?