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July 21, 2006
Ricardo Simões1,2, J.C. Viana1,G.R. Dias1, and A.M. Cunha1
MultiMulti--scale Hierarchical Approach for Mechanical scale Hierarchical Approach for Mechanical Analysis of Polymeric MaterialsAnalysis of Polymeric Materials
1 Institute for Polymers and Composites (IPC)University of Minho, Guimarães, Portugal;http://ipc.uminho.pt/ [email protected]
2 Escola Superior de TecnologiaInstituto Politécnico do Cávado e do AveBarcelos, Portugal [email protected]
8th MESOMECHANICS, 2006
MultiMulti--scale modelling scale modelling approachapproach
Skin-core structure
spherulitic structure
MolecularÅscale
Macroscalecmscale
Spheruliticµmscale
Lamelarnmscale
Skin- coremmscale
10-3 m10-2 m 10-6 m 10-8 m 10-9 m 10-10 m
continuous milieu
discontinuous milieu
lamellar structure
crystal structure
macromolecule
Experimental Experimental vsvs simulation capabilitiessimulation capabilities
SIMS, RBS
Optical
Length scale
Time scale
> 10-1 m
10-3 m
10-7 m
10-9 m
< 10-11 m
Quantum simulations
Atomistic /molecular simulations
Continuum simulations
10-5 m
< 10-14 s 10-12 s 10-6 s > 10-2 s10-10 s 10-4 s10-8 s
XPS
SXAS, SXES
Mesoscopic simulations
AES, ELS
Micromechanics simulations
XRDSEM, TEM
Neutron diffraction
LEED, RHEEDSTM, AFM
New material architecture concepts
Envisaged new
functionalities
Core modelling code
Applied multi-scale hierarchical simulation codes
New material architecture concepts validation
Materials with new / enhanced functionalities
Manufacturing and cost viability
assessment
Computer generation of material architectures
Mechanical
Thermal
Magnetic
BarrierMacroscale
Mesoscale
Molecular
Microscale
NC 1 NC 2 NC 3 ... NC n
3D visualization
andanimation
codes
Specifications
ConceptualizationModelling
Simulation
Visualization
Validation
FeasibilityNew Solutions
Recursive project flow
Main project flow
Hierarchical length scale
Computercode
Concept
General research strategyGeneral research strategy
MultiMulti--scale modelling approachscale modelling approach
MultiMulti--scale modelling approachscale modelling approach
Solid model
Prediction of local microstructurebased on thermomechanical conditions
Flow simulation
Research activitiesResearch activities
- Macroscale/microscale (FEM-based)structural simulations (Abaqus)flow simulations (Moldflow)processing-microstructure-properties relationships
- Molecular/mesoscale (MD)amorphous, semi-crystalline, and nano-filled structurestension, compression, shear, and complex loading modesmechanical, electrical, and barrier propertiesnanostructure-properties relationships
MacroMacro--micro couplingmicro coupling
MacroMacro--micro couplingmicro coupling
Stress Results S33
Skin
Core
Disp Results u3
MACRO- Element Formulation :C3D8r – Reduced Integration (Hourglass Control)
C3D8 – Full Integration
N1 N2
N3N4
N5 N6
N7 N8
ICE (implicit constitutive equation) – FormulationFEM model for local microstructure
Evaluation material point coincides with macro element
Gauss point
ICE1
ICE2
ICE3
ICEn
Microstructure 1
Microstructure 2
Microstructure 3
Microstructure n
Molecular dynamicsMolecular dynamics
Molecular DynamicsMolecular Dynamics
First MD in 1957: B. J. Alder and T.E. Wainwright, J. Chem. Phys. 27, 1208 (1957)
N ~ 100 – 100,000Periodic boundariesPrescribed U(r)
Specification of N, V, T
Solving Newton’s equations Fi = mi ai
Calculation of ri(t), vi(t)
Obtaining Properties (equilibrium and non-equilibrium)
Averaging
Statistical segment model of a polymer chain (mesoscale coarse-grain)
The molecular dynamics (MD) method was employed for simulating time-dependent behavior.
Simulation modelSimulation model
Interactions between particles are described by potentials.Different potentials for:- crystalline and amorphous;- primary and secondary bonds.
- Ecrystalline / Eamorphous
- Fprimary / Fsecondary
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
0.5 1 1.5 2 2.5r
F (r)
Intramolecular
Intermolecular
Nanofiber-Chain
MD material generationMD material generation
Material generationMaterial generation
We obtain a polymeric structure of coiled chains by emulating the step-wise polymerization process
InterlamelarInterlamelar phenomenaphenomena
InterlamelarInterlamelar simulationssimulations
Degree of
packing
Lamella thicknessAmorphous region thickness
Amorphousregion
orientation
InterlamelarInterlamelar simulationssimulations
Tension Shear
InterlamelarInterlamelar simulations simulations -- tensiletensileLamella and amorphous region size effects (0.85 y-or)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5
ε
(For
ce)
lt,at = 5 (15)lt = 5, at = 10 (20)lt = 5, at = 15 (25)lt = 10, at = 5 (25)lt,at = 10 (30)lt = 10, at = 15 (35)lt = 15, at = 5 (35)lt = 15, at = 10 (40)lt,at = 15 (45)
InterlamelarInterlamelar simulationssimulations
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
ε
σ
sheartensile
Nanofilled polymersNanofilled polymers
Nanofiber concentrationNanofiber length (and length distribution)OrientationDispersionNanofiber functionalizationMatrix strength
OffOff--lattice approach lattice approach –– main variablesmain variables
Nanofiber concentration : 0.65%, 1.2%, 2.5%, 5.3%Nanofiber length (and length distribution) : L/D = 4, 14, 21, 27 ± 0Orientation : parallel, perpendicular, randomDispersionNanofiber functionalizationMatrix strength
OffOff--lattice approach lattice approach –– main variablesmain variables
MD MD –– fiber concentration effectfiber concentration effect
Isotropic; L/D = 27
Effect of the nanofiber concentration
-0.5
0
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1 1.2
Nsteps (x1E6)
stra
in
Vf = 0%Vf = 0.65%Vf = 1.2%Vf = 2.5%Vf = 5.3%
Effect of the nanofiber concentration on properties
0
0.5
1
1.5
2
2.5
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Vf (%)
E
0.000.05
0.100.15
0.200.25
0.300.35
0.400.45
0.50
σy
MD MD –– fiber concentration effectfiber concentration effect
Isotropic; L/D = 27
Forces on fibersForces on fibers
AcknowledgmentsAcknowledgments
Fundação para a Ciência e a Tecnologia, Lisbon, through the
3º Quadro Comunitário de Apoio (RS) and the
POCTI and FEDER programmes (IPC)
Witold Brostow, University of North Texas
High-Performance Computing Initiative, Univ. North Texas, Denton TX, USA
United States Air Force Research Laboratories
Wright-Patterson Air Force Base, Dayton OH, USA
Selected referencesSelected references
W. Brostow, A. M. Cunha, J. Quintanilla and R. Simoes, Macromol. Theory & Simul. 11: 308 (2002)
R. Simoes, W. Brostow, and A. M. Cunha, Polymer 45: 7767 (2004)
R. Simoes, A.M. Cunha, W. Brostow, Computational Materials Science 36: 319, (2006)
R. Simoes, A.M. Cunha, W. Brostow, Modelling & Simulation in Materials Sci & Eng 14: 157 (2006)
