Materials need to meet structural, thermal, and electromagnetic and transport property requirements simultaneously for various new applications. This presentation provides an overview of multiphysics design of materials with special reference to composites using micromechanics. The unitcell modeling and property prediction methodology are detailed. The elastic modulus, thermal conductivity, diffusion coefficient prediction method and results are reported. A two stage sequentially coupled method is also outlined for accelerated application and material development for metamaterials. Composite processing related micromechanical models to predict permeability is also reported. The material properties related to product and process design aspect of fiber reinforced and cellular composites are highlighted.

1. Multiphysics Design of Materials
Dr Raj C Thiagarajan
ATOA Scientific Technologies
Materials need to meet structural, thermal, and electromagnetic and
transport property requirements simultaneously for various new
applications. This presentation provides an overview of multiphysics design of
materials with special reference to composites using micromechanics. The
unitcell modeling and property prediction methodology are detailed. The
elastic modulus, thermal conductivity, diffusion coefficient prediction method
and results are reported. A two stage sequentially coupled method is also
outlined for accelerated application and material development for
metamaterials. Composite processing related micromechanical models to
predict permeability is also reported. The material properties related to
product and process design aspect of fiber reinforced and cellular composites
are highlighted.
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2. Composite?
Composite Materials provide us the unique opportunity to
engineering material with required Designer properties.
Combination of two or more constituents to perform better
than individual constituents.
Macroscopically homogeneous and microscopically inhomogeneous.
Homogeneous at n length scale and heterogeneous at (n-1) length scale.
Nature
Designer Materials…
References:
Balsa wood : Gibson, L.J. and Ashby, M.F., 1999. Cellular Solids: Structure and Properties, Cambridge University Press, 1999.
Toucan beak: Seki Y. et.al.,Structure and mechanical behavior of a toucan beak, Acta Materialia, 53 ,5281–5296, 2005. http://www.theallineed.com/engineering/06012421.htm
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3. Multiphysics Design of Materials
Elastic
Structural constants
Super structural
Thermal
Thermal conductivity
Superinsulation
permeability
Electromagnetic
CAD Model
and permittivity Metamaterials
Sound
Acoustic
Acoustic transmission
loss
bandgaps
Diffusion
Transport Permeability
Super flow
Current Future
Designer properties Extremel Properties
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4. The Physics
Physics Governing Eqs* Constitute Eqs* Comments
Static:, Navier’s equation, Hooke’s law
Structural for stress strain relation. F, volume
forces, σ,stress tensor, ε, strain tensor,
D, stiffness matrix
Heat Equation, Fourier’s law: ρ,density.
Thermal Cp, heat capacity, k, thermal
conductivity, Q,heat source.
Helmholtz eq: ω, angular freq, ρ0, fluid
CAD Model
density, cs, speed of sound, q, source,
Acoustic Dtl, transmission-loss coefficient, Wi,
incident and Wt is the transmitted sound
power.
Diffusion N ave Fick’s law, Diffusion Coeff. c is the
Deff = concentration, D is the diffusion
coefficient, and R is a reaction rate
∆c
v η ∆x Darcy’s law, Permeability, : v, velocity, µ,
Porous flow K=
∆P
dynamic viscosity, K, permeability and P,
Pressure.
* Equations from COMSOL documentation
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5. Engineering of material properties
1
Nano >1X property
• Virtual Product and
0.8
process design
Normalized Property (e.g.
Nano
• Paradigm shift in 0.6
Micro = 1X property
• predicting properties Micro
0.4
@ 50 of weight
• to
Modulus)
Macro <1X property
• engineering properties. 0.2
Macro
0
0 0.2 0.4 0.6 0.8 1
Normalized Density / Vf
Engineered for Super and Unusual properties
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6. Computer Aided Micromechanics (CAMM)
• Study of composite
behavior from
constituents
• Aims at finding a volume
elements /unit cell Typical Micro structure/ morphology of composites
response to prescribed
Homogenization and
mechanical loads.
Fibre Unit cell are key CAMM
property prediction
Localization and Homogenization relationship
Statically equivalent / Where,
Periodic Ω−volume, Γ-surface,
u(x)– deformation vector
representation of t(x)– surface traction vector
nΓ – surface normal vector
morphology
Homogenized / Periodic
Boundary Conditions
Typical Unit cell Model
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7. Structural
• Advanced structural
composites are known
for their specific
strength and stiffness
properties.
• Constituent properties,
• Periodic BC
Schematics of stress-
• Global loads, strain behavior
• local stress and strain.
• Anisotropic Stiffness
and failure properties
are critical for
application
performance prediction Typical Results
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8. Thermal: k
• Low k: Insulation: Energy saving,
• High k: Conductor: Thermal management
• Thermal conductivity measurement method
was implemented for k prediction.
• Convection and radiation components of air
with equivalent conductivity for overall
performance.
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9. Transport : Diffusivity
Porous medium Composites
Application: Water
desalination,
filtration.
Fick’s law
D1 1 m2/s
D1 1 m2/s
D2 5 m2/s
C0 100 mol/m3
C0 100 mol/m3
k 5 m/s k 5 m/s
Effective diffusivity vf
dx
0.5
1m
vf
dx
0.5
1 m
prediction for porous Deff 0.32 m2/sec Deff 2.002101 m2/s
and composite
medium
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10. Acoustics:
PM L
Structural + acoustics coupling Ex cit a t io n o f
P la n e W a v e
Virtual Fluid domain A ir
Acoustics Flu id
St r u ct u r e
Tests I n t e r a ct io n
Flu id
St r u ct u r e
In t e r a ct io n
A ir
Solid – Fluid Interface Pe r io d ic
P e r io d ic
Bo u n d a r y
Co n d it io n s
Sound
Bo u n d a r y
Co n d it io n s
Load on solid domain PM L
Insulation
panels (STL) Acceleration – Fluid domain
Acoustic
Bandgaps M
Recent Developments
Γ X
Eig. Frequency = 5.07e14 Hz
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11. Electromagnetics: Unusual
properties
• Two stage sequentially
coupled process for
accelerated
development by
numerical experiments.
• Macro simulation to Macro: Performance Micro: Material
prediction Design
explore the Novel
application design with •Negative refractive •Dielectric
effective properties. index constant
•Super lens Focusing •Permeability
• Micro simulations to •Cloaking •Elastic
design the materials for properties
the required effective
properties.
Computational micromechanics for accelerated application development.
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12. Flow: Permeability: Composite processing
Input
Process parameters
injection port location/nos
• RTM, VARTM vacuum port location/ nos
Temperature, Pressure
• Impregnation is critical to quality and performance Gravity forces
• Macro flow through preform/ strands and micro Material
Reinforcement
flow through individual fibers. Lay-up sequence
No of layers
• Predict permeability from reinforcement morphology Fibre architecture
Resin Viscosity
Darcy’s law Flow chart
K ∆P illustrating
u=− ⋅
µ ∆x VARTM
v process
P1
simulation
P0
dx
k Output
Prediction
Pressure Volume fraction
Flow path Thickness
Permeability Flow time
Porosity Weight
Design of Material for Product and Process Design
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13. Multiphysics Design of materials
• Virtual material property prediction
• Engineering of constituents for
superior properties
• Virtual experimental characterization
of material properties
• Product and process performance
prediction
Acknowledgement and References:
Multiphysics Design of composites, Keynote talk,
The COMSOL Conference 2009 Bangalore,. November 13-14, 2009.
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14. Contact ATOA Scientific Technologies for
MULTIPHYSICS ENGINEERING SIMULATIONS
Structural ↔ Thermal ↔ Flow ↔ Dynamics ↔ Acoustics ↔ Optics
ATOA Scientific Technologies is an engineering 14
simulation service provider, with a specialty on
Multiphysics, Multiscale and Multimaterials, for
innovative product and process development to
cut cost and cycle time for our clients.
ATOA Scientific Technologies
www.atoastech.com
ATOAST.HQ@ATOAST.COM
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