ATOA Scientific TechnologiesEngineering Simulation For Innovation
Multiphysics Design of Materials
Dr Raj C ThiagarajanATOA 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.
ATOA Scientific Technologies Engineering Simulation For Innovation
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.
Composite?
Nature
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
Designer Materials…
ATOA Scientific Technologies Engineering Simulation For Innovation
Multiphysics Design of MaterialsC
AD
Mo
de
l
Structural Elastic constants
Super structural
Thermal Thermal conductivity
Superinsulation
Electromagnetic permeability and permittivity
Metamaterials
AcousticSound transmission loss
Acoustic bandgaps
TransportDiffusion
PermeabilitySuper flow
Current
Designer properties
Future
Extremel Properties
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The Physics
Physics Governing Eqs* Constitute Eqs* Comments
StructuralStatic:, Navier’s equation, Hooke’s law for stress strain relation. F, volume forces, σ,stress tensor, ε, strain tensor, D, stiffness matrix
ThermalHeat Equation, Fourier’s law: ρ,density.Cp, heat capacity, k, thermal conductivity, Q,heat source.
AcousticHelmholtz eq: ω, angular freq, ρ0, fluid density, cs, speed of sound, q, source, Dtl, transmission-loss coefficient, Wi, incident and Wt is the transmitted sound power.
DiffusionFick’s law, Diffusion Coeff. c is the concentration, D is the diffusion coefficient, and R is a reaction rate
Porous flowDarcy’s law, Permeability, : v, velocity, µ, dynamic viscosity, K, permeability and P,Pressure.P
xvK
∆
∆=
η
* Equations from COMSOL documentation
CA
D M
od
el
c
NDeff
∆= ave
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Engineering of material properties
• Virtual Product and
process design
• Paradigm shift in
• predicting properties
• to
• engineering properties. Macro
Micro
Nano
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Normalized Density / Vf
No
rmalized
Pro
pert
y
(e.g
.
Mo
du
lus)
@ 5
0 o
f w
eig
ht
Micro = 1X property
Nano >1X property
Macro <1X property
Engineered for Super and Unusual properties
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Computer Aided Micromechanics (CAMM)
• Study of composite
behavior from
constituents
• Aims at finding a volume
elements /unit cell
response to prescribed
mechanical loads.
Statically equivalent /
Periodic
representation of
morphology
Homogenized / Periodic
Boundary Conditions
Where,
Ω−volume, Γ-surface,
u(x)– deformation vector
t(x)– surface traction vector
nΓ – surface normal vector
Fibre
Homogenization and
Unit cell are key CAMM
property predictionLocalization and Homogenization relationship
Typical Micro structure/ morphology of composites
Typical Unit cell Model
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Structural
• Advanced structural composites are known for their specific strength and stiffness properties.
• Constituent properties,
• Periodic BC
• Global loads,
• local stress and strain.
• Anisotropic Stiffness and failure properties are critical for application performance prediction
Typical Results
Schematics of stress-
strain behavior
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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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Transport : Diffusivity
Application: Water desalination, filtration.
Fick’s law
Effective diffusivity prediction for porous and composite medium
Porous medium Composites
D1 1 m2/s
C0 100 mol/m3
k 5 m/s
vf 0.5
dx 1 m
Deff 0.32 m2/sec
D1 1 m2/s
D2 5 m2/s
C0 100 mol/m3
k 5 m/s
vf 0.5
dx 1 m
Deff 2.002101 m2/s
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Acoustics:
Virtual Acoustics Tests
Sound Insulation panels (STL)
Acoustic Bandgaps
Solid – Fluid Interface
Fluid domain
Load on solid domain
Acceleration – Fluid domain
ΓΓΓΓ X
M
Air
PM L
PM L
Air
Flu id St r uct ur e
In t e r a ct ion
Flu id St ru ct ur e
In t e r a ct ion
Excit a t ion of Pla ne W a ve
Pe r iod ic Bou nda r y
Con d it ions
Pe r iod ic Bounda ry
Cond it ions
Structural + acoustics coupling
Recent Developments
Eig. Frequency = 5.07e14 Hz
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Electromagnetics: Unusual
properties• Two stage sequentially
coupled process for
accelerated
development by
numerical experiments.
• Macro simulation to
explore the Novel
application design with
effective properties.
• Micro simulations to
design the materials for
the required effective
properties.
Micro: Material Design
•Dielectric constant
•Permeability
•Elastic properties
Macro: Performance prediction
•Negative refractive index
•Super lens Focusing
•Cloaking
Computational micromechanics for accelerated application development.
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Flow: Permeability: Composite processing
• RTM, VARTM
• Impregnation is critical to quality and performance
• Macro flow through preform/ strands and micro
flow through individual fibers.
• Predict permeability from reinforcement morphology
InputProcess parametersinjection port location/nos
vacuum port location/ nos
Temperature, Pressure
Gravity forces
Material
Reinforcement
Lay-up sequence
No of layers
Fibre architecture
Resin Viscosity
PredictionPressure
Flow path
Permeability
Porosity
OutputVolume fraction
Thickness
Flow time
Weight
x
PKu
∆
∆⋅−=
µ
Darcy’s law
v
P0P1dx
k
Flow chart illustrating VARTM process simulation
Design of Material for Product and Process Design
ATOA Scientific Technologies Engineering Simulation For Innovation
Multiphysics Design of materials
13
• Virtual material property prediction
• Engineering of constituents for
superior properties
• Virtual experimental characterization
of material properties
• Product and process performance
predictionAcknowledgement and References:
Multiphysics Design of composites, Keynote talk,
The COMSOL Conference 2009 Bangalore,. November 13-14, 2009.
ATOA Scientific Technologies Engineering Simulation For Innovation
ATOA Scientific Technologies
www.atoastech.com
14ATOA Scientific Technologies is an engineering
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.
Contact ATOA Scientific Technologies for
MULTIPHYSICS ENGINEERING SIMULATIONS
Structural ↔ Thermal ↔ Flow ↔ Dynamics ↔ Acoustics ↔ Optics
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