Multi Physics Design of Materials (composites)

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…


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


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


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


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


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


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.


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


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


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.


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


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.


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simulation service provider, with a specialty on

Multiphysics, Multiscale and Multimaterials, for

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cut cost and cycle time for our clients.

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MULTIPHYSICS ENGINEERING SIMULATIONS

Structural ↔ Thermal ↔ Flow ↔ Dynamics ↔ Acoustics ↔ Optics

Multi Physics Design of Materials (composites)

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