IMT Institute for Advanced Studies March 5, 2013, Lucca, Italy
Transcript of IMT Institute for Advanced Studies March 5, 2013, Lucca, Italy
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Emergent properties
in interface mechanical problems:
A paradigm of organized complexity
Dr. Ing. Marco Paggi
Politecnico di Torino
Centre for Risk Analysis and Durability of Structures
http://staff.polito.it/marco.paggi
IMT Institute for Advanced Studies
March 5, 2013, Lucca, Italy
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Outline
1. Organized complexity & emergent properties in
interface problems
2. An example in contact mechanics
3. An example in fracture mechanics
4. A multiphysics application: photovoltaics
5. Ongoing research topics
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Acknowledgements
FIRB Future in Research 2010
Vigoni 2010
ERC Starting Grant IDEAS 2011
AvH Fellowship in Hannover
2010-2011
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Emergent properties in ordered complexity
Organized complexity resides in the non-random, or
correlated, nonlinear interaction between the parts of a
system
Coordinated systems exhibit emergent properties not easily
predictable from the properties of their constituents
Classical examples of complex systems:
- Earthquakes
- Climate systems
- Living systems
- Social systems
- Economical systems
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Organized complexity in interface problems
Common features:
Nonlinear relations; multiple scales; fractality / hierarchy
Contact mechanics • Scaling of contact properties (friction coefficient,
adhesion, thermal contact conductance)
Fracture mechanics & fatigue
• Scaling of strength and toughness
Metamaterials
• Scaling of optical and elecromagnetic properties
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Two examples of emergent properties
Aim: study of the emergence of macro-properties from
micro-properties (bottom-up approach)
Methods: nonlinear mechanics, computational methods,
optimization
(2) Flaw-tolerance of hierarchical
polycrystalline materials
(1) Interface thermal
resistance due to roughness
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Interface contact conductance
Self-affinity
5-2D
1
1/d 1/D
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• Self-affinity (even of a random nature)
• Non integer dimension
Examples:
- mountains profiles
- clouds profiles
- coastlines profiles
- river patterns
- diffusion fronts
- moon craters
- arterial systems
dim. 1÷2 - sponge-cloths
- foams
- brain folds
- universe mass
dim. 2÷3
Fractality
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Interface contact conductance
d
p
p
The contact conductance is proportional to the contact
stiffness (Barber, PRS 2003; Paggi and Barber, IJHMT
2011):
-- 1
1
0
~~~ ddAp
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Inverse problem
Problem: extract the interface contact conductance (nonlinear
mesoscopic property) from global stiffness data (emergent
macroscopic property)
Macroscopic
curvature
effects
Finite size
effects
(boundary
effects)
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Global stiffness by varying the punch size L
Rough punch composed of
n x n RMD patches
n=4 D
L
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Proposed solution strategy
-- 1
1
0
~~~ ddAp
1. Solve the contact problem
between the rough punch and
the half-plane (global solution)
2. Imagine the surface as a
collection of nonlinear punches
whose constitutive equation is:
3. Solve the contact problem
and find the optimal values of
the 3 free parameters to match
the global solution
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Result of the optimization problem
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Optimal solution
independent of BCs
(model-independent interface
contact conductance):
d0=4.83
=0.80
F2=13
Result of the optimization problem
~ 8.0~13
~pC
5~83.401.0~ dp -
n n
n
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Hierarchical polycrystalline materials
M. Paggi, P. Wriggers (2012) J. Mech. Phys. Solids, 60:557-571.
How do the strength depend on the interaction between
interfaces at different scales?
Is there any emergence of an optimal configuration to
tolerate defects (flaw tolerance)?
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Mimicking nature: interfaces at different scales
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s
gN
S. Li, M.D. Thouless, A.M. Waas, J.A. Schroeder, P.D. Zavattieri (2005) Composites
Science and Technology 65:281-293.
The Cohesive Zone Model
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smax
s s s
s s s
dc gN
GIC
smax
dc gN
GIC GIC
GIC GIC GIC
dc gN
dc gN dc gN dc gN
smax
smax smax smax
Open issues:
(1) How to relate the shape of the CZM to physics?
(2) How to take into account the finite thickness of real interfaces?
The Cohesive Zone Model
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Damage evolution Shape of the CZM by varying a
A nonlocal CZM for finite thickness interfaces
2
2
1N
E Dg
l D
a
as
- Paggi & Wriggers (2011) Comp. Mat. Sci.
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Comparison with MD Shape of the CZM
Interpretation of MD simulations
Spearot et al. (2004) Mech. Mater., 36:825-847.
Copper (fcc crystal)
2l2+l1=43.38 Å, E1=E2=110 GPa
de=0.2 Å, dc=8.0 Å, a=0.9
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Weak form
SδSδVδSVV
ddd)(TTTtgfuσu
STδqSTδqVTδTcρVTδqS
s
V
n
V
V
V
dddd
CZM
contributions
S
q
TggGS
d,,
S
NTint
D s
ddd
S
TΔ
g
g
TΔδgδgδGΔS
d,, N
T
NTint
C
D
T
q
g
q
gg
gg
S
N
S
NT
NT
0
0
0
ss
C
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Finite element implementation in FEAP
M. Paggi, P. Wriggers: "A nonlocal cohesive zone model for finite thickness
interfaces – Part II: FE implementation and application to polycrystalline
materials", Comp. Mat. Sci., Vol. 50 (5), 1634-1643, 2011.
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Finite element implementation in FEAP
Body 1
Body 2
M. Paggi, P. Wriggers: "A nonlocal cohesive zone model for finite thickness
interfaces – Part II: FE implementation and application to polycrystalline
materials", Comp. Mat. Sci., Vol. 50 (5), 1634-1643, 2011.
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Application to polycrystalline materials
Grain size
Interface
thickness
1 μm dm
Fracture
energy
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3D Virtual tensile test Load
Displacement
Paggi, Lehmann, Weber,
Carpinteri, Wriggers (2012)
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Effect of hierarchy on anisotropy
1 1
2
2
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Effect of hierarchy on strength
Real
crack tip
Fictitious
crack tip
lCZM
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Effect of hierarchy on strength
Real
crack tip
Fictitious
crack tip
lCZM
Flaw
tolerance
lCZM = process zone size for the
grain boundaries of the level 2
dlevel 1 = diameter of the rods (level 1)
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Interfaces in multiphysics
Thermal
field Elastic
field
Electric
field Thermo-electric field Electro-elastic field
Thermo-elastic field
Electro-thermo-elastic
field
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A multiscale solution strategy
Macro-model:
Multi-layered plate
(homogeneous cells)
Micro-model:
Polycrystalline Si cells
with grain boundaries
M. Paggi, M. Corrado, M.A. Rodriguez (2013)
Composite Structures, 95:630-638.
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Micro-crack pattern in Silicon cells
X
Y
1 2 3
4 5 6
7 8 9
Simply
supported plate
subjected to a
pressure of
5400 Pa
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Electrically inactive areas
X
Y
1 2 3
4 5 6
7 8 9
Simply
supported plate
subjected to a
pressure of
5400 Pa
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Centre for Risk Analysis and Durability of Structures
3D confocal-
interferometric
profilometer
(LEICA, DCM 3D)
SEM
(ZEISS, EVO MA15)
Testing stage
(DEBEN, 5000S)
Thermocamera
(FLIR, T640bx)
Photocamera for
EL tests
(PCO, 1300 Solar)
Testing machine &
thermostatic chamber
(Zwick/Roell, Z010TH)
Server HP
Proliant DL585R07
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Ongoing research topics
Determination of interface properties via inverse analysis
of microstructure evolution of polycrystals during a
tensile tests
(with Dr. M. Schaper, Lebniz University Hannover)
SEM image with
superimposed digital
image correlation of the
strain field
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Ongoing research topics
Quantitative analysis of EL images via fractal concepts
and spectral methods
(with Ing. I. Berardone & ISFH)
EL image of a microcracked Silicon cell
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Ongoing research topics
Thermoelastic cohesive zone models
(with Dr. A. Sapora)
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Ongoing research topics
Nonlinear crack propagation in dynamics
(with Dr. M. Corrado)
v = 2 m/s