Tutorial I: Mechanics of CONFINED Granular Solids
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Transcript of Tutorial I: Mechanics of CONFINED Granular Solids
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IHPC-IMS Program onAdvances & Mathematical Issues
in Large Scale Simulation(Dec 2002 - Mar 2003 & Oct - Nov 2003)
Tutorial I:Mechanics of CONFINED Granular Solids
Alberto M. CuitiñoMechanical and Aerospace Engineering
Rutgers UniversityPiscataway, New [email protected]
Institute of High Performance Computing Institute for Mathematical Sciences, NUS
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Collaborators
• Gustavo Gioia • Shanfu Zheng
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Overview
10-4 10-3 10-2 10-1
Normalized Compaction Force
0.4
0.5
0.6
0.7
0.8
0.9
1
Re
lativ
eD
en
sity
MacroscopicCompaction Curve
1st Stage 2nd Stage
Compaction Force
3rd Stage
0th Stage
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Overview
Die Filling Rearrangement
Large Deformation Localized Deformation
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Pore Structure
Increasing Pressure
PEG 8000
Higher Magnification
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Pore Structure
1mm/sec
100mm/secPEG 8000 Visco-plastic material
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Pore Structure
1mm/sec
100mm/secHPDE Visco-elastic material
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Compact Properties
0
50
100
150
200
0 10 20 30 40 50
Har
dnes
s (N
)
Compaction force (KN)
P
(N
)
HPDE 1 mm/sec
HPDE 100 mm/sec
PEG 100 mm/sec
PEG 1 mm/sec
P
Brazilian Compression
Test
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Goal
Understand and quantitatively predict the MACROSCOPIC
behavior of powder systems under compressive loading based on
MICROSCOPIC properties such as particle/granule behavior and spatial arrangement
Load
Need for MULTISCALE Study PARTICLES POWDERS (discrete) (continuum)
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No cohesion Cohesion 2 degrees
misalignment
Cohesion Vertical dropping
Die Filling
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Role of Cohesion on Die Filling
Numerical Experimental
Numerical Experimental
Cohesion No Cohesion
Open Configuration Dense Configuration
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Rearrangement Process(a discontinuous process, advancing front)
Video ImagingGlass Beads, Diameter = 1.2 mmGioia and Cuitino, 1999
Increasing Pressure Increasing Pressure
Process by which open structures collapse into dense configurations• Cohesive Powders are susceptible to rearrangement while• Non-Cohesive Powders are not
X-Ray Tomography-Density MapsAl2O3 Granules. Diameter = 30 micronsLannutti, 1997
Punch
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Physical Description(a theoretical interpretation)
Energy landscape exhibits a Spinoidal Structure (nonconvex)
H H
Convexification implies coexistence of two phases
H
Total
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Energy Landscape
Total Energy
Energy
Relaxation Energy(non-convex part)
Inter-particle Energy (frozen initial configuration)
Wedging & Friction
W = Wt+ Wf+ Ww+ Wb
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Relaxation Mechanism
Particle Rearrangement Mechanism
Snap-Through of Rings (Kuhn et al. 1991) Ring Structures in Cohesive Powders
Numerical
Experimental
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Rearrangement
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Non Convex Analysis
Minimization with constrain (Lagrange Multiplier)
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Non Convex Analysis
Effective Energy Density
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Density Evolution
Transformation Front
High Density Phase
Low Density Phase
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Wall Friction
Equilibrium in the current configuration
Generalized Friction Coefficient
Exponential decay from the transformation front
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Particle Deformability
Deformability of High Density Phase
Deformability of Low Density Phase
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Particle Deformability
High Density Phase
Low Density Phase
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Pressure Density Profiles
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Comparison with experiment
Al2O3
Theoretical Experimental
Kong et al., 1999
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Compaction Curves
H = 2L = 0.4
Theoretical Experimental(Deis and Lannutti, 1998)
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Density Histograms
Theoretical Experimental(Deis and Lannutti, 1998)
Incr
easi
ng p
ress
ure
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Effect of RH (low pressure)
p = 0.14 MPa
Experimental(Deis and Lannutti, 1998)
Low pressure range
Theoretical
Unimodal Distribution
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Effect of RH (higher pressure)
Experimental (Deis and Lannutti, 1998) Theoretical
Higher deformability increases the transformed region at constant applied pressure
Bimodal Distribution
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Other Systems with NC Energy
Preferred Term
THIN FILM BUCKLING
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Other Systems with NC Energy
COMPRESSION OF FOAMS
Gibson and Ashby, 1997
Structure Mechanical Response
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Implication: Heterogeneous Deformation
Spinoidal Energy Landscape
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Comparison with Experiment
Theory
Experiment
Material Tested Polyurethane Foam
Theory
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Comparison with Experiment
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Experimental Evidence
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x
y
Surface Measurement
Displacement field measurement using Digital Image Speckle Correlation
(Wang, Gioia and Cuitino, 2001)
Peters & Ranson (1982),
Kahn-Jetter & Chu (1990)
Vendroux & Knauss (1998)
Zhang et al . (1999)
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Digital Image Speckle Correlation
U
V
G(X)
g(x)
where, U, V are the rigid body motion and Ux, Uy, Vx, Vy are the spatial gradients
Actual ImagesUndeformed
Deformed (load step 2)
2
2
,,,,,XG
xgXGVyVxUyUxVUCC
Gray scale values, G and g, characterize point in original and deformed images
Minimization of Correlation function C provides deformation field
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Digital Image Speckle Correlation
Fiber OpticLight Source
CCD Camera
Loading System
Specimen
Computer with Frame Grabber
Setup
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Displacement MapsProgressive Field
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Displacement MapsProgressive Field
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Comparison with Experiment
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Multiscale Modeling
Cascade of length scales
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Simulation