SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS
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SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS Katalin Bagi Hungarian Academy of Sciences [email protected] Matthew R. Kuhn Portland University [email protected]
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SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS. Katalin Bagi Hungarian Academy of Sciences [email protected]. Matthew R. Kuhn Portland Universit y [email protected]. AIMS & MOTIVATIONS Representative domain: “ a small, finite subset of the assembly which contains enough - PowerPoint PPT Presentation
Transcript of SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS
SIZE EFFECT IN
DISCRETE ELEMENT SIMULATIONS
Katalin Bagi
Hungarian Academy of Sciences [email protected]
Matthew R. Kuhn
Portland [email protected]
AIMS & MOTIVATIONS
Representative domain:
“a small, finite subset of the assembly which contains enough grains to reflect the material behavior”
How many grains are “enough”?If more grains are taken, how it affects the behavior?
Discrete Element Modeling of real problems:
identify the parameters of a small sample to a lab test;
Can we use this DEM model for the real (i.e. large) problem?
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THE PRESENTATION
Literature overview What is size effect?Size effect in cemented granular materials
Experiences Sources of size effect
Our simulationsseveral assemblies of different sizes;different sample preparation methodsbiaxial loading: Shear strength?
Initial Young-modulus? Deformation patterns?
Summary
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SIZE EFFECT
Meaning: a property of the structure/sample e.g. strength Young-modulus
etc. which should be independent of the size of the structure/sample
according to the usual deterministic theories (“simple materials”), still depends on the size of the structure/sample
Examples:large strength
small strength
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SIZE EFFECTIN CEMENTED GRANULAR MATERIALS
e.g. Bazant, 1998 (etc):
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size
strength
usual determi-nistic theories
linear elastic fracture mechanics
SIZE EFFECTIN CEMENTED GRANULAR MATERIALS
Possible sources of size effect: The wall effect
boundary layer: different stress state different material properties
“Fracture mechanics size effect”fracture process zone size: depends on the particle size
Statistical size effectWeibull: strength of a chain = strength of its weakest linkfor metals etc.; not for cemented granular media
[stress redistribution] Others
diffusion phenomena; hydratation heat etc.
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!!
!!
THE PRESENTATIONLiterature overview
What is size effect?Size effect in cemented granular materials
Experiences Sources of size effect
Our simulationslaboratory experiments computer simulations OVAL; PFC
several assemblies of different sizes; grain size distribution: same for all assemblies two different methods to prepare the initial arrangements walls periodic boundaries biaxial loading: Shear strength?
Initial Young-modulus? Deformation patterns?
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OUR SIMULATIONS
Sample preparation: samples with the same porosity, coordination #, pressure
Method 1:
Assemblies with periodic boundaries Initial assemblies of different sizes Biaxial shear tests Compare: shear strength, stiffness, deformation patterns
Method 2:
Assemblies with walls Initial assemblies of different sizes Biaxial shear tests Compare: shear strength, stiffness, deformation patterns
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ASSEMBLIES WITH PERIODIC BOUNDARIES
Sample preparation:
size 15 15 size 30 30 size 60 60 size 97,5 97,5 100 assemblies of 100 assemblies of 100 assemblies of 20 assemblies of 256 grains 1024 grains 4096 grains 10816 grains
the same grain size distribution ; the same porosity different pressure 9 / 21
ASSEMBLIES WITH PERIODIC BOUNDARIES
Sample preparation: Assemblies with size 97,5 97,5 :
20 assemblies of 10816 grains average coordination number: 3,9885 average porosity: 0,1444 average normalized pressure: 1,04110-3
Assemblies with size 60 60 : 4096 grains average coord.number
select a subset of assemblies whose average porosity is the same! average pressure
Assemblies with size 30 30 : 1024 grainsdo the same selection!
Assemblies with size 15 15 : 256 grainsdo the same selection! 10 / 21
ASSEMBLIES WITH PERIODIC BOUNDARIES
Biaxial shear tests:linear contacts;Coulomb friction;quasi-static loading
256 grains 1024 grains 4096 grains 10816 grains
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shear stress
strain??
ASSEMBLIES WITH PERIODIC BOUNDARIES
Biaxial shear tests:
Deformation patterns:blue: volume increase
10816 grains: red: volume decrease
4096 grains:
1024 grains:
256 grains: 12 / 21
ASSEMBLIES WITH PERIODIC BOUNDARIES
Effect of size on the shear strength & Young modulus:
Conclusions: increasing size decreasing shear strength ( 4 %) slightly increasing stiffness ( 0,3 % )
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# of particles porosity
average coord.
number
average normalized
pressure
average normalized
shear strength
average normalized
Young modulus
15 15 256 0,1444 3,9885 1,041 10-3 2,062 0,433
30 30 1024 0,1444 3,9886 1,043 10-3 1,873 0,435
60 60 4096 0,1444 3,9886 1,040 10-3 1,829 0,435
97,597,5 10816 0,1444 3,9886 1,04110-3 1,811 0,436
ASSEMBLIES WITH WALLS
Sample preparation:
size 30 30 size 60 60 size 120 120 size 240 240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of 1040 grains 4150 grains 16 600 grains 66 600 grains
the same grain size distribution the same porosity
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ASSEMBLIES WITH WALLS
Biaxial shear tests:
30 30 60 60 120 120 240 240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of 1040 grains 4150 grains 16 600 grains 66 600 grains
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ASSEMBLIES WITH WALLS
Biaxial shear tests:
Deformation patterns: 66 600 grains blue: volume increase
red: volume decrease
16 600 grains
4150 grains
1040 grains16 / 21
ASSEMBLIES WITH WALLS
Effect of size on the shear strength & Young modulus:
Conclusion: increasing size decreasing shear strength ( 4 % )
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# of particles porosityaverage coord.
number
average normalized
pressure
average normalized
shear strength
average normalized
Young modulus
30 30 1038 0,1306 4,550 85,1 10-3 1,764
60 60 4151 0,1306 4,494 72,8 10-3 1,707
120 120 16589 0,1305 4,404 65,0 10-3 1,691
240 240 66580 0,1306 4,278 63,610-3 1,691
ASSEMBLIES WITH WALLS
Effect of size on the shear strength & Young modulus:
modified assemblies to have the same coordination number:
Conclusion: increasing size slightly increasing stiffness ( 0,8 % )
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# of particles porosity
average coord.
number
average normalized
pressure
average normalized
shear strength
average normalized
Young modulus
30 30 1038 4,491 87,2 10-3 0,536
60 60 4151 4,491 71,9 10-3 0,537
120 120 16589 4,491 63,5 10-3 0,540
ASSEMBLIES WITH WALLS
The problem of DEM modeling: to fill up the same domain with increasing number of grains
Sample preparation:
size 240 240 size 240 240 size 240 240 size 240 240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of 66 600 grains 16 600 grains 4150 grains 1040 grains grain size 1 grain size 2 grain size 4 grain size 8
the same porosity 19 / 21
ASSEMBLIES WITH WALLS
The problem of DEM modeling : to fill up the same domain with increasing number of grains
Shear strength:
Conclusion: increasing number of grains slightly decreasing strength20 / 21
# of particles porosityaverage coord.
number
average normalized
pressure
average normalized
shear strength
average normalized
Young modulus
240 240 1038 0,1306 4,550 85,1 10-3 1,764 0,485
240 240 4151 0,1306 4,494 72,8 10-3 1,707 0,502
240 240 16589 0,1305 4,404 65,0 10-3 1,691 0,502
240 240 66580 0,1306 4,278 63,610-3 1,691 0,464
SUMMARY
Size effect on shear strength
a few thousand hundred thousandsdiscrete elements discrete elements: the shear strength decreases only a few %
Size effect on stiffness
a few thousand hundred thousandsdiscrete elements discrete elements:
negligible increase of the stiffness
Our message for DEM simulations:
use at least a few thousand elements; and then
DO NOT WORRY ABOUT THE SIZE EFFECT
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SUMMARY
Our doubts
The size effect is perhaps more significant for
non-circular elements?
anisotropic arrangements?
samples deposited under gravity?
TO BE CONTINUED
Acknowledgements: OTKA 48998, Bolyai grant 22 / 21
