Implementation of Nano-mechanics in
Geotechnical Engineering
Hyungrae Cho
And
Chung R. Song
Department of Civil Engineering
The University of Mississippi
University, MS 38677
Contents
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Introduction
Background
Nano-mechanics
Tentative Results
Conclusions
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Introduction
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The macro-scale material behavior is a representation
of the average micro-scale material behavior.
The micro-scale material behavior is a representation
of the average molecular-scale (Nano- scale) material
behavior.
By obtaining molecular-scale material properties, the
macro-scale material behavior is obtained,
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with limited input parameters and
with great accuracy and details.
With the blooming Nano-technology, molecular-scale
material properties have more importance than ever.
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Theoretical Background
(Traditional MM, MD, NM)
ETotal  ECoul  EVDW  E Bond Stretch  E Angle Bend  ETorsion
ECoul 
EVDW
e2
4o

i j
qi q j
rij
6
  Ro  12
 Ro  
  Do     2  
i j
rij  
  rij 




E Bond Stretch  k1 (r  ro )
Well developed.
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2
Theoretical Background
(Traditional Continuum Mechanics)
 K
n

t


 n
 n  U   n  


 W   n  
n t 

Where,
nK is the stiffness matrix, n is the coupling matrix,
n is the flow matrix, U is the incremental nodal displacement,
W is the incremental pore water pressure, t is the incremental time,
n
is the equilibrium force, and n is the flow vector
Well developed.
Most things are smeared into the equilibrium equation.
-Elasticity, Plasticity, grain rotation, grain interaction, damage, …..
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Theoretical Background
(Advantages/Disadvantages)
Items
Advantages
Disadvantages
Nano- Capture
mech detailed
anics Information
Need minimal
input data
Paramount
amount of
computation.
Unfamiliar
theory to
common
engineers
Continuum
mech
anics
Difficult to
capture
detailed
information
Capture
averaged real
scale behavior.
Familiar theory
Need to bridge NanoMechanics and Continuum
Mechanics
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Theoretical Background
Bridging Nano- and Continuum(Equivalent frame element method)
E Bond Stretch  k1 (r  ro ) 2
 E axial stretch
1 EA

(L) 2
2 L
Ku  f
Li and Chou (2003)
Odegard et al. (2001)
Ostoja-Starzewski, (2002)
Ansys
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Molecular potential energy =Strain energy
Theoretical Background
Bridging Nano- and Continuum(RVE method)
1
A   AdV
Vv
A: Properties in molecular level
A’: Properties in continuum level
Voyiadjis et al. (2004)
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DPD: Maiti et. al. (2004)
Theoretical Background
Bridging Nano- and Continuumfor soils
•Soil grains are continuum in Nano- to micro scale (sand
grains and clay minerals).
•But they are discrete media in macro scale (soil masss).
•Therefore, bridging b/t Nano-, micro, and macro scales for
soils shall be done as follows;
Molecular
Mechanics
(Nanoscale)
Particula
te
Continuum
Mechanics
Mechanic
s
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(Mesoscal
(Macroscale)
Tentative Results
(Surface charge of clay minerals)
Muscovite:
Montmorillonite:
Kaolinite:
-194.165 kcal/mol
-65604 kcal/mol
-162.832 kcal/mol
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Tentative Results
(Properties of muscovite)
Elastic Constants (GPa)
_______________________
397.3
341
453.2 -1.847e-010
341
503.4
459.4 3.126e-010
-102.7 -8.669e-010
453.2
459.4
672 5.684e-011
-40.49 -2.558e-010
-9.419e-012 -1.377e-011 -1.421e-011
15.76
-102.7
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238.3 5.689e-012
-40.46 -2.078e-010
-7.529e-012 8.329e-012 -1.61e-011
15.78 8.953e-010
-71.75
123.5 -7.194e-010
-71.75 7.336e-012
229.5
Tentative Results
(Properties of Quartz-beta)
Elastic Constants (GPa)
_______________________
103.8
11.6
12.28
0.02317
-0.01545
-2.309
11.48
103.9
12.25
0.1154
-0.05009
2.353
12.13
12.23
95.51
0.2123
-0.07562
0.1028
0.01682
-0.03887
-0.02016
46.08
-2.373
0.01008
-0.08894
-0.0679
-0.04894
-2.455
40.21
0.09949
-2.259
2.331
0.004098
0.1255
40.33
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0.02657
Tentative Results
(Bridging nano- and micro using DEM)
Continuum?
Molecular Mechanics:
E=104 GPa
Particulate Mechanics
Continuum Mechanics
μ=0.1061
DEM: φ = 26.5o
FEM:
for e=0.763
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What can we do?
Conclusions/Remarks
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With the aid of accessible software to Nano-mechanics,
material scientists can predict the detailed material
properties that was never possible in the past.
Application of Nano-mechanics to obtain the property of
macro-scale requires substantial computational efforts,
but it is impossible.
For soils bridging nano-, micro- and macro scales is
achieved by combination of molecular mechanics,
particular mechanics and continuum mechanics.
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Thank you for your attention.
Questions?
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