Implementation of Nano-mechanics in Geotechnical

Engineering

Hyungrae ChoAnd

Chung R. Song

Department of Civil EngineeringThe University of Mississippi

University, MS 38677

Introduction Background Nano-mechanics Tentative Results Conclusions

Contents

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Introduction

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, 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)

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TorsionBend AngleStretch BondVDWCoulTotal EEEEEE

21 )( oStretch Bond rrkE

ji ij

ji

oCoul r

qqeE

4

2

ji ij

o

ijoVDW r

R

r

RoDE

612

2

Well developed.

Theoretical Background (Traditional Continuum Mechanics)

n

n

nt

n

nn

W

U

t

K

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

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Well developed.

Most things are smeared into the equilibrium equation.

-Elasticity, Plasticity, grain rotation, grain interaction, damage, …..

Theoretical Background (Advantages/Disadvantages)

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Items Advantages Disadvantages

Nano-mechanics

Capture detailed Information

Need minimal input data

Paramount amount of computation.

Unfamiliar theory to common engineers

Conti-nuum mechanics

Capture averaged real scale behavior.

Familiar theory

Difficult to capture detailed information Need to bridge Nano-

Mechanics and Continuum Mechanics

Theoretical Background Bridging Nano- and Continuum-

(Equivalent frame element method)

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fKu

Li and Chou (2003)

Odegard et al. (2001)

Ostoja-Starzewski, (2002)

2

21

)(2

1

)(

LL

EAE

rrkE

stretchaxial

oStretch Bond

Ansys

Theoretical Background Bridging Nano- and Continuum-

(RVE method)

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v

AdVV

A1

A: Properties in molecular level

A’: Properties in continuum level

DPD: Maiti et. al. (2004)

Voyiadjis et al. (2004)

Theoretical Background Bridging Nano- and Continuum-

for soils

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•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)

Particulate

Mechanics

(Mesoscale)

Continuum

Mechanics

(Macroscale)

Tentative Results(Surface charge of clay minerals)

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Muscovite:

-194.165 kcal/mol

Montmorillonite:

-65604 kcal/mol

Kaolinite:

-162.832 kcal/mol

Tentative Results(Properties of muscovite)

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Elastic Constants (GPa)

_______________________

397.3 341 453.2 -1.847e-010 15.78 8.953e-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-011 238.3 5.689e-012 -71.75

15.76 -102.7 -40.46 -2.078e-010 123.5 -7.194e-010

-7.529e-012 8.329e-012 -1.61e-011 -71.75 7.336e-012 229.5

Tentative Results(Properties of Quartz-beta)

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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 0.02657 0.004098 0.1255 40.33

Tentative Results(Bridging nano- and micro using DEM)

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Particulate Mechanics

DEM: φ = 26.5o

for e=0.763

Molecular Mechanics: E=104 GPa

μ=0.1061

Continuum?

Continuum Mechanics

FEM:

What can we do?

Conclusions/Remarks

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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