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Implementation of Nano-mechanics in Geotechnical Engineering. Hyungrae Cho And Chung R. Song. Department of Civil Engineering The University of Mississippi University, MS 38677. Olemiss Civil Engineering. Contents. Introduction Background Nano-mechanics Tentative Results Conclusions.

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slide1
Implementation of Nano-mechanics in Geotechnical Engineering

Hyungrae Cho

And

Chung R. Song

Department of Civil Engineering

The University of Mississippi

University, MS 38677

slide2

Olemiss Civil Engineering

Contents

  • Introduction
  • Background
  • Nano-mechanics
  • Tentative Results
  • Conclusions
introduction

Olemiss Civil Engineering

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.
theoretical background traditional continuum mechanics

Olemiss Civil Engineering

Theoretical Background(Traditional Continuum Mechanics)

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, …..

theoretical background advantages disadvantages

Olemiss Civil Engineering

Theoretical Background(Advantages/Disadvantages)

Need to bridge Nano- Mechanics and Continuum Mechanics

theoretical background bridging nano and continuum equivalent frame element method

Olemiss Civil Engineering

Theoretical Background Bridging Nano- and Continuum-(Equivalent frame element method)

Li and Chou (2003)

Odegard et al. (2001)

Ostoja-Starzewski, (2002)

Ansys

Molecular potential energy =Strain energy

theoretical background bridging nano and continuum rve method

Olemiss Civil Engineering

Theoretical Background Bridging Nano- and Continuum-(RVE method)

A: Properties in molecular level

A’: Properties in continuum level

Voyiadjis et al. (2004)

DPD: Maiti et. al. (2004)

theoretical background bridging nano and continuum for soils

Olemiss Civil Engineering

Continuum

Mechanics

(Macroscale)

Particulate

Mechanics

(Mesoscale)

Molecular Mechanics

(Nanoscale)

Theoretical Background Bridging Nano- and Continuum-for 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;
tentative results surface charge of clay minerals

Olemiss Civil Engineering

Tentative Results(Surface charge of clay minerals)

Muscovite:

-194.165 kcal/mol

Kaolinite:

-162.832 kcal/mol

Montmorillonite:

-65604 kcal/mol

tentative results properties of muscovite

Olemiss Civil Engineering

Tentative Results(Properties of muscovite)

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

Olemiss Civil Engineering

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 0.02657 0.004098 0.1255 40.33

tentative results bridging nano and micro using dem

Olemiss Civil Engineering

Tentative Results(Bridging nano- and micro using DEM)

Continuum?

Molecular Mechanics: E=104 GPa

μ=0.1061

Continuum Mechanics

FEM:

What can we do?

Particulate Mechanics

DEM: φ = 26.5o

for e=0.763

conclusions remarks

Olemiss Civil Engineering

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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