1. Implementation of Nano-mechanics in Geotechnical Engineering Hyungrae Cho And Chung R. Song Department of Civil Engineering The University of Mississippi University, MS 38677

2. Introduction Background Nano-mechanics Tentative Results Conclusions Contents Olemiss Civil Engineering

3. 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. Olemiss Civil Engineering

4. Theoretical Background (Traditional MM, MD, NM) Olemiss Civil Engineering Well developed.

5. Theoretical Background ( Traditional Continuum Mechanics) Where, n K 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 Olemiss Civil Engineering Well developed. Most things are smeared into the equilibrium equation. -Elasticity, Plasticity, grain rotation, grain interaction, damage, …..

6. Theoretical Background (Advantages/Disadvantages) Olemiss Civil Engineering ItemsAdvantagesDisadvantages Nano- mech anics Capture detailed Information Need minimal input data Paramount amount of computation. Unfamiliar theory to common engineers Conti- nuum mech anics Capture averaged real scale behavior. Familiar theory Difficult to capture detailed information Need to bridge Nano- Mechanics and Continuum Mechanics

7. Theoretical Background Bridging Nano- and Continuum- (Equivalent frame element method) Olemiss Civil Engineering Molecular potential energy =Strain energy Li and Chou (2003) Odegard et al. (2001) Ostoja-Starzewski, (2002) Ansys

8. Theoretical Background Bridging Nano- and Continuum- (RVE method) Olemiss Civil Engineering A: Properties in molecular level A’: Properties in continuum level DPD: Maiti et. al. (2004) Voyiadjis et al. (2004)

9. Theoretical Background Bridging Nano- and Continuum- for soils Olemiss Civil Engineering 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 Mechanic s (Mesoscal e) Continuum Mechanics (Macroscale)

10. Tentative Results (Surface charge of clay minerals) Olemiss Civil Engineering Muscovite: -194.165 kcal/mol Montmorillonite: -65604 kcal/mol Kaolinite: -162.832 kcal/mol

11. Tentative Results (Properties of muscovite) Olemiss Civil Engineering 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

12. Tentative Results (Properties of Quartz-beta) Olemiss Civil Engineering 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

13. Tentative Results (Bridging nano- and micro using DEM) Olemiss Civil Engineering Particulate Mechanics DEM: φ = 26.5 o for e=0.763 Molecular Mechanics: E=104 GPa μ=0.1061 Continuum? Continuum Mechanics FEM: What can we do?

14. Conclusions/Remarks l With the aid of accessible software to Nano-mechanics, material scientists can predict the detailed material properties that was never possible in the past. l Application of Nano-mechanics to obtain the property of macro-scale requires substantial computational efforts, but it is impossible. l For soils bridging nano-, micro- and macro scales is achieved by combination of molecular mechanics, particular mechanics and continuum mechanics. Olemiss Civil Engineering

15. Thank you for your attention. Questions? Olemiss Civil Engineering