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

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

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

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, …..

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

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

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)

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)

Tentative Results (Surface charge of clay minerals) Olemiss Civil Engineering Muscovite: kcal/mol Montmorillonite: kcal/mol Kaolinite: kcal/mol

Tentative Results (Properties of muscovite) Olemiss Civil Engineering Elastic Constants (GPa) _______________________ e e e e e e e e e e e e e e e e

Tentative Results (Properties of Quartz-beta) Olemiss Civil Engineering Elastic Constants (GPa) _______________________

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= Continuum? Continuum Mechanics FEM: What can we do?

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

Thank you for your attention. Questions? Olemiss Civil Engineering