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Tutorial I: Mechanics of CONFINED Granular Solids

Tutorial I: Mechanics of CONFINED Granular Solids. Alberto M. Cuitiño Mechanical and Aerospace Engineering Rutgers University Piscataway, New Jersey cuitino@jove.rutgers.edu. IHPC-IMS Program on Advances & Mathematical Issues in Large Scale Simulation

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Tutorial I: Mechanics of CONFINED Granular Solids

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  1. Tutorial I:Mechanics of CONFINEDGranular Solids Alberto M. Cuitiño Mechanical and Aerospace Engineering Rutgers University Piscataway, New Jersey cuitino@jove.rutgers.edu IHPC-IMS Program on Advances & Mathematical Issues in Large Scale Simulation (Dec 2002 - Mar 2003 & Oct - Nov 2003) Institute of High Performance Computing Institute for Mathematical Sciences, NUS

  2. Collaborators • Gustavo Gioia • Shanfu Zheng Singapore 2003 cuitiño@rutgers

  3. Overview Macroscopic Compaction Curve Compaction Force 3rd Stage 1st Stage 2nd Stage 0th Stage Singapore 2003 cuitiño@rutgers

  4. Overview Die Filling Rearrangement Large Deformation Localized Deformation Singapore 2003 cuitiño@rutgers

  5. Pore Structure Increasing Pressure PEG 8000 Higher Magnification Singapore 2003 cuitiño@rutgers

  6. 1mm/sec 100mm/sec Visco-plastic material PEG 8000 Pore Structure Singapore 2003 cuitiño@rutgers

  7. 1mm/sec 100mm/sec HPDE Visco-elastic material Pore Structure Singapore 2003 cuitiño@rutgers

  8. Compact Properties PEG 1 mm/sec P PEG100 mm/sec P (N) HPDE1 mm/sec Brazilian Compression Test HPDE 100 mm/sec Singapore 2003 cuitiño@rutgers

  9. Goal Load Understand and quantitatively predict the MACROSCOPIC behavior of powder systems under compressive loading based on MICROSCOPIC properties such as particle/granule behavior and spatial arrangement PARTICLES POWDERS (discrete) (continuum) Need for MULTISCALE Study Singapore 2003 cuitiño@rutgers

  10. Die Filling Cohesion Vertical dropping Cohesion 2 degrees misalignment No cohesion Singapore 2003 cuitiño@rutgers

  11. Role of Cohesion on Die Filling Cohesion No Cohesion Open Configuration Dense Configuration Numerical Experimental Numerical Experimental Singapore 2003 cuitiño@rutgers

  12. Rearrangement Process(a discontinuous process, advancing front) • Process by which open structures collapse into dense configurations • Cohesive Powders are susceptible to rearrangement while • Non-Cohesive Powders are not X-Ray Tomography-Density Maps Al2O3 Granules. Diameter = 30 microns Lannutti, 1997 Punch Video Imaging Glass Beads, Diameter = 1.2 mm Gioia and Cuitino, 1999 Increasing Pressure Increasing Pressure Singapore 2003 cuitiño@rutgers

  13. Physical Description(a theoretical interpretation) Convexification implies coexistence of two phases Energy landscape exhibits a Spinoidal Structure (nonconvex) Total H H  H Singapore 2003 cuitiño@rutgers

  14. Energy Landscape Energy W=Wt+ Wf+ Ww+Wb Total Energy Wedging & Friction Inter-particle Energy (frozen initial configuration) Relaxation Energy (non-convex part) Singapore 2003 cuitiño@rutgers

  15. Relaxation Mechanism Particle Rearrangement Mechanism Snap-Through of Rings (Kuhn et al. 1991) Ring Structures in Cohesive Powders Numerical Experimental Singapore 2003 cuitiño@rutgers

  16. Rearrangement Singapore 2003 cuitiño@rutgers

  17. Non Convex Analysis Minimization with constrain (Lagrange Multiplier) Singapore 2003 cuitiño@rutgers

  18. Non Convex Analysis Effective Energy Density Singapore 2003 cuitiño@rutgers

  19. Density Evolution High Density Phase Transformation Front Low Density Phase Singapore 2003 cuitiño@rutgers

  20. Wall Friction Equilibrium in the current configuration Generalized Friction Coefficient Exponential decay from the transformation front Singapore 2003 cuitiño@rutgers

  21. Particle Deformability Deformability of High Density Phase Deformability of Low Density Phase Singapore 2003 cuitiño@rutgers

  22. Particle Deformability High Density Phase Low Density Phase Singapore 2003 cuitiño@rutgers

  23. Pressure Density Profiles Singapore 2003 cuitiño@rutgers

  24. Comparison with experiment Experimental Kong et al., 1999 Theoretical Al2O3 Singapore 2003 cuitiño@rutgers

  25. Compaction Curves Theoretical Experimental (Deis and Lannutti, 1998) fL = 0.4 fH = 2 Singapore 2003 cuitiño@rutgers

  26. Density Histograms Theoretical Experimental (Deis and Lannutti, 1998) Increasing pressure Singapore 2003 cuitiño@rutgers

  27. Effect of RH (low pressure) Experimental (Deis and Lannutti, 1998) Theoretical Low pressure range p = 0.14 MPa Unimodal Distribution Singapore 2003 cuitiño@rutgers

  28. Effect of RH (higher pressure) Experimental (Deis and Lannutti, 1998) Theoretical Higher deformability increases the transformed region at constant applied pressure Bimodal Distribution Singapore 2003 cuitiño@rutgers

  29. Preferred Term Other Systems with NC Energy THIN FILM BUCKLING Singapore 2003 cuitiño@rutgers

  30. Other Systems with NC Energy COMPRESSION OF FOAMS Structure Mechanical Response Gibson and Ashby, 1997 Singapore 2003 cuitiño@rutgers

  31. Implication: Heterogeneous Deformation Spinoidal Energy Landscape Singapore 2003 cuitiño@rutgers

  32. Comparison with Experiment Theory Theory Experiment Material Tested Polyurethane Foam Singapore 2003 cuitiño@rutgers

  33. Comparison with Experiment Singapore 2003 cuitiño@rutgers

  34. Experimental Evidence Singapore 2003 cuitiño@rutgers

  35. y x Surface Measurement Displacement field measurement using Digital Image Speckle Correlation (Wang, Gioia and Cuitino, 2001) Peters & Ranson (1982), Kahn-Jetter & Chu (1990) Vendroux & Knauss (1998) Zhang et al . (1999) Singapore 2003 cuitiño@rutgers

  36. G(X) U V g(x) Digital Image Speckle Correlation Gray scale values, G and g, characterize point in original and deformed images Actual Images Undeformed Minimization of Correlation function C provides deformation field Deformed (load step 2) where, U, V are the rigid body motion and Ux, Uy, Vx, Vy are the spatial gradients Singapore 2003 cuitiño@rutgers

  37. Digital Image Speckle Correlation Setup Computer with Frame Grabber CCD Camera Fiber Optic Light Source Loading System Specimen Singapore 2003 cuitiño@rutgers

  38. Displacement MapsProgressive Field Singapore 2003 cuitiño@rutgers

  39. Displacement MapsProgressive Field Singapore 2003 cuitiño@rutgers

  40. Comparison with Experiment Singapore 2003 cuitiño@rutgers

  41. Multiscale Modeling Cascade of length scales Singapore 2003 cuitiño@rutgers

  42. Simulation Singapore 2003 cuitiño@rutgers

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