1 / 42

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

jasper
Download Presentation

Tutorial I: Mechanics of CONFINED Granular Solids

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related