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Seminar: Multiscale Modeling of Heterogeneous Granular Systems

Seminar: Multiscale Modeling of Heterogeneous Granular Systems. 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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Seminar: Multiscale Modeling of Heterogeneous Granular Systems

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  1. Seminar:Multiscale Modeling of Heterogeneous Granular Systems 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. 1869 First American College Football Game, (6) Rutgers vs. Princeton (4) 1914 School of Engineering Named Separate School 1970 University of Medicine and Dentistry Founded 2003 Richard L. McCormick 19th president of Rutgers 50,000 Students 10,000 Faculty and Staff 175 Academic Departments 1989 Rutgers is elected into Association of American Universities 1864 Named New Jersey’s Land Grant College 1956 The Colleges and Schools of Rutgers Become the State University of New Jersey Rutgers 1. Harvard University 2. William and Mary 3. Yale University 4. Princeton University 5. Columbia University 6. University of Pennsylvania 7. Brown University 8. Rutgers University (1766) 9. Dartmouth 1766 Rutgers Founded as Queen’s College Rutgers University RU Singapore 2003 cuitiño@rutgers

  4. Newark New Brunswick NYC Camden Philadelphia Rutgers Rutgers University Singapore 2003 cuitiño@rutgers

  5. College Ave Livignston Busch Douglass Cook Rutgers, New Brunswick Singapore 2003 cuitiño@rutgers

  6. Hairston Leads Rutgers Past Navy 48-27SEPTEMBER 27, 2003 Golf Stadium Science and Engineering Rutgers, Busch Singapore 2003 cuitiño@rutgers

  7. Doyle D. Knight Michael R. Muller Timothy Wei Abdelfattah M.G. Zebib Norman J. Zabusky Jerry Shan Tobias Rossman S. Bachi Fluid Mechanics Haym Benaroya William Bottega Alberto Cuitiño Mitch Denda Ellis Dill Andrew Norris Kook Pae Assimina Pelegri George Weng Solids, Materials and Structures Zhixiong (James) Guo Yogesh Jaluria Constantine E. Polymeropoulos Kyung T. Rhee Stephen D. Tse Haim Baruh Hae Chang Gea Noshir A. Langrana Constantinos Mavroidis Madara M. Ogot Dajun Zhang Thermal Sciences Design and Dynamics Entrance Rutgers, Mechanical and Aerospace Rutgers, Engineering Singapore 2003 cuitiño@rutgers

  8. Current Research • Granular Systems (G. Gioia and S. Zheng) • Crystal Plasticity • Multiscale Modeling • Foam Mechanics • Folding of Thin Films • Microelectronics • Digital Image Correlation • Computational Material Design (Ferroelectric Polymers) Support from NSF, DOE, DARPA, FAA, NJCST, IFPRI, CAFT is gratefully acknowledged Singapore 2003 cuitiño@rutgers

  9. Damage due to Electromigration in Interconnect Lines Sequence of pictures showing void and hillock formation in an 8µm wide Al interconnect due to electromigration (current density 2x107 A/cm², temperature 230°C) Thomas Göbel (t.goebel@ifw-dresden .de), 18.04.02 Singapore 2003 cuitiño@rutgers

  10. Schimschak and Krug, 2000 Schimschak and Krug, 2000 E  0, s = 0 V T Singapore 2003 cuitiño@rutgers

  11. Grain Boundary Effects VOID MOTION @ GRAIN BOUNDARY Initial Defect Grain 1 Grain 2 VOID RELEASE From GRAIN BOUNDARY VOID TRAPPING by GRAIN BOUNDARY e- Atkinson and Cuitino ‘03 Singapore 2003 cuitiño@rutgers

  12. 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

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

  14. Stages Mixing Die Filling Rearrangement Large Deformation Localized Deformation Singapore 2003 cuitiño@rutgers

  15. Identifying Processes and Regimes • Early Consolidation • Pre-compression • Characteristics: • Limited relative motion of particles • Low particle acceleration • Same neighbors • Quasi-static • Low forces among particles • Small particle deformation (elastic) • Mixing • Transport • Granulation • Characteristics: • Large relative motion of particles • Differential acceleration between particles • Large number of distinct neighbors • Low forces among particles • Long times, relatively slow process • Quasi steady state • Discharge • Die Filling • Vibration • Characteristics: • Large relative motion of particles • Differential acceleration between particles • Large number of distinct neighbors • Low forces among particles • Short times • Transient • Consolidation • Characteristics: • No relative motion of particles • Low acceleration • Same neighbors • Quasi-static • Sizable forces among particles • Small particle deformation (elastic + plastic) • Compact Formation • Characteristics: • No relative motion of particles • Low acceleration • Same neighbors • Quasi-static • Large forces among particles • Large particle deformation Singapore 2003 cuitiño@rutgers

  16. Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Pre-compression PD/DEM/MC Mixing Transport Granulation PD/DEM/MC Discharge Die Filling Vibration PD/DEM/MC Ballistic Deposition Consolidation GCC Compact Formation GQC Numerical tools appropriate for process OUR SCOPE Singapore 2003 cuitiño@rutgers

  17. Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Pre-compression PD/DEM/MC Mixing Transport Granulation PD/DEM/MC Discharge Die Filling Vibration PD/DEM/MC Ballistic Deposition Consolidation GCC Compact Formation GQC Numerical tools appropriate for process OUR SCOPE Singapore 2003 cuitiño@rutgers

  18. Die Filling Cohesion No Cohesion Open Configuration Dense Configuration Numerical Experimental Numerical Experimental Singapore 2003 cuitiño@rutgers

  19. Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Pre-compression PD/DEM/MC Mixing Transport Granulation PD/DEM/MC Discharge Die Filling Vibration PD/DEM/MC Ballistic Deposition Consolidation GCC Compact Formation GQC Numerical tools appropriate for process OUR SCOPE Singapore 2003 cuitiño@rutgers

  20. Rearrangement • 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

  21. A physical description Convexification implies coexistence of two phases Energy landscape exhibits a Spinoidal Structure (nonconvex) Total H H  H Singapore 2003 cuitiño@rutgers

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

  23. Relaxation process Numerical Experimental Singapore 2003 cuitiño@rutgers

  24. Experiments and Theory Experimental Kong et al., 1999 Theoretical Al2O3 Singapore 2003 cuitiño@rutgers

  25. 2D: simulation and experiment Singapore 2003 cuitiño@rutgers

  26. Rearrangement Front Simulation Experiment Singapore 2003 cuitiño@rutgers

  27. “Grains” Singapore 2003 cuitiño@rutgers

  28. 2D Simulations (Size Distribution) Singapore 2003 cuitiño@rutgers

  29. 3D Simulations Singapore 2003 cuitiño@rutgers

  30. Comparison with Experiment Mueth, Jaeger, Nagel 2000 Simulation Experiment Singapore 2003 cuitiño@rutgers

  31. Further Predictions Simulation Experiment Singapore 2003 cuitiño@rutgers

  32. Particle Rearrangement 3D • Homogeneous particle size; • r = 0.5 mm; • Particles = 120,991 Singapore 2003 cuitiño@rutgers

  33. Quantitative Predictions • Rearrangement front; • Density increase; • Relative movement stops; • Contact number increase; Singapore 2003 cuitiño@rutgers

  34. Heterogeneous System(Same Material) • Log-normal distribution; d = 2.16 ~ 9.10 mm; particles=13,134 Without rearrangement After rearrangement Singapore 2003 cuitiño@rutgers

  35. Multiphase Systems Singapore 2003 cuitiño@rutgers

  36. Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Pre-compression PD/DEM/MC Mixing Transport Granulation PD/DEM/MC Discharge Die Filling Vibration PD/DEM/MC Ballistic Deposition Consolidation GCC Compact Formation GQC Numerical tools appropriate for process OUR SCOPE Singapore 2003 cuitiño@rutgers

  37. Granular Quasi-Continuum Combined System FEM Mesh Set of Particles A quasi-continuum approach Constrain kinematics of the particles by overimposing a displacement field described by a set of the displacements in a set of points (nodes) and a corresponding set of interpolation functions (a FEM mesh) Singapore 2003 cuitiño@rutgers

  38. Governing Equations PVW Euler Equation Local Equilibrium Singapore 2003 cuitiño@rutgers

  39. Force Fields • Elastic contact follows Hertz contact law; • Plastic deformation follows similarity solution; Contacts on each particle are independent. • Volume change after inter-particle voids are filled in. Singapore 2003 cuitiño@rutgers

  40. Role of FF parameters - y • Effect of yielding stress is significant; • Lower y yield higher deformation under the same pressure and thus higher density; • Solidification force differ significantly but the solidification density relative unchange. Singapore 2003 cuitiño@rutgers

  41. Role of FF parameters: hardening • Effect of hardening parameter n is significant; • Soft material (n) iseasy to be solidified. Singapore 2003 cuitiño@rutgers

  42. Role of FF parameters:Poisson’s ratio Singapore 2003 cuitiño@rutgers

  43. Case of Study: Multiphase System Singapore 2003 cuitiño@rutgers

  44. Spatial Distribution Phase I Variant 1 Phase I Variant 2 Phase I Variant 3 Singapore 2003 cuitiño@rutgers

  45. Spatial Distribution Phase II Variant 1-4 Singapore 2003 cuitiño@rutgers

  46. Spatial Distribution Phase III Needs an uniform distribution Singapore 2003 cuitiño@rutgers

  47. Multiphase SystemRearrangement Full mixed + Cohesion force Singapore 2003 cuitiño@rutgers

  48. Multiphase SystemPost-Rearrangement Input for GQC Singapore 2003 cuitiño@rutgers

  49. Calibration of FF Singapore 2003 cuitiño@rutgers

  50. Multiphase SystemComparison with Experiment MACROSCOPIC Behavior • Density diversity at initial state is mainly due to the irregular shape of real particles; • At early stage of experiment the deformation is the mainly from the particle rearrangement. Singapore 2003 cuitiño@rutgers

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