IHPC-IMS Program on Advances & Mathematical Issues in Large Scale Simulation (Dec Mar 2003 & Oct - Nov 2003) Seminar: Multiscale Modeling of Heterogeneous Granular Systems Alberto M. Cuitiño Mechanical and Aerospace Engineering Rutgers University Piscataway, New Jersey Institute of High Performance Computing Institute for Mathematical Sciences, NUS

Singapore 2003 cuiti ñ Collaborators Gustavo Gioia Shanfu Zheng

Singapore 2003 cuiti ñ 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 Rutgers University 1766 Rutgers Founded as Queens College 1864 Named New Jerseys Land Grant College 1989 Rutgers is elected into Association of American Universities RU 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 1869 First American College Football Game, (6) Rutgers vs. Princeton (4) 1914 School of Engineering Named Separate School 1956 The Colleges and Schools of Rutgers Become the State University of New Jersey

Singapore 2003 cuiti ñ Rutgers University Philadelphia NYC New Brunswick Camden Newark

Singapore 2003 cuiti ñ College Ave Livignston Douglass Busch Rutgers, New Brunswick Cook

Singapore 2003 cuiti ñ Rutgers, Busch Stadium Golf Science and Engineering Hairston Leads Rutgers Past Navy SEPTEMBER 27, 2003

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

Singapore 2003 cuiti ñ 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 cuiti ñ 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 2x10 7 A/cm², temperature 230°C) Thomas Göbel

Singapore 2003 cuiti ñ E 0, V T Schimschak and Krug, 2000

Singapore 2003 cuiti ñ Grain Boundary Effects Grain 1Grain 2 VOID TRAPPINGD TRAPPING by GRAIN BOUNDARY Initial Defect VOID MOTIOND GRAIN BOUNDARY VOID RELEASE RELEASE From GRAIN BOUNDARY e-e- Atkinson and Cuitino 03

Singapore 2003 cuiti ñ Goal 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 Load Need for MULTISCALE Study PARTICLES POWDERS (discrete) (continuum)

Singapore 2003 cuiti ñ Background Macroscopic Compaction Curve 1 st Stage 2 nd Stage Compaction Force 3 rd Stage 0 th Stage

Singapore 2003 cuiti ñ Stages Mixing Die Filling Rearrangement Large Deformation Localized Deformation

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

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

Singapore 2003 cuiti ñ Die Filling Numerical Experimental Cohesion No Cohesion Open Configuration Dense Configuration

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

Singapore 2003 cuiti ñ Rearrangement Video Imaging Glass Beads, Diameter = 1.2 mm Gioia and Cuitino, 1999 Increasing Pressure 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 Al 2 O 3 Granules. Diameter = 30 microns Lannutti, 1997 Punch

Singapore 2003 cuiti ñ A physical description Energy landscape exhibits a Spinoidal Structure (nonconvex) H H Convexification implies coexistence of two phases H Total

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

Singapore 2003 cuiti ñ Relaxation process Numerical Experimental

Singapore 2003 cuiti ñ Experiments and Theory Al 2 O 3 Theoretical Experimental Kong et al., 1999

Singapore 2003 cuiti ñ 2D: simulation and experiment

Singapore 2003 cuiti ñ Rearrangement Front Experiment Simulation

Singapore 2003 cuiti ñ Grains

Singapore 2003 cuiti ñ 2D Simulations (Size Distribution)

Singapore 2003 cuiti ñ 3D Simulations

Singapore 2003 cuiti ñ Mueth, Jaeger, Nagel 2000 Comparison with Experiment Experiment Simulation

Singapore 2003 cuiti ñ Further Predictions Experiment Simulation

Singapore 2003 cuiti ñ Force Frequency High force frequency near average; Decay quickly beyond the average force. Decay slope increase with the applied force.

Singapore 2003 cuiti ñ Particle Rearrangement 3D Homogeneous particle size; r = 0.5 mm; Particles = 120,991

Singapore 2003 cuiti ñ Quantitative Predictions Rearrangement front; Density increase; Relative movement stops; Contact number increase;

Singapore 2003 cuiti ñ Heterogeneous System (Same Material) Without rearrangementAfter rearrangement Log-normal distribution; d = 2.16 ~ 9.10 mm; particles=13,134

Singapore 2003 cuiti ñ Multiphase Systems

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

Singapore 2003 cuiti ñ 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) A quasi-continuum approach FEM MeshSet of Particles Combined System Granular Quasi-Continuum

Singapore 2003 cuiti ñ Governing Equations PVW Euler Equation Local Equilibrium

Singapore 2003 cuiti ñ Nomenclature umum rmrm rnrn r mn RmRm RnRn R mn Particle m Particle n

Singapore 2003 cuiti ñ 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 cuiti ñ 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 cuiti ñ Role of FF parameters: hardening Effect of hardening parameter n is significant; Soft material (n ) is easy to be solidified.

Singapore 2003 cuiti ñ Role of FF parameters: Poissons ratio

Singapore 2003 cuiti ñ Case of Study: Multiphase System

Singapore 2003 cuiti ñ Spatial Distribution Phase I Variant 1 Phase I Variant 2 Phase I Variant 3

Singapore 2003 cuiti ñ Spatial Distribution Phase II Variant 1-4

Singapore 2003 cuiti ñ Spatial Distribution Phase III Needs an uniform distribution

Singapore 2003 cuiti ñ Multiphase System Rearrangement Full mixed + Cohesion force

Singapore 2003 cuiti ñ Multiphase System Post-Rearrangement Input for GQC

Singapore 2003 cuiti ñ Calibration of FF

Singapore 2003 cuiti ñ Multiphase System Comparison with Experiment 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. MACROSCOPIC Behavior

Singapore 2003 cuiti ñ Multiphase System: effect of sample size

Singapore 2003 cuiti ñ Multiphase System: density evolution Movie Here Full Field Predictions

Singapore 2003 cuiti ñ Multiphase System: pressure evolution Movie Here

Singapore 2003 cuiti ñ Granular Quasi-Continuum Allows for explicit account of the particle level response on the effective behavior of the powder Provides estimates of global fields such as stress, strain density Is numerically efficient, can also be improved by using stochastic integration Provides variable spatial resolution Is not well posed to handle large non- affine motion of particles Particle deformation is only considered in an approximate manner (as in PD/DEM) GOOD BAD

Singapore 2003 cuiti ñ Towards Computationally Aided Material Design FORCE PARAMETERS NANO COMPOSITE PARAMETERS MICRO SCALE ACCEPATLE MAXIMUM PORE SIZE PORE SIZE ACCEPTABLE RANGE OF FORCE PARAMTERS ACCEPTABLE RANGE OF NANOCOMPOSITE PARAMETERS TO NANO SCALE

Singapore 2003 cuiti ñ Summary and conclusions Powder compaction is a complex process where many dissimilar entities (particles) consolidate by various concurrent mechanisms. In the low pressure regime, rearrangement and localized particle deformation dominates the mechanical response. In this initial regime, compaction proceeds in a discontinuous fashion by an advancing front. The physics of the rearrangement can be traced to a spinoidal structure in the energy density of the system. This process can be theoretically described using the framework of non-convex analysis. The effect of particle deformability and die wall roughness are incorporated into the analysis in a clear and physical manner. Numerical simulations verify the theoretical model Experimental studies validate the model and simulations 3D simulations show a similar behavior that 2D ones, indicating the same physics operates in 2D and 3D cases.