Tutorial II: Modeling and Simulation Techniques for Granular Materials

1. Tutorial II:Modeling and Simulation Techniques for Granular Materials 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. ContextCascade of Length and Time Scales Sub-particle Resolution Range Supra-particle Resolution Range Effective Behavior Design Models Highly Confined Flow Consolidation Particle deformation Sintering Time Scale (particle size/wave speed) > 106 Continuum Particle Packing Particle Rearrangement Particle Mixing Granulation Early Consolidation Mesoscopic Models 105-106 Particle Contact Stress Concentration Internal Localization Fracture Particle Dynamics Discrete Element Monte Carlo 104-105 Bonding Energies Activation Barrier Phase Transformations Phase Fields Fast Fourier FEM 102-103 Atomistics Molecular Dynamics 10-1-102 Length Scale (particle size) 101 - 102 103 to 106 particles 102 - 103 106 to 109 particles 10-3 - 100 One or less 100 - 101 1 to 103 particles >103 Too many Singapore 2003 cuitiño@rutgers

4. OUTPUT Large regions / Long times Global Constrains (shapes, friction) Good for component DESIGN* OUTPUT Limited to small regions and/or Short Times Particle Dynamics Discrete Element Monte Carlo Continuum INPUT From: Parameter fitting with macroscopic experiments Supra-Particle Resolution GAP INPUT From sup-particle resolution simulations (Multiscale) From DIRECT Experimental Particle-Level Studies(Higashitani, Granick, …) * If a “good”constitutive relation is provided Singapore 2003 cuitiño@rutgers

5. Aside: MD/DEM Domain Computation Time/Physical Time PROPORTIONALpressure*number of particles/particle size Ct/Pt PROPORTIONAL p*n/d n n Constant Ct/Pt Constant Ct/Pt Volume Sample = Vo e.g. = 1mm3 Volume Sample = Vo 1003 Volume Sample = V = Vo /1,000,000,000 e.g. V = 1mm3 Volume Sample = V = Vo /1,000 103 p d 100 10-9 100 10-6 Po (mixing range) P = 103 Po (consolidation range) Singapore 2003 cuitiño@rutgers

6. Aside: PD/DEM Domain Computation Time/Physical Time PROPORTIONALpressure*number of particles/particle size Ct/Pt PROPORTIONAL p*n/d PRESSURE Case 1a: Constant Ct/Pt (for example, 1 CPU hour/ 1 second of physical time) Constant particle size If pressure is increased 1,000 the sample size is decreased 1,000 times (for example, from 1mm3 to 100mm3) Case 1b: Constant sample size (for example, 1mm3) Constant physical time (for example 1 second) Constant particle size If pressure is increased 1,000 the Computational time is increased by 1,000 times (for example, 1 CPU hour to 1.5 CPU month) PARTICLE SIZE Case 2a: Constant Ct/Pt (for example, 1 CPU Hour/ 1 second of physical time) Constant pressure If particle size is reduced by 1,000 the sample size is decreased 109 times (for example, from 1mm3 to 1mm3) Case 2b: Constant sample size (for example, 1mm3) Constant physical time (for example 1 second) Constant pressure If particle size is reduced by 1,000 the Computational time is increased 109 times (for example, 1 CPU Hour to 116,000 CPU years) High pressures and small particles conspired against PD/DEM simulations Singapore 2003 cuitiño@rutgers

7. OUTPUT Limited to small regions and/or Short Times GRANULAR QUASI CONTINUUM INPUT From: Parameter fitting with macroscopic experiments Supra-Particle Resolution OUTPUT Large regions / Long times Global Constrains (shapes, friction) Good for component DESIGN* Particle Dynamics Discrete Element Monte Carlo Continuum INPUT From sup-particle resolution simulations (Multiscale) From DIRECT Experimental Particle-Level Studies(Higashitani, Granick, …) * If a “good”constitutive relation is provided Singapore 2003 cuitiño@rutgers

8. 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) Granular Quasi-Continuum BAD GOOD Singapore 2003 cuitiño@rutgers

9. 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

10. 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

11. Continuum with Microstructure Numerical Strategies for assembly of particles Continuum Plasticity models for frictional materials such as Drucker-Prager Discrete Molecular Dynamics Discrete Element Method Singapore 2003 cuitiño@rutgers

12. Continuum with Microstructure Cyclic Singapore 2003 cuitiño@rutgers

13. Granular Quasi Continuum PARTICLES POWDERS (discrete) (continuum) Numerical Strategies for assembly of particles Continuum Plasticity models for frictional materials such as Drucker-Prager Discrete Molecular Dynamics Discrete Element Method Continuum with Microstructure Singapore 2003 cuitiño@rutgers

14. 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

15. Particle m um Rmn Particle n rm rmn Rn Rm rn Nomenclature Singapore 2003 cuitiño@rutgers

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

17. Constrained Kinematics Displacement Field is constrained by the selection of the mesh Displacement of particle m Displacement of Node a Relative Displacement of particle m with respect to particle n Singapore 2003 cuitiño@rutgers

18. Discrete Version Singapore 2003 cuitiño@rutgers

19. Local/Non-local Formulation u u*(hm) d u*(hn) u(hm) u(hn) h hm hn Singapore 2003 cuitiño@rutgers

20. Additional relaxation by adding internal nodes Still within the framework of FEM Additional Freedom/Mesh Adaption Indicator Singapore 2003 cuitiño@rutgers

21. Load Paths Singapore 2003 cuitiño@rutgers

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

23. Simulations Pre-rearrangement Singapore 2003 cuitiño@rutgers

24. Simulations Post-rearrangement Singapore 2003 cuitiño@rutgers

25. Macroscopic Behavior Singapore 2003 cuitiño@rutgers

26. Macroscopic Behavior RED – Group I BLUE – Group II Singapore 2003 cuitiño@rutgers

27. Macroscopic Behavior RED – Group I BLUE – Group II Singapore 2003 cuitiño@rutgers

28. Comparison with Experiment Simulation Experiment Singapore 2003 cuitiño@rutgers

29. Adjusting Force Fields Experimental Numerical Lactose 1.5% PEG 0.5% Glycerin (Courtesy of P&G P. Mort and M. Roddy) Elastic Properties Plastic Properties Fracture Properties SURFACE PROPERTIES BULK PROPERTIES Singapore 2003 cuitiño@rutgers

30. Numerical StudiesUnit Cell Approach Singapore 2003 cuitiño@rutgers

31. Numerical StudiesYield Stress Effects Singapore 2003 cuitiño@rutgers

32. Numerical StudiesYoung Modulus Effects Singapore 2003 cuitiño@rutgers

33. Numerical StudiesHardening Effects Singapore 2003 cuitiño@rutgers

34. SolidMaterials Granulated Materials Materials HPDE (high density polyethylene) PEG 8000 (Polyethylene glycol) Lactose 1.5% PEG (binder) 0.5% Glycerin (lubricant) Singapore 2003 cuitiño@rutgers

35. Experimental Studies PEG 8000 PEG 3350 PEG 1450 Glycerin 0% 0.5% 1.0% 1.5% Singapore 2003 cuitiño@rutgers

36. Experimental StudiesGlycerin (Yield Stress) Singapore 2003 cuitiño@rutgers

37. Experimental StudiesPEG (Elastic Modulus + Hardening) Singapore 2003 cuitiño@rutgers

38. Future TO FROM • Specific applications • More validation • Pre die filling • Post ejection behavior, in particular bonding using the GQC Emerging trend in the material system design: using computer simulations to probe the space of best candidates for manufacturing. We have developed a basic framework capable of simulating the consolidation process, including: • die filling (with/without cohesion) • particle rearrangement in both 2D and 3D • powder densification in both 2D and 3D, with • materials with a wide range of elastic and plastic properties • powders with a wide range of size distributions • particle different shapes (by agglomeration of spherical particles) • wall friction • complex shapes • dynamic effects This approach will provide estimates of the local and global strength of the material by following the temperature and pressure dependent evolution of the bonding process Singapore 2003 cuitiño@rutgers