1. FINITE ELEMENT ANALYSIS OF IN-CONTACT SPHERES 4 TH I NT. C ONFERENCE OF M ULTIPHYICS, L ILLE, F RANCE, 9-11 D EC 09 H. A. K HAWAJA (PhD Student, Dept. of Engineering) S. A. S COTT (Lecturer, Dept. of Engineering) K. P ARVEZ (Professor, Research Centre for Modelling & Simulation)

2. P OINTS FOR D ISCUSSION  B ACKGROUND  I NTRODUCTION  Normal Contact  Tangential Contact  F INITE E LEMENT A NALYSIS  Finite Element Modelling  Loading and Boundary Conditions  Finite Element Analysis Results  Comparison of Results with Available Models  S UMMARY & C ONCLUSION  REFERNCES  A CKNOWLEDGEMENTS H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 2

3. B ACKGROUND  Particle-particle interaction is observed in many physical phenomena; fluidized beds, particle kiln, etc.  Fluidized Bed VideoFluidized Bed Video  Kiln VideoKiln Video  Particle sizes may vary and can be classified using Geldart Classifications; Geldart A (20-100 µm), Geldart B (40-500 µm), Geldart C (20-30 µm), Geldart D (>600 µm).  Available models for contact are quite old. Their basis of development were experiments.  This work addresses:  To understand the phenomenon of interaction between spherical particles.  Validation of available models  Re-modelling of contact models, if required.  Extension to cases for which models is not available H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 3

4. I NTRODUCTION  Normal Contact: SPHERE 1 SPHERE 2 CONTACT CIRCLE H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 4 Caution: Exaggerated Animation for Understanding

5. I NTRODUCTION  Normal Contact:  Hertz Normal Contact Model (1882) JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge. H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 5 DOES NOT CATER FRICTIONAL FORCE HERTZ, H. (1882). Journal der rennin und angewandeten Mathematik, 92, 136

6. I NTRODUCTION  Tangential Contact: SPHERE 1 SPHERE 2 CONTACT CIRCLE H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 6 Caution: Exaggerated Animation for Understanding

7. I NTRODUCTION  Tangential Contact Force:  Mindlin & Dresewicz (MD) Contact Model (1953) H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 7 JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge. MINDLIN, R. (1953). Journal of Applied Mechanics, 20, 327. Normal force and contact area is computed using Hertz (1882) model Whenever there is change in normal traction it will bring change in tangential traction and if that change is more than the product of coefficient of friction and normal traction slip will occur. There is annulus of slip that progresses concentrically inwards. When slip occurs then the product of normal traction and coefficient of friction will be equal to tangential traction. At the annulus of slip there is tangential displacement that can be calculated by mathematical relations. Contact parameters are computable if every previous step of loading is known from the equilibrium state. HISTORY DEPENDENT !!!!!!!!!!!!!!!!!!!!!!!!! VERY VERY EXPENSIVE IN COMPUTATIONS

8. F INITE E LEMENT M ODELLING H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 8  Finite Element Mesh:  Part of sphere is modelled to reduce number of elements  Mesh sensitivity analysis is carried out to ensure the quality of results  Parameters taken for analysis are as follows: ParameterValues Radius of Sphere0.1m Modulus of Elasticity70GPa Poisson Ratio0.3 Coefficient of Friction0.2 Solid ElementSolid 186, 20-Noded Hexahedral Solid Element Contact ElementContac 174, 8-Noded Surface to Surface Quadrilateral 3-D Contact Element Target ElementTarge 170, 8-Noded Surface to Surface Quadrilateral 3-D Target Element

9. H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 9 F INITE E LEMENT M ODELLING  Loading and Boundary Conditions:  Loading Locations  Normal Loading Only  Normal and Tangential Loading Combined

10. H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 10 F INITE E LEMENT M ODELLING  Finite Element Analysis Results:  Contact Pressure (Normal & Tangential Contact) In accordance with as defined by Hertz (1882)

11. H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 11 F INITE E LEMENT M ODELLING  Finite Element Analysis Results:  Frictional Stress (Tangential Contact) Traction profile is not exactly depicted by MD (1953). It is axisymmetric in sliding region and non-axisymmetric in stick region, which conflicts with their theory.

12. H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 12 F INITE E LEMENT M ODELLING  Finite Element Analysis Results:  Contact Status (Tangential Contact) In case of full sliding, Frictional force is Frictional Constant multiplied with Normal Force (μN). In case of partial sliding, Frictional Force has to be computed and cases could be very complicated.

13. F LUIDIZED B ED H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 13 F INITE E LEMENT M ODELLING  Comparison of Results with Available Models:  Normal Contact Force with Hertz Model (1882)  Tangential Contact Force with MD Model (1954)

14. S UMMARY & C ONCLUSION H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 14  Summary:  Normal Contact Model given by Hertz (1882)  Tangential Contact Force given by MD (1954)  Setting up FEM Contact Simulation  Comparison of results  Conclusion:  Contact Pressure and Normal Contact Force is in agreement with the Hertz (1882) Normal Contact Model  Frictional Stress Contour doesn't match with MD (1953). However, Frictional Force is in agreement with the model.

15. F UTURE W ORK H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 15  Tangential Contact Model needs to refined to support extensive computations  Removal of Historical Dependency  Simplification of mathematical process  FEA of contact model for 2-D Tangential Motion  Development of numerical model for 2-D Tangential Motion

16. R EFERENCES H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 16 ANSYS® Multiphysics FEM Package, Release 11.0 ANSYS® Technical Manuals, Release 11.0 Documentation for ANSYS® CUNDALL, P., STRACK, O. (1979). Geotechnique, 29,47. HERTZ, H. (1882). Journal der rennin und angewandeten Mathematik, 92, 136. JAEGER, J. (2205) New Solutions in Contact Mechanics, WIT Press Southampton, Boston. JOHNSON, K., ed. (1984). Contact Mechanics. Cambridge University Press, Cambridge. LIAN, G., THORNTON, C., KAFUI, D. (1998) TRUBAL, Aston University, Brimingham, UK. MINDLIN, R. (1953). Journal of Applied Mechanics, 20, 327. SCOTT, S., MUELLER, C., (2009) PONG3-D, University of Cambridge, UK. THORNTON, C., YIN, K., K. (1991) Powder Technology, 65, 155. TSUJI, Y., TANAKA, T., ISHIDA, T. (1992) Powder Technology, 71, 239. VU-QUOC, L., ZHANG, X. (2007). Mechanics of Materials, 31, 235-269. VU-QUOC, L., ZHANG, X., LESBURG, L. (2001). International Journal of Solids and Structures, 38, 6455-6489. WALTON, O., BRAUN, R. (1986). Journal of Rheology, 30, 949.

17. A CKNOWLEDGEMENTS  Institute of Space Technology (IST) – Pakistan  Cambridge Commonwealth Trust – Cambridge, UK  Research Centre for Modelling & Simulation, National University of Sciences & Technology (NUST) - Pakistan H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 17

18. T HANK Y OU Trust me, I am not drunk!!!!!!!!!! C ONTACT H ASSAN K HAWAJA Email: hak23@cam.ac.uk Webpage: http://hassanabbaskhawaja.blogspot.com

19. BACK K ILN H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 19 Courtesy of J.R. Third, PhD Student, Engineering Dept., University of Cambridge, UK *Tangential Contact is Prominent

20. F LUIDIZED B ED H. A. K HAWAJA MULTIPHYSICS 2009, L ILLE, F RANCE, 9-11 D EC 09 20 Source: http://www.youtube.com/watch?v=EB0r6A5VxFU BACK