A semi-analytical model for oblique impacts of elastoplastic spheres

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 465, Issue 2103, 2009, Pages 937-960

  Wu, Chuan Yu ^a   Thornton, Colin ^a   Li, Long Yuan ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Coefficient of restitution; Contact mechanics; Granular materials; Impact dynamics; Oblique impact

Indexed keywords

DYNAMICS; ELASTOPLASTICITY; GRANULAR MATERIALS; KINEMATICS; POISSON DISTRIBUTION; POISSON EQUATION; SPHERES; YIELD STRESS;

COEFFICIENT OF RESTITUTION; CONTACT MECHANICS; CONTACT PATCH; ELASTO-PLASTIC; EMPIRICAL EQUATIONS; FINITE ELEMENT ANALYSIS; FLAT SUBSTRATES; IMPACT ANGLES; IMPACT DYNAMICS; IMPULSE RATIO; NUMERICAL DATA; OBLIQUE IMPACT; PLASTIC SPHERES; POISSON'S RATIO; REBOUND VELOCITY; RIGIDBODY DYNAMICS; ROTATIONAL SPEED; SEMI-ANALYTICAL MODEL; SIMPLE MODEL; TANGENTIAL COEFFICIENT; THEORETICAL SOLUTIONS; TWO-REGIME;

POISSON RATIO;

EID: 62749204019     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0221     Document Type: Article

References (43)

1. Andrews, J. P. 1930 Experiment on impact. Proc. Phys. Soc. 43, 8-17. (doi:10.1088/0959-5309/43 /1/303)
2. Batlle, J. A. 1993 On Newton's and Poisson's rules of percussive dynamics. Trans. ASME J. Appl. Mech. 60, 376-381. (doi:10.1115/1.2900804)
3. Batlle, J. A. and Cardona, S. 1998 The jamb (self-locking) process in three-dimensional rough collisions. Trans. ASME J. Appl. Mech. 65, 417-423.
4. Brach, R. M. 1988 Impact dynamics with applications to solid particle erosion. Int. J. Impact Eng. 7, 37-53. (doi:10.1016/0734-743X (88) 90011-5)
5. Brach, R. M. 1991 Mechanical impact dynamics-rigid body collisions. New York, NY: Wiley Interscience.
6. Brach, R. M. 1998 Formulation of rigid body impact problems using generalized coefficients. Int. J. Eng. Sci. 36, 61-72. (doi:10.1016/S0020-7225 (97) 00057-8)
7. Brauer, H. 1980 Report on investigations on particle movement in straight horizontal tubes, particle/wall collisions and erosion of tubes and tube bends. J. Powder Bulk Solids Technol. 4, 3-12.
8. Brogliato, B. 1996 Nonsmooth impact mechanics. London, UK: Springer.
9. Cheng, W., Brach, R. M. and Dunn, P. F. 2002 Three-dimensional modeling of microsphere contact/impact with smooth, flat surfaces. Aerosol Sci. Technol. 36, 1045-1060. (doi:10.1080 /02786820290092203)
10. Cross, R. 2002 Measurements of the horizontal coefficient of restitution for a superball and a tennis ball. Am. J. Phys. 70, 482-489. (doi:10.1119/1.1450571)
11. Foerster, S. F., Louge, M. Y., Chang, H. and Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 6, 1108-1115. (doi:10.1063/1.868282)
12. Goldsmith, W. 1960 Impact. London, UK: Arnold.
13. Goldsmith, W. and Lyman, P. T. 1960 The penetration of hard-steel spheres into plane met al. surfaces. Trans. ASME J. Appl. Mech. 27, 717-725.
14. Gorham, D. A. and Kharaz, A. H. 2000 The measurement of particle rebound characteristics. Powder Technol. 112, 193-202. (doi:10.1016/S0032-5910 (00) 00293-X)
15. Hertz, H. 1896 In Miscellaneous papers by H. Hertz (eds D. E. Jones and G. A. Schott). London, UK: Macmillan and Co.
16. Hunter, S. C. 1957 Energy absorbed by elastic waves during impact. J. Mech. Phys. Solids 5, 162-171. (doi:10.1016/0022-5096 (57) 90002-9)
17. Horak, F. 1948 Impact of a rough ball spinning round its vertical diameter onto a horizontal plane. In Transactions of the faculty of mechanical and electrical engineering. Czechoslovakia, Czech Republic: Technical University of Prague.
18. Hutchings, I. M. 1979 Energy absorbed by elastic waves during plastic impact. J. Phys. D Appl. Phys. 12, 1819-1824. (doi:10.1088/0022- 3727/12/11/010)
19. Johnson, K. L. 1983 The bounce of 'superball'. Int. J. Mech. Eng. Educ. 111, 57-63. Johnson, K. L. 1987 Contact mechanics. Cambridge, UK: Cambridge University Press.
20. Keller, J. B. 1986 Impact with friction. Trans. ASME J. Appl. Mech. 53, 1-4.
21. Kharaz, A. H., Gorham, D. A. and Salman, A. D. 2001 An experimental study of the elastic rebound of spheres. Powder Technol. 120, 281-291. (doi:10.1016/S0032-5910 (01) 00283-2)
22. Labous, L. R., Rosato, A. D. and Dave, R. N. 1997 Measurements of collisional properties of spheres using high-speed video analysis. 0Phys. Rev. E 56, 5717-5725. (doi:10.1103/PhysRevE.56.5717)
23. Li, L.-Y., Thornton, C. and Wu, C.-Y. 2000 Impact behaviour of the elastoplastic sphere with a rigid wall. Proc. I. Mech. E. C. J. Mech. Eng. Sci. 214, 1107-1114. (doi:10.1243/0954406001523551)
24. Li, L.-Y., Wu, C.-Y. and Thornton, C. 2002 A theoretical model for the contact of elastoplastic bodies. Proc. I. Mech. E. C. J. Mech. Eng. Sci. 216, 421-431. (doi:10.1243/0954406021525214)
25. Lorenz, A., Tuozzolo, C. and Louge, M. Y. 1997 Measurements of impact properties of small, nearly spherical particles. Exp. Mech. 37, 292-298. (doi:10.1007/BF02317421)
26. Maw, N., Barber, J. R. and Fawcett, J. N. 1976 The oblique impact of elastic spheres. Wear 38, 101-114. (doi:10.1016/0043-1648 (76) 90201-5)
27. Maw, N., Barber, J. R. and Fawcett, J. N. 1981 The role of elastic tangential compliance in oblique impact. Trans. ASME J. Lub. Tech. 103,74-80.
28. Mindlin, R. D. 1949 Compliance of elastic bodies in contact. Trans. ASME J. Appl. Mech. 16, 259-268.
29. Mindlin, R. D. and Deresiewicz, H. 1953 Elastic spheres in contact under varying oblique force. Trans. ASME J. Appl. Mech. 20, 327-344.
30. Ning, Z. 1995 Elasto-plastic impact of fine particles and fragmentation of small agglomerates. PhD thesis, University of Aston, Birmingham, UK.
31. Smith, C. E. 1991 Predicting rebounds using rigid-body dynamics. Trans. ASME J. Appl. Mech. 58, 754-758. (doi:10.1115/1.2897260)
32. Stronge, W. J. 1993 Two-dimensional rigid-body collisions with friction. Trans. ASME J. Appl. Mech. 60, 564-566. (doi:10.1115/1.2900835)
33. Stronge, W. J. 1994 Planar impact of rough compliant bodies. Int. J. Impact Eng. 15, 435-450. (doi:10.1016/0734-743X (94) 80027-7)
34. Thornton, C. 1997 Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Trans. ASME J. Appl. Mech. 64, 383-386. (doi:10.1115/1.2787319)
35. Thornton, C. and Ning, Z. 1998 A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres. Powder Technol. 99, 154-162. (doi:10.1016/S0032-5910 (98) 00099-0)
36. Thornton, C., Ning, Z., Wu, C.-Y., Nasrullah, M. and Li, L.-Y. 2001 Contact mechanics and coefficients of restitution. In Granular gases (eds T. Poschel and S. Luding), pp. 56-66. Berlin, Germany: Springer.
37. Walton, O. R. 1992 Numerical simulation of inelastic, frictional particle-particle interactions. In Particulate two-phase flow (ed. M. C. Roco), ch. 25. Boston, MA: Butterworth-Heinemann.
38. Wang, Y. and Mason, M. T. 1992 Two-dimensional rigid-body collisions with friction. Trans. ASME J. Appl. Mech. 59, 635-642. (doi:10.1115/1.2893771)
39. Whirley, R. G. and Engelmann, B. E. 1993 DYNA3D-A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics-user manual. Livermore, CA: Lawrence Livermore National Laboratory.
40. Wu, C.-Y. 2001 Finite element analysis of particle impact problems. PhD thesis, University of Aston, Birmingham, UK.
41. Wu, C.-Y., Li, L.-Y. and Thornton, C. 2003a Rebound behaviour of spheres for plastic impacts. Int. J. Impact Eng. 28, 929-946. (doi:10.1016/S0734-743X (03) 00014-9)
42. Wu, C.-Y., Thornton, C. and Li, L.-Y. 2003b Coefficient of restitution for elastoplastic oblique impacts. Adv. Powder Technol. 14, 435-448. (doi:10.1163/156855203769710663)
43. Wu, C.-Y., Li, L.-Y. and Thornton, C. 2005 Energy dissipation during normal impact of elastic and elastic-plastic spheres. Int. J. Impact Eng. 32, 593-604. (doi:10.1016/j.ijimpeng.2005.08.007)