Criteria for static equilibrium in particulate mechanics computations

International Journal for Numerical Methods in Engineering

Volumn 75, Issue 13, 2008, Pages 1581-1606

  Tu, Xuxin ^a   Andrade, José E ^a  

^a Northwestern University   (United States)

Author keywords

Algorithmic calibration; Boundary stress; Discrete element; External stress; Homogenized stress; Static equilibrium

Indexed keywords

CALIBRATION; GEOMORPHOLOGY; NUMERICAL ANALYSIS; NUMERICAL METHODS; REAL TIME SYSTEMS; SURVEYING; TRACKING RADAR;

ALGORITHMIC CALIBRATION; BOUNDARY STRESS; DISCRETE ELEMENT; EXTERNAL STRESS; HOMOGENIZED STRESS; STATIC EQUILIBRIUM;

MECHANICS;

EID: 53749096400     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2322     Document Type: Article

References (48)

1. Cundall PA, Strack ODL. A discrete numerical model for granular assemblies. Géotechnique 1979; 29:47-65.
2. Cambou B. Behaviour of Granular Materials. Springer: New York, NY, 1998.
3. Oda M, Iwashita K. Mechanics of Granular Materials: An Introduction. A.A. Balkema: Brookfield, VT, 1999.
4. Barbosa-Carrillo RE. Discrete element models for granular materials and rock masses. Ph.D. Thesis, University of Illinois, Urbana-Champaign, IL, 1990.
5. You Z. Development of a micromechanical modeling approach to predict asphalt mixture stiffness using the discrete element method. Ph.D. Thesis, University of Illinois, Urbana-Champaign, IL, 2003.
6. Tavarez FA. Discrete element method for modeling solid and particulate materials. Ph.D. Thesis, University of Wisconsin, Madison, CA, 2005.
7. Anandarajah A. Multiple time-stepping scheme for the discrete element analysis of colloidal particles. Powder Technology 1999; 106:132-141.
8. Deen NG, Van Sint Annaland M, Van der Hoef MA, Kuipers JAM. Review of discrete particle modeling of fluidized beds. Chemical Engineering Science 2007; 62:28-44.
9. Sheng Y, Lawrence CJ, Briscoe BJ, Thornton C. Numerical studies of uniaxial powder compaction process by 3D DEM. Engineering Computations 2004; 21(2-4):304-317.
10. Severson B. A nano to macro study of friction and adhesion in granular materials. Ph.D. Thesis, Northwestern University, Evanston, IL, 2007.
11. Cundall PA. Formulation of a three-dimensional distinct element model. I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks. International Journal of Rock Mechanics and Mining Sciences 1988; 25(3):107-116.
12. Lin X, Ng TT. A three-dimensional discrete element model using arrays of ellipsoids. Géotechnique 1997; 47:319-329.
13. Sallam AM. Studies on modeling angular soil particles using the discrete element method. Ph.D. Thesis, University of South Florida, Tampa, FL, 2004.
14. Tavarez FA, Plesha ME. Discrete element method for modelling solid and particulate materials. International Journal for Numerical Methods in Engineering 2007; 70:379-404.
15. Borja RI, Wren JR. Micromechanics of granular media. Part I: generation of overall constitutive equation for assemblies of circular disks. Computer Methods in Applied Mechanics and Engineering 1995; 127:13-36.
16. Wellmann C, Lillie C, Wriggers P. Homogenization of granular material modeled by a three-dimensional discrete element method. Computers and Geotechnics 2007; DOI: 10.1016/j.compgeo.2007.06.010.
17. Bardet JP, Proubet J. A numerical investigation of the structure of persistent shear bands in granular media. Géotechnique 1991; 41:599-613.
18. Ng TT. Input parameters of discrete element methods. Journal of Engineering Mechanics 2006; 132:723-729.
19. Cundall PA. A discontinuous future for numerical modelling in geomechanics. Geotechnical Engineering, ICE 2001; 149:41-47.
20. Miehe C, Dettmar J. A framework for micro-macro transitions in periodic particle aggregates of granular materials. Computer Methods in Applied Mechanics and Engineering 2004; 193:225-256.
21. Munjiza A. The Combined Finite-Discrete Element Method. Wiley: Hoboken, NJ, 2004.
22. Underwood P. Dynamic relaxation. In Computational Methods for Transient Analysis, Belytschko T, Hughes TJR (eds), vol. 1. Elsevier: New York, NY, 1983; 245-265.
23. Timoshenko SP. History of Strength of Materials. McGraw-Hill: New York, 1953.
24. Cassell AC, Hobbs RE. Numerical stability of dynamic relaxation analysis of non-linear structures. International Journal for Numerical Methods in Engineering 1976; 10: 1407-1410.
25. Key SW, Stone CM, Kreig RD. Dynamic relaxation applied to the quasi-static large deformation inelastic response of axisymmetric solids. In Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich W, Stein E, Bathe KJ (eds). Springer: Berlin, 1981; 585-621.
26. Park KC. A family of solution algorithms for nonlinear structural analysis based on relaxation equations. International Journal for Numerical Methods in Engineering 1982; 18:1337-1347.
27. Papadrakakis M. A method for the automatic evaluation of the dynamic relaxation parameters. Computer Methods in Applied Mechanics and Engineering 1981; 25:35-48.
28. Zhang L, Kadkhodayan M, Mai YW. Development of the maDR method. Computers and Structures 1994; 52:1-8.
29. Bardet JP, Proubet J. Adaptive dynamic relaxation for statics of granular materials. Computers and Structures 1991; 39:221-229.
30. Christoffersen J, Mehrabadi MM, Nemat-Nasser S. A micromechanical description of granular material behavior. Journal of Applied Mechanics 1981; 48:339-344.
31. Johnson KL. Contact Mechanics. Cambridge University Press: Cambridge, U.K., 1985.
32. Mindlin RD, Deresiewicz H. Elastic spheres in contact under varying oblique forces. Journal of Applied Mechanics - Transactions of ASME, Series E 1953; 20:327-344.
33. van Baars S. Discrete element analysis of granular materials. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 1996.
34. Hughes TJR. The Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1987.
35. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: West Sussex, U.K., 2000.
36. O'Sullivan C, Bray JD. Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme. Engineering Computations 2004; 21:278-303.
37. Thornton C. Numerical simulations of deviatoric shear deformation of granular media. Géotechniquen 2000; 50(1):43-53.
38. Drescher A, de Josselin de Jong G. Photoelastic verification of a mechanical model for the flow of a granular material. Journal of the Mechanics and Physics of Solids 1972; 20:337-351.
39. Goddard J. An elastohydrodynamics theory for the rheology of concentrated suspensions of deformable particles. Journal of Non-Newtonian Fluid Mechanics 1977; 2:169-189.
40. Rothenburg L, Selvadurai APS. A micromechanical definition of the cauchy stress tensor for particulate media. In Mechanics of Structured Media, Selvadurai APS (ed.). Elsevier: Amsterdam, 1981; 469-486.
41. Bardet JP, Vardoulakis I. The asymmetry of stress in granular media. International Journal of Solids and Structures 2001; 38:353-367.
42. Chang CS, Kuhn MR. On virtual work and stress in granular media. International Journal of Solids and Structures 2005; 42:3773-3793.
43. Rowe PW. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of the Royal Society of London, Series A 1962; 269:500-527.
44. Belytschko T, Hughes TJR. Computational Methods for Transient Analysis. Computational Methods in Mechanics Series, vol. 1. North-Holland: New York, NY, 1983.
45. Tu X, Andrade JE. Criteria for static equilibrium in discrete element method. ASME 2007 International Mechanical Engineering Congress Exposition, Seattle, WA, 2007 (in CD).
46. Itasca Consulting Group. PFC2D Particle Flow Code in Two Dimensions. Itasca Consulting Group: Minneapolis, 1998.
47. Bardet JP. Observations on the effects of particle rotations on the failure of idealized granular materials. Mechanics of Materials 1994; 18:159-182.
48. Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of heterogeneous Materials. Elsevier: Amsterdam, 1993.