Granular element method for computational particle mechanics

Computer Methods in Applied Mechanics and Engineering

Volumn 241-244, Issue , 2012, Pages 262-274

  Andrade, José E ^a   Lim, Keng Wit ^a   Avila, Carlos F ^a   Vlahinić, Ivan ^a  

^a California Institute of Technology   (United States)

Author keywords

Discrete element method; Multiscale analysis; NURBS; Particle mechanics

Indexed keywords

COMPUTATIONAL MODEL; COMPUTATIONAL POWER; DISCRETE ELEMENTS; DISCRETE MECHANICS; GRAIN SHAPES; GRANULAR ELEMENT METHOD; GRANULAR SHAPE; MULTI SCALE ANALYSIS; NURBS; PARTICLE MECHANICS; PARTICLE SHAPE; PHYSICS-BASED; PREDICTIVE MODELING; RAPID ADVANCEMENT; SAND GRAINS; VISUALIZATION TOOLS; X-RAY CT;

FINITE DIFFERENCE METHOD; GRANULAR MATERIALS; MECHANICS; VISUALIZATION;

PARTICLES (PARTICULATE MATTER);

EID: 84864058675     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.06.012     Document Type: Article

References (37)

1. Cho G.C., Dodds J., Santamarina J.C. Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. Journal of Geotechnical and Geoenvironmental Engineering 2006, 132(5):591-602.
2. Sukumaran B., Ashmawy A.K. Quantitative characterisation of the geometry of discrete particles. Geotechnique 2001, 51:619-627.
3. Garcia X., Akanji L.T., Blunt M.J., Matthai S.K., Latham J.P. Numerical study of the effects of particle shape and polydispersity on permeability. Physical Review E 2009, 80:021304.
4. Cundall P.A., Strack O.D.L. A discrete numerical model for granular assemblies. Géotechnique 1979, 29:47-65.
5. Christoffersen J., Mehrabadi M.M., Nemat-Nasser S. A micromechanical description of granular material behavior. Journal of Applied Mechanics 1981, 48:339-344.
6. A.K. Ashmawy, B. Sukumaran, A.V. Hoang, Evaluating the influence of particle shape on liquefaction behavior using discrete element method, in: Proceedings of the Thirteenth International Offshore and Polar Engineering Conference (ISOPE 2003), Honolulu, Hawaii, 2003.
7. Garcia X., Latham J.-P., Xiang J., Harrison J.P. A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Geotechnique 2009, 59:779-784.
8. Cundall P.A. Formulation of a three-dimensional distinct element model - part 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.
9. Hashash Y.M.A., Zhao D., Nezami E.G., Ghaboussi J. Three-dimensional discrete element simulation for granular materials. Engineering Computations 2006, 23:749-770.
10. Alonso-Marroquin F., Herrmann H.J. Calculation of the incremental stress-strain relation of a polygonal packing. Physical Review E 2002, 66:021301.
11. Peña A.A., Lind P.G., Herrmann H.J. Modeling slow deformation of polygonal particles using dem. Particuology 2008, 6:506-514.
12. O'Sullivan C. Particulate Discrete Element Modelling: A Geomechanics Perspective. Applied Geotechnics 2011, Spon Press/Taylor & Francis.
13. Rothenburg L., Bathurst R.J. Numerical simulation of idealized granular assemblies with plane elliptical particles. Computers and Geotechnics 1991, 11(4):315-329.
14. Ting J.M., Khwaja M., Meachum L.R., Rowell J.D. An ellipse-based discrete element model for granular materials. International Journal for Numerical and Analytical Methods in Geomechanics 1993, 17(9):603-623.
15. Houlsby G.T. Potential particles: a method for modelling non-circular particles in DEM. Computers & Geotechnics 2009, 36:953-959.
16. Rogers D.F. An Introduction to NURBS with Historical Perspective 2001, Academic Press, San Diego.
17. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005, 194:4135-4195.
18. Piegl L., Tiller W. The NURBS Book 1997, Springer-Verlag, Inc., New York, NY, USA. second ed.
19. C.-K. Shene, CS3621 introduction to computing with geometry, 2011. http://www.cs.mtu.edu/shene/COURSES/cs3621/NOTES/.
20. Lowther J., Fisher J., Shene C.-K. If you know B-Splines well, you also know NURBS!. SIGCSE Bulletin 2004, 36:343-347.
21. M.G. Cox, The numerical evaluation of B-splines. Technical report, National Physics Laboratory DNAC 4, 1971.
22. De Boor C. On calculation with B-splines. Journal of Approximation Theory 1972, 6:50-62.
23. Tu X., Andrade J.E. Criteria for static equilibrium in particulate mechanics computations. International Journal for Numerical Methods in Engineering 2008, 75:1581-1606.
24. Hart R., Cundall P.A., Lemos J. Formulation of a three-dimensional distinct element model - part II: mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. International Journal of Rock Mechanics and Mining Sciences 1988, 25(3):117-125.
25. Hogue C., Newland D. Efficient computer simulation of moving granular particles. Powder Technology 1994, 78(1):51-66.
26. Džiugys A., Peters B. An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers. Granular Matter 2001, 3(4):231-266.
27. A.M. Sallam, Studies on modeling angular soil particles using the discrete element method, PhD thesis, University of South Florida, Tampa, FL, 2004.
28. Mrken Knut, Reimers Martin, Schulz Christian Computing intersections of planar spline curves using knot insertion. Computer Aided Geometric Design 2009, 26:351-366.
29. Dokken T. Finding intersections of B-spline represented geometries using recursive subdivision techniques. Computer Aided Geometric Design 1985, 2(1-3):189-195.
30. Sintef, ICT, Department of Applied Mathematics, Norway. The SINTEF Spline Library. http://www.sintef.no/sisl.
31. Sederberg T.W., Nishita T. Curve intersection using Bézier clipping. Computer Aided Design 1990, 22:538-549.
32. Schulz Christian Bézier clipping is quadratically convergent. Computer Aided Geometric Design 2009, 26(1):61-74.
33. Krishnamurthy A., Khardekar R., McMains S., Haller K., Elber G. Performing efficient NURBS modeling operations on the GPU. Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling, SPM '08 2008, 257-268. ACM.
34. M. Babić, Discrete particle numerical simulation of granular material behavior, Technical report 88-11, Department of Civil and Environmental Engineering, Clarkson University, 1988.
35. Mindlin R.D. Compliance of elastic bodies in contact. Journal of Applied Mechanics 1949, 71:259-268.
36. Andrade J.E., Avila C.F., Lenoir N., Hall S.A., Viggiani G. Multiscale modeling and characterization of granular matter: from grain scale kinematics to continuum mechanics. Journal of the Mechanics and Physics of Solids 2011, 59:237-250.
37. Andrade J.E., Avila C.F. Granular element method (GEM): linking inter-particle forces with macroscopic loading. Granular Matter 2012, 14:1-13.