A local constitutive model with anisotropy for various homogeneous 2d biaxial deformation modes

Chemie-Ingenieur-Technik

Volumn 83, Issue 5, 2011, Pages 672-688

  Luding, Stefan ^a   Perdahcäoälu, Emin Semih ^a  

^a Multi Scale Mechanics   (Netherlands)

Author keywords

Anisotropy; Deformation; Modeling; Particles; Shearing strength

Indexed keywords

ARBITRARY ORIENTATION; AXIAL DEFORMATIONS; BULK MODULUS; CO-ORDINATE SYSTEM; DEFORMATION MODES; DISCRETE ELEMENT METHOD; EVOLUTION EQUATIONS; FABRIC TENSORS; MODELING; NEW PARAMETERS; NON-LINEAR; PARTICLES; SCALAR VALUES; SELF-CONSISTENCY; SHEAR-RATE; SHEARING STRENGTH;

CONSTITUTIVE MODELS; DEFORMATION; ELASTICITY; SHEAR STRESS; SHEARING; SHEARING MACHINES; STRAIN; YIELD STRESS;

ANISOTROPY;

EID: 79955449873     PISSN: 0009286X     EISSN: 15222640     Source Type: Journal    
DOI: 10.1002/cite.201000180     Document Type: Article

References (39)

1. H. M. Jaeger, S. R. Nagel, R. P. Behringer, Rev. Mod. Phys. 1996, 68 (4), 1259-1273.
2. P. G. de Gennes, Rev. Mod. Phys. 1999, 71 (2), 374-382.
3. I. Vardoulakis, J. Sulem, Bifurcation Analysis in Geomechanics, Chapman & Hall, London 1995.
4. A. J. Liu, S. R. Nagel, Nature 1998, 396 (6706), 21.
5. C. S. O'Hern, S. A. Langer, A. J. Liu, S. R. Nagel, Phys. Rev. Lett. 2002, 88 (7), 075507.
6. T. S. Majmudar, M. Sperl, S. Luding, R. P. Behringer, Phys. Rev. Lett. 2007, 98 (5), 058001.
7. S. Luding, Granular Matter 2008, 10 (4), 235-246.
8. P.-E. Peyneau, J.-N. Roux, Phys. Rev. E 2008, 78 (4), 041307.
9. J. Zhang, T. S. Majmudar, A. Tordesillas, R. P. Behringer, Granular Matter 2010, 12, 159-172.
10. L. R. Aarons, J. Sun, S. Sundaresan, Ind. Eng. Chem. Res. 2010, 49, 5153-5165.
11. J. Sun, S. Sundaresan, J. Fluid Mech. submitted.
12. F. Radjai, D. E. Wolf, M. Jean, J. J. Moreau, Phys. Rev. Lett. 1998, 80 (1), 61-64.
13. F. Radjai, S. Roux, J. J. Moreau, Chaos 1999, 9 (3), 544.
14. F. Radjai, S. Roux, Phys. Rev. Lett. 2002, 89 (6), 064302-1.
15. S. D. C. Walsh, A. Tordesillas, Act. Mech. 2004, 167, 145-169.
16. F. Alonso-Marroquin, S. Luding, H. J. Herrmann, I. Vardoulakis, Phys. Rev. E 2005, 71 (24), 051304.
17. Continuous and Discontinuous Modelling of Cohesive Frictional Materials (Eds: P. A. Vermeer, S. Diebels, W. Ehlers, H. J. Herrmann, S. Luding, E. Ramm), Springer, Berlin 2001.
18. S. Luding, J. Phys.: Condens. Matter 2005, 17, S2623-S2640.
19. M. Lätzel, S. Luding, H. J. Herrmann, Granular Matter 2000, 2 (3), 123-135.
20. M. Lätzel, S. Luding, H. J. Herrmann, in Continuous and Discontinuous Modelling of Cohesive Frictional Materials (Eds: P. A. Vermeer, S. Diebels, W. Ehlers, H. J. Herrmann, S. Luding, E. Ramm), Springer, Berlin 2001, 215-230.
21. S. Luding, M. Lätzel, W. Volk, S. Diebels, H. J. Herrmann, Comp. Methods Appl. Mech. Eng. 2001, 191, 21-28.
22. S. Luding, in Modelling of Cohesive-Frictional Materials (Eds: P. A. Vermeer, W. Ehlers, H. J. Herrmann, E. Ramm) Balkema, Leiden, Netherlands 2004, 195-206.
23. S. Luding, Particuology 2008, 6 (6), 501-505.
24. I. Goldhirsch, Granular Matter 2010, 12, 239-252.
25. J. Goddard, in IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows (Eds: J. Goddard, P. Giovine, J. T. Jenkins), AIP, New York 2010, 323-332.
26. H. Muhlhaus, L. Moresi, L. Gross, J. Grotowski, Granular Matter 2010, 12, 229-238.
27. J. Sun, S. Sundaresan, in IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows (Eds: J. Goddard, P. Giovine, J. T. Jenkins), AIP, New York 2010, 280-289.
28. J. P. Bardet, I. Vardoulakis, Int. J. Solids Struct. 2001, 38 (2), 353-367.
29. I. Vardoulakis, Ing.-Arch. 1989, 59, 106-113.
30. J. Tejchman, W. Wu, Int. J. of Non-Linear Mechanics 2007, 42, 882-894.
31. S. Luding, in IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows (Eds: J. Goddard, P. Giovine, J. T. Jenkins), AIP, New York 2010, 208-213.
32. J. D. Goddard, Granular Matter 2010, 12, 145-150.
33. Y. Jiang, M. Liu, Granular Matter 2009, 11, 139-156.
34. S. Mahle, Y. Jiang, M. Liu, The critical state as a steady-state solution of granular solid hydrodynamics, preprint. arxiv.org/abs/1006.5131v3.
35. F. Nicot, F. Darve, Granular Matter 2006, 8, 221-237.
36. V. Magnanimo, S. Luding, Granular Matter 2011, in press. DOI: 10.1007/s10035-011-0266-3
37. D. O. Brush, B. O. Almroth, Buckling of Bars, Plates, and Shells, McGraw Hill, New York 1975.
38. S. Luding, F. Alonso-Marroquin, Granular Matter. 2011, 13 (2), 109-119. DOI: 10.1007/s10035-010-0241-4
39. F. Göncü, O. Duran, S. Luding, C. R. Mecanique 2010, 338 (10-11), 570-586.