Role of anisotropy in the elastoplastic response of a polygonal packing

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 5, 2005, Pages

  Alonso Marroquin F ^a,b,c   Luding, S ^a,b,c   Herrmann, H J ^b,c   Vardoulakis, I ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

FABRIC COEFFICIENTS; POISSON RATIOS; POLYGONAL PACKING; SOIL PLASTICITY;

ANISOTROPY; ELASTIC MODULI; GRANULAR MATERIALS; PACKING;

ELASTOPLASTICITY;

EID: 26944453935     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.051304     Document Type: Article

References (74)

1. I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics (Blakie Academic & Professional, London, 1995), Chap., pp. 191-196.
2. G. Gudehus, F. Darve, and I. Vardoulakis, Constitutive Relations of Soils (Balkema, Rotterdam, 1984).
3. I. Vardoulakis, Acta Mech. AMHCAP 0001-5970 10.1007/BF01181755 49, 57 (1983).
4. I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics (Ref.), Chap., pp. 281-283.
5. M. E. Cates, J. P. Wittmer, J.-P. Bouchaud, and P. Claudin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1841 81, 1841 (1998).
6. D. Coppersmith, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.4673 53, 4673 (1996).
7. J. Geng, D. Howell, E. Longhi, R. P. Behringer, G. Reydellet, L. Vanel, E. Clément, and S. Luding, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.035506 87, 035506 (2001).
8. F. Radjai, M. Jean, J. J. Moreau, and S. Roux, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.274 77, 274 (1996).
9. C. Goldenberg and I. Goldhirsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.084302 89, 084302 (2002).
10. F. Radjai, D. E. Wolf, M. Jean, and J.-J. Moreau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.61 80, 61 (1998).
11. A. Tordesillas, S. D. C. Walsh, and B. S. Gardiner, BIT BITTEL 0006-3835 44, 539 (2004).
12. T. Dietrich, Ph.D. thesis, Universität Karlsruhe, 1976.
13. I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics (Ref.), Chap., pp. 232-237.
14. P. A. Cundall, Ing.-Arch. INARAS 0020-1154 10.1007/BF00538368 59, 148 (1989).
15. I. Vardoulakis, Ing.-Arch. INARAS 0020-1154 10.1007/BF00538364 59, 106 (1989).
16. F. Radjai, D. E. Wolf, M. Jean, and J.-J. Moreau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.61 80, 61 (1998).
17. G. Royer-Carfagni and W. Salvatore, Mech. Cohesive-Frict. Mater. MCFMFA 1082-5010 5, 535 (2000).
18. F. Kun and H. J. Herrmann, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/S0045-7825(96)01012-2 138, 3 (1996).
19. F. Kun and H. J. Herrmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.2623 59, 2623 (1999).
20. H. J. Tillemans and H. J. Herrmann, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00111-J 217, 261 (1995).
21. F. Alonso-Marroquin, H. J. Herrmann, and I. Vardoulakis, Modeling of Cohesive-Frictional Materials (A. A. Balkema, Leiden, 2004).
22. F. Alonso-Marroquin and H. J. Herrmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.054301 92, 054301 (2004).
23. G. Royer-Carfagni, Novel Approaches in Civil Engineering (Springer-Verlag, Berlin, 2004), pp. 177-185.
24. C. Moukarzel and H. J. Herrmann, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01048880 68, 911 (1992).
25. A. Okabe, B. Boots, and K. Sugihara, Spatial Tessellations. Concepts and Applications of Voronoi Diagrams, Wiley Series in Probability and Mathematical Statistics (John Wiley & Sons, Chichester, 1992).
26. P. A. Cundall and O. D. L. Strack, Geotechnique GTNQA8 0016-8505 29, 47 (1979).
27. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1987).
28. E. Buckingham, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.4.345 4, 345 (1914).
29. A. Pena, A. Lizcano, F. Alonso-Marroquin, and H. J. Herrmann (unpublished).
30. I. O. Georgopoulus, F. Alonso-Marroquin, I. Vardoulakis, and J. F. Labuz (unpublished).
31. P. A. Vermeer, Geotechnique GTNQA8 0016-8505 40, 223 (1990).
32. M. Madadi, O. Tsoungui, M. Lätzel, and S. Luding, Int. J. Solids Struct. IJSOAD 0020-7683 41, 2563 (2004).
33. S. Luding, Int. J. Solids Struct. IJSOAD 0020-7683 41, 5821 (2004).
34. S. Luding, Modeling of Cohesive-Frictional Materials (A. A. Balkema, Leiden, 2004), pp. 195-206.
35. S. Luding and H. J. Herrmann, Bericht Nr. II-7 (Inst. für Mechanik, Universität Stuttgart, 2001), pp. 121-133.
36. K. Bagi, J. Appl. Mech. JAMCAV 0021-8936 66, 934 (1999).
37. K. Bagi, Mech. Mater. MSMSD3 0167-6636 10.1016/0167-6636(95)00044-5 22, 165 (1996).
38. F. Alonso-Marroquin, Ph.D. thesis, University of Stuttgart, 2004, Logos Verlag Berlin ISBN 3-8325-0560-1.
39. F. Darve, E. Flavigny, and M. Meghachou, Int. J. Plast. IJPLER 0749-6419 10.1016/S0749-6419(95)00037-2 11, 927 (1995).
40. D. Kolymbas, Arch. Appl. Mech. AAMEEA 0939-1533 61, 143 (1991).
41. G. Gudehus, Can. Geotech. J. CGJOAH 0008-3674 20, 502 (1979).
42. F. Alonso-Marroquin and H. Herrmann, J. of Eng. Math. (to be published), e-print cond-mat/0403065.
43. P. A. Vermeer, Constitutive Relations of Soils (Balkema, Rotterdam, 1984), pp. 175-197.
44. H. B. Poorooshasb, I. Holubec, and A. N. Sherbourne, Can. Geotech. J. CGJOAH 0008-3674 4, 277 (1967).
45. J. P. Bardet, Int. J. Plast. IJPLER 0749-6419 10.1016/0749-6419(94)90019-1 10, 879 (1994).
46. F. Calvetti, C. Tamagnini, and G. Viggiani, Numerical Models in Geomechanics (Swets & Zeitlinger, Lisse, 2002), pp. 3-9.
47. L. Landau and E. M. Lifshitz, Theory of Elasticity, Course of Theoretical Physics Vol. 7 (Pergamon Press, Moscow, 1986).
48. C. Thornton and D. J. Barnes, Acta Mech. AMHCAP 0001-5970 10.1007/BF01180097 64, 45 (1986).
49. P. A. Cundall, A. Drescher, and O. D. L. Strack, IUTAM Conference on Deformation and Failure of Granular Materials (Balkema, Rotterdam, Delft, 1982), pp. 355-370.
50. S. Luding, R. Tykhoniuk, and A. Thomas, Chem. Eng. Technol. CETEER 0930-7516 10.1002/ceat.200303236 26, 1229 (2003).
51. A. Drescher and G. de Josselin de Jong, J. Mech. Phys. Solids JMPSA8 0022-5096 10.1016/0022-5096(72)90029-4 20, 337 (1972).
52. M. Lätzel, S. Luding, H. J. Herrmann, D. W. Howell, and R. P. Behringer, Eur. Phys. J. E EPJSFH 1292-8941 10.1140/epje/i2002-10160-7 11, 325 (2003).
53. M. Lätzel, Ph.D. thesis, Universität Stuttgart, 2002.
54. C. Goldenberg and I. Goldhirsch, Granular Matter GRMAFE 1434-5021 6, 97 (2004).
55. J. R. Ray, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.423 40, 423 (1989).
56. R. J. Bathurst and L. Rothenburg, J. Appl. Mech. JAMCAV 0021-8936 55, 17 (1988).
57. S. Nemat-Nasser, J. Mech. Phys. Solids JMPSA8 0022-5096 28, 1541 (2000).
58. D. M. Wood, Soil Behaviour and Critical State Soil Mechanics (ISBN: 0-521-33782-8) (Cambridge University Press, Cambridge, England, 1990).
59. R. Nova and D. Wood, Int. J. Numer. Analyt. Meth. Geomech. IJNGDZ 0363-9061 3, 277 (1979).
60. D. W. Taylor, Fundamentals of Soils Mechanics (John Wiley, New York, 1948).
61. P. W. Rowe, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 269, 500 (1962).
62. M. A. Stroud, Ph.D. thesis, University of Cambridge, 1971.
63. M. Gutierrez and K. Ishihara, Soils Found. SOIFBE 0038-0806 40, 49 (2000).
64. R. Lagioia, A. M. Puzrin, and D. M. Potts, Comput. Geotech. 0266-3524 19, 171 (1996).
65. I. Vardoulakis and I. O. Georgopoulos, Soils Found. SOIFBE 0038-0806 45 (2), 61 (2005).
66. X. S. Li and Y. F. Dafalias, Geotechnique GTNQA8 0016-8505 50, 449 (2000).
67. D. Drucker and W. Prager, Q. Appl. Math. QAMAAY 0033-569X 10, 157 (1952).
68. F. Tatsouka and K. Ishihara, Soils Found. SOIFBE 0038-0806 14, 63 (1974).
69. R. Hill, J. Geotech. Eng. 6, 239 (1958).
70. G. R. McDowell, M. D. Bolton, and D. Robertson, J. Mech. Phys. Solids JMPSA8 0022-5096 44, 2079 (1996).
71. Y. Kishino, Italian Geotechnical Journal 3, 3 (2003).
72. F. Calvetti, G. Viggiani, and C. Tamagnini, Constitutive Modelling and Analysis of Boundary Value Problems in Geotechnical Engineering (Hevelius Edizioni, Benevento, 2003), pp. 187-216.
73. R. Garcia-Rojo and H. J. Herrmann, Granular Matter (to be published), e-print cond-mat/0404176.
74. H. Matsouka, Soils Found. SOIFBE 0038-0806 14, 47 (1974).