Multi-mechanism anisotropic model for granular materials

International Journal of Plasticity

Volumn 24, Issue 5, 2008, Pages 804-846

  Anandarajah, A ^a  

^a Johns Hopkins University   (United States)

Author keywords

Constitutive behavior; Elasto plastic materials; Fabric anisotropy; Geologic materials; Granular materials

Indexed keywords

ANISOTROPY; ELASTOPLASTICITY; ROLLING; SHEAR STRENGTH;

CONSTITUTIVE BEHAVIOR; FABRIC ANISOTROPY;

GRANULAR MATERIALS;

EID: 38949104820     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2007.07.012     Document Type: Article

References (82)

1. Anand L. Plane deformation of ideal granular materials. J. Mech. Phys. Solids 31 (1983) 105-122
2. Anand L., and Gu C. Granular materials: constitutive equations and strain localization. J. Mech. Phys. Solids 48 (2000) 1701-1733
3. Anandarajah, A., 1993. VELACS project: elasto-plastic finite element prediction of the liquefaction behavior of centrifuge models nos. 1, 3 and 4a. In: Arulanandan, K., Scott, R.F. (Eds.), Proceedings of the International Conference on Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems, Davis, California, October 17-20, vol. 1, pp. 1075-1104.
4. Anandarajah A. A constitutive model for granular materials based on associated flow rule. Soils Found. Jpn. Soc. Soil Mech. Found. Eng. 34 3 (1994) 81-98
5. Anandarajah A. Procedures for elasto-plastic liquefaction modeling of sands. J. Engr. Mech. Div., ASCE 120 7 (1994) 1563-1589
6. Anandarajah A. Sliding and rolling constitutive theory for granular materials. J. Eng. Mech. ASCE 130 6 (2004) 665-681
7. Anandarajah, A., in press. The critical state of granular materials based on the sliding-rolling theory. J. Geotech. Geoenviron. Eng. Am. Soc. Civil Eng.
8. Anandarajah, A., Dafalias, Y.F., 1985. An anisotropic hardening bounding surface constitutive model for clays. In: Proceedings of the Fifth International Conference on Numerical Methods on Geomechanics, Nagoya, 1-5 April, 1985, pp. 267-276.
9. Anandarajah A., and Dafalias Y.F. Bounding surface plasticity, Part 3: Application to anisotropic soils. J. Eng. Mech. Div. ASCE 112 12 (1986) 1292-1318
10. Anandarajah A., and Kuganenthira N. Some aspects of fabric anisotropy of soils. Geotechnique 45 1 (1995) 69-81
11. Argyris, J.H. et al., 1973. Recent developments in finite element analysis of PCRV. In: 2nd International Conference, SMIRT, Berlin.
12. Arulmoli, K., Muraleetharan, K.K., Hossain, M.M., Fruth, L.S., (1992). VELACS-Verification of liquefaction analysis by centrifuge studies: Laboratory testing program soil data report. Prepared for the U.S. National Science Foundation.
13. Balendran B., and Nemat-Nasser S. Double sliding model for cyclic deformation of granular materials, including dilatancy effects. J. Mech. Phys. Solids 41 3 (1993) 573-612
14. Been K., and Jefferies M.G. A state parameter for sands. Geotechnique 35 2 (1985) 99-112
15. Been K., Jefferies M.G., and Hachey J. The critical state of sands. Geotech. London 41 3 (1991) 365-381
16. Castro G. Liquefaction and cyclic mobility of saturated sands. J. Geotech. Eng. Div. ASCE 101 GT6 (1975) 551-569
17. Castro G., and Poulos S.J. Factors affecting liquefaction and cyclic mobility. J. Geotech. Eng. Div. ASCE 103 GT6 (1977) 501-516
18. Chang K.-T., and Sture S. Microplane modeling of sand behavior under non-proportional loading. Comput. Struct. 33 (2006) 177-187
19. Cundall P.A., and Strack O.D.L. A discrete numerical model for granular assemblies. Geotechnique 29 1 (1979) 47-65
20. Dafalias Y.F., and Papov E.P. A model of nonlinearly hardening materials for complex loadings. Acta Mech. 21 (1975) 173-192
21. De Josselin de Jong, G., 1959. Statics and Kinematics in the Failable Zone of Granular Materials, Thesis, University of Delft.
22. De Josselin de Jong G. The double sliding, free rotating model for granular assemblies. Geotechnique 21 2 (1971) 155-163
23. Ghaboussi J., and Momen H. Modeling and analysis of cyclic behavior of sands. In: Pande G.N., and Zienkiewicz O.C. (Eds). Soil Mechanics - Transient and Cyclic Loads (1982), John Wiley & Sons, Chichester, UK 313-342
24. Habib, P., Luong, M.P., 1978. Sols pulverulents sous chargement cyclique ingenieurs anciens eleves de l'ecole nationale des ponts et chausses, Palaiseau, 28-29 September, pp. 49-79.
25. Hashiguchi, K., 1977. An expression of anisotropy in plastic constitutive equations of soils. In: Constitutive Equations of Soils, Proceedings of the 9th International Conference on Soil Mechanics Found. Engr., Special Session 9, Tokyo, ISSMFE, pp. 302-305.
26. Hashiguchi K. A mathematical modification of two surface model formulation in plasticity. Int. J. Solids Struct. 24 (1988) 987-1001
27. Hashiguchi, K., 1994. Subloading surface model with rotational hardening for soils. In: Proceedings of the International Conference on Comptational Methods Struct. Geotech. Eng., Hong Kong, pp. 807-812.
28. Hashiguchi K. Description of inherent/induced anisotropy of soils: rotational hardening rule with objectivity. Soils Found. 41 6 (2001) 139-145
29. Hashiguchi K., and Chen Z.-P. Elastoplastic constitutive equations of soils with the subloading surface and the rotational hardening. Int. J. Numer. Anal. Meth. Geomech. 22 (1998) 197-227
30. Hashiguchi, K., Ueno, M., 1977. Elasto-plastic constitutive laws of granular materials. In: Constitutive Equations of Soils, Proceedings of the 9th International Conference on Soil Mech. Found. Engr., Special Session 9, Tokyo, ISSMFE, pp. 73-82.
31. Hattamleh O.Al., Muhunthan B., and Zbib H.M. Multi-slip gradient formulation for modeling microstructure effects on shear bands in granular materials. Int. J. Solids. Struct. 44 10 (2007) 3393-3410
32. Hill R. Mathematical Theory of Plasticity (1950), Oxford University Press, Oxford
33. Hill R. Generalized constitutive relations for incremental deformation of metal crystals by multislip. J. Mech. Phys. Solids 14 (1966) 309
34. Hodge, P.G., 1957. Piecewise linear plasticity. In: Proceedings of the 9th ICAM, 8, p. 65.
35. Ishihara K. Liquefaction and flow failure during earthquakes, 33rd Rankine Lecture. Geotechnique 43 3 (1993) 351-415
36. Ishihara K., Tatsuoka F., and Yasuda S. Undrained deformation and liquefaction of sand under cyclic stresses. Soils Found. 15 1 (1975) 29-44
37. Iwan W.D. On a class of models for yielding behavior of continuous and composite systems. J. Appl. Mech. 34 (1967) 612-617
38. Jefferies M., and Been K. Implications for critical state theory from isotropic compression of sands. Geotechnique 50 4 (2000) 419-430
39. Kavvadas, M.J., 1983. A constitutive models for clays based on non-associated anisotropic elasto-plasticity. In: Proceedings of the International Conference on Constitutive Laws for Engineering Materials - Theory and Application. Tucson, Arizona, January 10-14, pp. 263-270.
40. Klisinski M., Mroz Z., and Runesson K. Structure of constitutive equations in plasticity for different choices of state and control variables. Int. J. Plast. 8 (1992) 221-243
41. Koiter W.T. Stress-strain relations, uniqueness and variational theorems for elasto-plastic materials with singular yield surfaces. Quart. Appl. Math. 11 (1953) 350
42. Kolymbas D. An outline of hypoplasticity. Arc. App. Mech. 61 (1991) 143-151
43. Konishi J., Oda M., and Nemat-Nasser S. Inherent anisotropy and shear strength of assembly of oval cross-sectional rods. In: Vermeer P.A., and Luger H.J. (Eds). Deformation and Failure of Granular Materials (1982), A.A. Balkema, Rotterdam 403-412
44. Kreig R.D. A practical two-surface plasticity theory. J. Appl. Mech. 42 (1975) 641-646
45. Lambe T.W., and Whitman R.V. Soil Mechanics - SI Version (1979), John Wiley & Sons, New York 553p
46. Lashkari A., and Latifi M. A simple plasticity model for prediction of non-coaxial flow of sands. Mech. Res. Commun. 34 2 (2007) 191-200
47. Li X.S., and Dafalias Y.F. Dilatancy for cohesionless soils. Geotechnique 50 4 (2000) 449-460
48. Li X.S., and Dafalias Y.F. Constitutive modeling of inherently anisotropic soil behavior. J. Geotech. Geoenviron. Eng. Div. ASCE 128 (2002) 868-880
49. Loret B. Geomechanical applications of the theory of multimechanisms. In: Darve F. (Ed). Constitutive Equations and Modeling (1990), Elsevier, New York 187-211
50. Mandel J. Sur les lignes de glissement el le calcul des deplacements dans la deformation plastique. Compt. rendus l'Acad. Sci. 225 (1947) 1272-1273
51. Mandel J. Generalisation de la theorie de plasticite de W. T. Koiter. Int. J. Solids. Struct. 1 (1965) 273
52. Manzari M.T., and Dafalias Y.F. A critical state two-surface plasticity model for sands. Geotechnique 47 2 (1997) 255-272
53. Mehrabadi M.M., and Cowin S.C. Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26 (1978) 269-284
54. Mehrabadi M.M., Nemat-Nasser S., and Oda M. On statistical description of stress and fabric in granular materials. Int. J. Numer. Anal. Methods Geomech. 6 (1982) 95-98
55. Mould, J.C., 1983. Stress Induced Anisotropy in Sand and the Evaluation of a Multi-Surface Elasto-Plastic Material Mode. Ph.D. Thesis. University of Colorado. Boulder.
56. Mould, J.C., Sture, S., Ko, H.Y., 1985. Sand deformation tests with rotating principal stress directions. In: Proceedings of the Fifth International Conference on Numer. Methods Geomechanics, Nagoya, 1-5 April, 1985, pp. 531-538.
57. Mroz Z. On the description of anisotropic hardening. J. Mech. Phys. Solids 15 (1967) 163-175
58. Mroz Z., Norris V.A., and Zienkiewicz O.C. Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique 29 1 (1979) 1-34
59. Nemat-Nasser S. A micromechanically-based constitutive model for frictional deformation of granular materials. J. Mech. Phys. Solids 48 (2000) 1541-1563
60. Nemat-Nasser S., and Zhang J. Constitutive relations for cohesionless frictional granular materials. Int. J. Plast. 18 (2002) 531-547
61. Nemat-Nasser S., Mehrabadi M.M., and Iwakuma T. On certain microscopic and macroscopic aspect of plastic flow of ductile materials. In: Nemat-Nasser S. (Ed). Three Dimensional Constitutive Relations and Ductile Fracture (1981), North Holland, Amsterdam 157-172
62. Oda M. Initial fabrics and their relations to mechanical properties of granular materials. Soils Found. 12 2 (1972) 1-18
63. Pestana J.M., and Whittle A.J. Compression model for cohesionless soils. Geotechnique 45 4 (1995) 611-631
64. Poorooshasb H.B., and Pietruszczak S. A generalized flow theory for sands. Soils Found. 26 2 (1986) 1-15
65. Prevost J.H. Mathematical modeling of monotonic and cyclic undrained clay behavior. Int. J. Numer. Methods Geomech. 1 2 (1977) 195-216
66. Prevost J.H. A simple plasticity theory for frictional cohesionless soils. Soil Dyn. Earthquake Eng. 4 1 (1985) 9-17
67. Richart R.E., Hall J.R., and Woods W.D. Vibrations of Soils and Foundations (1970), Prentice-Hall, Inglewood Cliffs, NJ
68. Rowe P.W. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc. Roy. Soc. Lond. Ser. A 269 (1962) 500-527
69. Satake M. Fundamental quantities in the graph approach to granular materials. Proceedings of the US/Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials (1982), Elsevier, New York, NY 9-19
70. Schofield A., and Wroth P. The Critical State Soil Mechanics (1968), McGraw Hill
71. Sekiguchi, H., Ohta, K., 1977. Induced anisotropy and time dependency in clays. In: Constitutive Equations of Soils, Proceedings of the 9th International Conference on Soil Mech. Found. Eng., Special Session 9, Tokyo, ISSMFE, pp. 229-238.
72. Simo J.C., and Taylor R.L. Return mapping algorithm for plane stress elastoplasticity. Int. J. Numer. Methods. Eng. 22 (1986) 649-670
73. Simo J.C., Kennedy J.G., and Govindjee S. Int. J. Numer. Methods Eng. 26 (1988) 2161-2185
74. Spencer A.J.M. A theory of the kinematics of ideal soils under plane strain conditions. J. Mech. Phys. Solids 12 (1964) 337-351
75. Spencer A.J.M. Deformation of Ideal Granular Materials. Mechanics of Solids (1982), Pergamon Press, Oxford and New York pp. 607-652
76. Taylor D.W. Fundamentals of Soil Mechanics (1948), John Wiley & Sons, New York
77. Valanis K.C. A theory of viscoplasticity without a yield surface, Part I: general theory. Arch. Mech. 23 (1971) 517
78. Wan R.G., and Guo R.G. A simple constitutive model for granular soils: modified stress-dilatancy approach. Comput. Geotech. 22 2 (1998) 109-133
79. Wood D.M., Belkheir K., and Liu D.F. Strain softening and state parameter for sand modeling. Geotechnique 44 2 (1994) 335-339
80. Zhu H., Mehrabadi M.M., and Massoudi M. Incorporating the effect of fabric in the dilatant double shearing model for planar deformation of granular materials. Int. J. Plast. 22 (2006) 628-653
81. Zhu H., Mehrabadi M.M., and Massoudi M. Three-dimensional constitutive relations for granular materials based on the Dilatant Double Shearing mechanism and the concept of fabric. Int. J. Plast. 22 (2006) 826-857
82. Zhu H., Mehrabadi M.M., and Massoudi M. A comparative study of hypoplasticy and the fabic-dependent dilatant double shearing model for granular materials. Int. J. Numer. Anal. Methods Geomech. (2006) 10.1002/nag.559