Micro-mechanical bases of some salient constitutive features of granular materials

International Journal of Solids and Structures

Volumn 44, Issue 22-23, 2007, Pages 7420-7443

  Nicot, François ^a   Darve, Félix ^b  

^a Cemagref   (France)

^b CNRS   (France)

Author keywords

Flow rule; Force chains; Granular material; Homogenization; Micro structure; Multi scale modeling; Nonassociativeness; Softening effect

Indexed keywords

FORCE MEASUREMENT; HARDENING; MICROMECHANICS; MICROSTRUCTURE; PLASTIC DEFORMATION; STRAIN MEASUREMENT;

FLOW RULES; FORCE CHAINS; HOMOGENIZATION; MULTI-SCALE MODELING; NONASSOCIATIVENESS; SOFTENING EFFECTS;

GRANULAR MATERIALS;

EID: 34748875480     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.04.017     Document Type: Article

References (64)

1. Alonso-Marroquin F., and Herrmann H.J. Calculation of the incremental stress-strain relation of a polygonal packing. Phys. Rev. E 66 (2002) 021301
2. Alonso-Marroquin F., Vardoulakis I., Hermann H.J., Weatherley D., and Mora P. Effect of rolling on dissipation in fault gouges. Phys. Rev. E 74 (2006) 031306
3. Bader, H., 1939. Der schnee und seine metamorphose. USA Snow Ice and Permafrost Research, available from the National Technical Information Service.
4. Bardet J.P. Numerical simulations of the incremental responses of idealized granular materials. Int. J. Plast. 10 8 (1994) 879-908
5. Bardet, J.P., Proubet, J., 1989. Application of micro-mechanics to incrementally nonlinear constitutive equations for granular media. In: Biarez, J., Gourvès, R. (Eds.), Powdersand Grains, pp. 265-273.
6. Bathurst R.J., and Rothenburg L. Observations on stress-force-fabric relationships in idealized granular materials. Mechanics of Materials 9 1 (1990) 65-80
7. Bazant Z.P., and Gambarova P.G. Crack shear in concrete: crack band microplane model. ASCE J. Struct. Eng. 110 9 (1984) 2015-2035
8. Calvetti F., Combe G., and Lanier J. Experimental micro-mechanical analysis of a 2D granular material, relation between structure evolution and loading path. Mechanics of Cohesive-Frictional Materials 2 (1997) 121-163
9. Calvetti F., Viggiani C., and tamagnini C. A numerical investigation of the incremental behavior of granular soils. Italian Geotechnical J. 3 (2003) 11-29
10. Cambou B. From global to local variables in granular materials. In: Thornton (Ed). Powders & Grains (1993), Balkema, Rotterdam 73-86
11. Cambou B., Dubujet P., Emeriault F., and Sidoroff F. Homogenization for granular materials. Eur. J. Mech. A/Solids 14 2 (1995) 255-276
12. Cambou B. Micromechanical approach in granular materials. In: Cambou B. (Ed). Behaviour of granular materials (1998), Springer Wien, New York 170-216
13. Cambou, B., Chaze, M., Dedecker, F., 2000. Change of scale in granular materials. Eur. J. Mech. A/Solids, vol. 19, Elsevier Ed., pp. 999-1014.
14. Chang C.S. Micromechanical modelling of deformation and failure for granulates with frictional contacts. Mechanics of Materials 16 (1992) 13-24
15. Chang C.S., and Hicher P.Y. An elasto-plastic model for granular materials with microstructural consideration. Int. J. Solids Struct. 42 14 (2005) 4258-4277
16. Chang C.S., and Liao C.L. estimates of elastic modulus for media of randomly packed granulates. Appl. Mech. Rev. 47 (1994) 197-206
17. Christoffersen J., Mehrabadi M.M., and Nemat-Nasser S. A micro-mechanical description of granular material behavior. J. Appl. Mech. 48 (1981) 339-344
18. Collins I.F. Associated and nonassociated aspects of the constitutive laws for coupled elastic/plastic materials. Int. J. Geomechanics 2 2 (2002) 259-267
19. Cundall P.A., and Strack O.D.L. A discrete numerical model for granular assemblies. Géotechnique 29 (1979) 47-65
20. Cundall P.A., and Roger D.H. Numerical modelling of discontinua. Eng. Comput. 9 (1992) 101-113
21. Darve F., and Labanieh S. Incremental constitutive law for sands and clays, simulations of monotonic and cyclic tests. Int. J. Numer. Anal. Methods Geomech. 6 (1982) 243-275
22. Darve F., and Servant G. Fundamentals of constitutive equations for geomaterials. In: Darve F., and Vardoulakis I. (Eds). Degradations and Instabilities in Geomaterials (2004), Springer Wien Publication, New York 1-34
23. Darve F., and Nicot F. On flow rule in granular media: phenomenological and multi-scale views (Part II). Int. J. Num. Anal. Methods Geomech. 29 (2005) 1411-1432
24. De Josselin de Jong, G., 1959. Statics and kinematics in the failable zone of granular material. Thesis, University of Delft.
25. DeJosselindeJong G. The double sliding, free rotating model for granular assemblies. Géotechnique 21 (1971) 155-163
26. Drucker, D., 1951. A more fundamental approach to stress-strain relations. 1st US Nat. Cong. Appl. Mech. ASME, pp. 487-491.
27. Fillot N., Iordanoff I., and Berthier Y. A granular dynamic model for the degradation of material. ASME J. Tribol. 126 (2004) 606-614
28. Gudehus, G.,1 979. A comparison of some constitutive laws for soils under radially symmetric loading and unloading. In: Aachen and Wittke, (Eds.), 3rd Int. Conf. Numerical Methods in Geomech., Balkema Publisher, vol. 4, pp. 1309-1324.
29. Hill R. A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6 (1958) 236-249
30. Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 2 (1967) 79-95
31. Horne M.R. The behaviour of an assembly of rotund, rigid cohesionless particles-I, II. Proc. R. Soc. London 286 (1965) 62-97
32. Kanatani K.I. Dilatant plastic deformation of granular materials. Int. J. Eng. Sci. 20 (1982) 879-884
33. Kanatani K.I. Mechanical properties of ideal granular materials. In: Jenkins J.T., and Satake M. (Eds). Mechanics of granular materials, new models and constitutive relations (1983), Elsevier 235-244
34. Kanatani K.I. Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22 2 (1984) 149-164
35. Kishino Y. Disc model analysis of granular media. In: Satake M., and Jenkins J.T. (Eds). Micromechanics of granular materials. 2nd US-Japan Sem. Mech. Granular Mat. (1988), Elsevier 143-152
36. Kishino Y. On the incremental non-linearity observed in a numerical model for granular media. Italian Geotechnical J. 3 (2003) 30-38
37. Kry P.R. The relationship between the visco-elastic and structural properties of fine-grained snow. J. Glaciol. 14 72 (1975) 467-477
38. Love A.E.H. A Treatise of Mathematical Theory of Elasticity (1927), Cambridge University Press, Cambridge
39. Mandel J. Generalisation de la Theorie de la Plasticite de W.T. Koiter. Int. J. Solids Struct. I (1965) 273
40. Mehrabadi M.M., and Cowin S.C. : Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26 (1978) 269-284
41. Mehrabadi M.M., Oda M., and Nemat-Nasser S. On statistical description of stress and fabric in granular materials. Int. J. Num. Anal. Meth. Geomech. 6 (1982) 95-108
42. Nemat-Nasser, S., Mehrabadi, M.M., Iwakuma, T., 1981. On certain macroscopic and microscopic aspects of plastic flow of ductile materials. In: Nemat-Nasser, S. (Ed.), Three-dimensional constitutive relations and ductile fracture, North Holland. pp. 157-172.
43. Nemat-Nasser S., and Mehrabadi M.M. Stress and fabric in granular masses. In: Jenkins J.T., and Satake M. (Eds). Mechanics of granular materials, new models and constitutive relations (1983), Elsevier Scientific Publishers 1-8
44. Nicot F. Constitutive modelling of a snowcover with a change in scale. Eur. J. Mech. A/Solids 22-3 (2003) 325-340
45. Nicot F. Constitutive modelling of snow as a cohesive granular material. Granular Matter 6 (2004) 47-60
46. Nicot F. From a constitutive modelling of a snowcover to the design of flexible structures. Part I, Mechanical modelling. Int. J. Solids Struct. 41/11-12 (2004) 3317-3337
47. Nicot F., and Darve F. A multiscale approach to granular materials. Mechanics of Materials 37 9 (2005) 980-1006
48. Nicot F., and Darve F. Micro-mechanical investigation of material instability in granular assemblies. Int. J. Solids Struct. 43 (2006) 3569-3595
49. Nicot F., and Darve F. On the elastic and plastic strain decomposition in granular materials. Granular Matter 8 3-4 (2006) 221-237
50. Nicot F., Sibille L., Donzé F., and Darve F. From microscopic to macroscopic second-order works in granular assemblies. Mechanics of Materials 39 7 (2007) 664-684
51. Nicot, F., Darve, F., in press. Basic features of plastic strains: from micro-mechanics to incrementally nonlinear models. Int. J. Plast.
52. Nouguier-Lehon C., Vincens E., and Cambou B. Structural changes in granular materials, the case of irregular polygonal particles. Int. J. Solids Struct. 42 24-25 (2005) 6356-6375
53. Oda M. The mechanism of fabric changes during compressional deformation of sand. Soils and Foundations 12 (1972) 1-23
54. Oda M., Konishi J., and Nemat-Nasser S. : Experimental evaluation of strength of granular materials, effects of particle rolling. Mechanics of Materials 1 (1982) 269-283
55. Radjai F., Wolf D., Jean M., and Moreau J.J. Bimodal character of stress transmission in granular packing. Phys. Rev. Lett. 80 1 (1998) 61-64
56. Radjai F., Roux S., and Moreau J.J. Contact forces in a granular packing. Chaos 9 3 (1999) 544-550
57. Reynolds O. On the dilatancy of media composed of rigid particles in contact with experimental illustrations. Philos. Mag. Ser. 5 20 (1885) 469
58. Roscoe K.H., Schofield A.N., and Wroth C.P. On the yielding of soils. Géotechnique 8 1 (1958) 22-53
59. Rothenburg L., and Selvadurai A.P.S. A micromechanical definition of the Cauchy stress tensor for particulate media. In: Selvadurai A.P.S. (Ed). Mechanics of Structured Media (1981), Elsevier, Amsterdam 469-486
60. Satake M. Constitution of mechanics of granular materials through graph representation. Theoretical And Applied Mechanics vol. 26 (1978), University of Tokyo Press 257-266
61. Satake, M., 1982. Fabric tensor in granular materials. In: IUTAM Conference on Deformation and Failure of Granular Materials, Delft, pp. 63-68.
62. Shapiro, L.H., 1997. Snow mechanics, review of the state of knowledge and applications. CRREL Report, vol. 97.3, pp. 1-34.
63. Spencer A.J.M. A theory of the kinematics of ideal soils under plane strain conditions. J. Mech. Phys. Solids 12 (1964) 337-351
64. Weber J. Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents. Bull. Liaison P. et Ch 20 (1966) 1-20