References
- Adams, G. G., and Nosonovsky, M. (2000), 'Contact modeling forces', Tribology international, 33, 431-442 https://doi.org/10.1016/S0301-679X(00)00063-3
- Bazant, Z. P., Caner, F. c., Carol, L, Adley, M. D., and Akers, S. A. (2000), 'Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress', Journal of Engineering Mechanics-ASCE, 126(9), 944-953 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(944)
- Chang, C. S., Chao, S. J., and Chang, Y. (1995), 'Estimates of Elastic-Moduli for Granular Material with Anisotropic Random Packing Structure', International Journal of Solids and Structures, 32(14), 1989-2008 https://doi.org/10.1016/0020-7683(94)00225-L
- Chang, C. S., and Gao, J. (1996), 'Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation', Acta Mechanica, 115(1-4), 213-229 https://doi.org/10.1007/BF01187424
- Chang, C. S., Misra, A., and Sundaram, S. S. (1991), 'Properties of granular packings under low amplitude cyclic loading', Soil Dynamics and Earthquake Engineering, 10(4), 201-211 https://doi.org/10.1016/0267-7261(91)90034-W
- Chang, C. S., Sundaram, S. S., and Misra, A. (1989), 'Initial Moduli of Particulated Mass with Frictional Contacts', International Journal for Numerical and Analytical Methods in Geomechanics, 13(6), 629-644 https://doi.org/10.1002/nag.1610130605
- Christoffersen, J., Mehrabadi, M. M., and Nematnasser, S. (1981), 'A Micromechanical Description of Granular Material Behavior', Journal of Applied Mechanics-Transactions of the Asme, 48(2), 339-344 https://doi.org/10.1115/1.3157619
- Cundall, P. A., and Strack, O. D. L. (1979), 'Discrete NumericalModel for Granular Assemblies', Geotechnique, 29(1), 47-65 https://doi.org/10.1680/geot.1979.29.1.47
- Darve, F., and Nicot, F. (2005), 'On incremental non-linearity in granular media: phenomenological and multi-scale views (Part I)', International Journal for Numerical and Analytical Methods in Geomechanics, 29(14), 1387-1409 https://doi.org/10.1002/nag.466
- Einav, I., and Puzrin, A. M. (2004), 'Continuous hyperplastic critical state (CHCS) model Derivation', International Journal of Solids and Structures, 41(1), 199-226 https://doi.org/10.1016/j.ijsolstr.2003.09.012
- Emeriault, F., and Cambou, B. (1996), 'Micromechanical modelling of anisotropic non-linear elasticity of granular medium', International Journal of Solids and Structures, 33(18), 2591-2607 https://doi.org/10.1016/0020-7683(95)00170-0
- Emeriault, F., and Chang, C. S. (1997), 'Interparticle forces and displacements in granular materials', Computers and Geotechnics, 20(3-4), 223-244 https://doi.org/10.1016/S0266-352X(97)00004-9
- Fang, H. L. (2003), 'A state-dependent multi-mechanism model for sands', Geotechnique, 53(4), 407-420 https://doi.org/10.1680/geot.53.4.407.37320
- Goddard, J. D. (1990), 'Nonlinear Elasticity and Pressure-Dependent Wave Speeds in Granular Media', Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 430(1878), 105-131
- Hertz, H. (1882), 'Uber die Beruhrung fester elastischer Korper (On the contact of elastic solids)', Journal of reine und angewandte mathematik, 92, 156-171
- Hicher, P. Y., and Chang, C. S. (2005), 'Evaluation of two homogenization techniques for modeling the elastic behavior of granular materials', Journal of Engineering Mechanics-ASCE, 131(11), 1184-1194 https://doi.org/10.1061/(ASCE)0733-9399(2005)131:11(1184)
- Jager, J. (1999), 'Uniaxial deformation of a random packing of particles', Archive of Applied Mechanics, 69(3), 181-203 https://doi.org/10.1007/s004190050213
- Johnson, K. L. (1985), Contact mechanics, Cambridge University Press, Cambridge
- lung, Y. H., Chung, C. K., and Finno, R. J. (2004), 'Development of nonlinear cross-anisotropic model for the pre-failure deformation of geomaterials', Computers and Geotechnics, 31(2), 89-102 https://doi.org/10.1016/j.compgeo.2004.01.002
- Kuwano, R., and Jardine, R. J. (2002), 'On the applicability of cross-anisotropic elasticity to granular materials at very small strains', Geotechnique, 52(10), 727-749 https://doi.org/10.1680/geot.52.10.727.38848
- Liao, C. L., Chan, T. C., Suiker, A. S. J., and Chang, C. S. (2000), 'Pressure-dependent elastic moduli of granular assemblies', International Journal for Numerical and Analytical Methods in Geomechanics, 24(3), 265-279 https://doi.org/10.1002/(SICI)1096-9853(200003)24:3<265::AID-NAG65>3.0.CO;2-X
- Liao, C. L., Chang, T. P., Young, D. H., and Chang, C. S. (1997), 'Stress-strain relationship for granular materials based on the hypothesis of best fit', International Journal of Solids and Structures, 34(31-32), 4087-4100 https://doi.org/10.1016/0020-7683(95)00287-1
- Love, A. E. H. (1927), A Treatise of the mathematical theory of elasticity, Cambridge university press, Cambridge, UK
- Madadi, M., Tsoungui, O., Latzel, M., and Luding, S. (2004), 'On the fabric tensor of polydisperse granular materials in 2D', International Journal of Solids and Structures, 41(9-10), 2563-2580 https://doi.org/10.1016/j.ijsolstr.2003.12.005
- Mehrabadi, M. M., Nematnasser, S., and Oda, M. (1982), 'On Statistical Description of Stress and Fabric in Granular-Materials', International Journal for Numerical and Analytical Methods in Geomechanics, 6(1), 95-108 https://doi.org/10.1002/nag.1610060107
- Mindlin, R. D. (1949), 'Comliance of elastic bodies in contact', Journal of applied mechanics, 16, 259-270
- Mindlin, R. D., and Deresiewicz, H. (1953), 'Elastic spheres in contact under varying oblique forces', Journal of applied mechanics, ASME, 20(3), 327-344
- Mulhearn, T. O. (1959), 'Deformation of metals by Vickers-type pyramidal indenters', J. Mech. Physics Solids, 7, 85-92 https://doi.org/10.1016/0022-5096(59)90013-4
- Nicot, F., and Darve, F. (2006), 'Micro-mechanical investigation of material instability in granular assemblies', International Journal of Solids and Structures, 43(11-12), 3569-3595 https://doi.org/10.1016/j.ijsolstr.2005.07.008
- Oda, M., Nematnasser, S., and Mehrabadi, M. M. (1982), 'A Statistical Study of Fabric in a Random Assembly of Spherical Granules', International Journal for Numerical and Analytical Methods in Geomechanics, 6(1), 77-94 https://doi.org/10.1002/nag.1610060106
- Ouadfel, H., and Rothenburg, L. (2001), 'Stress-force-fabric' relationship for assemblies of ellipsoids', Mechanics of Materials, 33(4), 201-221 https://doi.org/10.1016/S0167-6636(00)00057-0
- Pestana, J. M., Whittle, A. J., and Salvati, L. A. (2002), 'Evaluation of a constitutive model for clays and sands: Part I - sand behaviour', International Journal for Numerical and Analytical Methods in Geomechanics, 26(11), 1097-1121 https://doi.org/10.1002/nag.237
- Puzrin, A. M., and Burland, J. B. (2000), 'Kinematic hardening plasticity formulation of small strain behaviour of soils', International Journal for Numerical and Analytical Methods in Geomechanics, 24(9), 753-781 https://doi.org/10.1002/1096-9853(20000810)24:9<753::AID-NAG97>3.0.CO;2-2
- Samuels, L. E., and Mulhearn, T. O. (1956), 'The deformation zone associated with indentation hardness impressions', J. Mech. Physics Solids, 5, 125-130 https://doi.org/10.1016/0022-5096(57)90056-X
- Stallebrass, S. E., and Taylor, R. N. (1997), 'The development and evaluation of a constitutive model for the prediction of ground movements in overconsolidated clay', Geotechnique, 47(2), 235-253 https://doi.org/10.1680/geot.1997.47.2.235
- Walton, O. R., and Braun, R. L. (1986), 'Viscosity, granulartemperature, and stress calculations for shearing assemblies of inelastic, friction disks', Journal of rheology, 30(5), 949-980 https://doi.org/10.1122/1.549893
- Yimsiri, S., and Soga, K. (2000), 'Micrornechanics-based stress-strain behaviour of soils at small strains', Geotechnique, 50(5), 559-571 https://doi.org/10.1680/geot.2000.50.5.559
- Yu, P., and Richart, F. E., Jr. (1984), 'Stress ratio effects on shear modulus of dry sands', Journal of Geotechnical Engineering, 110(3), 331-345 https://doi.org/10.1061/(ASCE)0733-9410(1984)110:3(331)