Modeling Failure and Deformation of an Assembly of Spheres with Frictional Contacts
Publication: Journal of Engineering Mechanics
Volume 130, Issue 3
Abstract
A novel mesoscale granular continuum model is derived by homogenizing the mechanical behavior of six particles in contact forming an octahedron structure. The elastic behavior at the particle contacts is simulated in accordance with Hertz theory and the frictional behavior is taken into account by means of an evolution law for the contact shear stiffness. The mesoscale continuum model is calibrated on discrete element simulations of a cuboidal volume filled with identical spheres and loaded under axisymmetric compression. By imposing a set of radial deviatoric stress paths, the failure contour is computed in the deviatoric plane of the principal stress space.
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References
Aifantis, E. C.(1992). “On the role of gradients in the localization of deformation and fracture.” Int. J. Eng. Sci., 30, 1279–1299.
Bardet, J. P.(1990). “Lode dependences for isotropic pressure-sensitive elastoplastic materials.” J. Appl. Mech., 57, 498–506.
Bathurst, R. J., and Rothenburg, L.(1988). “Micromechanical aspects of isotropic granular assemblies with linear contact interactions.” J. Appl. Mech., 55, 17–23.
Bathurst, R. J., and Rothenburg, L.(1990). “Observations on stress-force-fabric relationships in idealized granular materials.” Mech. Mater., 9, 65–80.
Chang, C. S. (1988). “Micromechanical modelling of constitutive relations for granular material.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, The Netherlands, 271–279.
Chang, C. S.(1993). “Micromechanical modeling of deformation and failure for granulates with frictional contacts.” Mech. Mater., 16, 13–24.
Chang, C. S., Chao, S. J., and Chang, Y.(1995). “Estimates of elastic moduli for granular material with anisotropic random packing structure.” Int. J. Solids Struct., 32, 1989–2008.
Chang, C. S., and Gao, J.(1995). “Second-gradient constitutive theory for granular material with random packing structure.” Int. J. Solids Struct., 32, 2279–2293.
Chang, C. S., and Gao, J.(1996). “Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation.” Acta Mech., 115, 213–229.
Chang, C. S., Sundaram, S. S., and Misra, A.(1989). “Initial moduli of particulated mass with frictional contacts.” Int. J. Numer. Analyt. Meth. Geomech., 13, 629–644.
Christofferson, J., Mehrabadi, M. M., and Nemat-Nasser, S.(1981). “A micromechanical description of granular material behavior.” J. Appl. Mech., 48, 339–344.
Cundall, P. A. (1988). “Computer simulations of dense sphere assemblies.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, The Netherlands, 113–123.
Cundall, P. A., and Strack, O. D. L.(1979). “A discrete numerical model for granular assemblies.” Geotechnique, 1, 47–65.
De Borst, R., and Mühlhaus, H.-B.(1992). “Gradient-dependent plasticity: Formulation and algorithmic aspects.” Int. J. Numer. Methods Eng., 35, 521–539.
De Borst, R., and Van der Giessen, E. (1998). Material instabilities in solids, Wiley, Chichester.
de Josselin de Jong, G.(1977). “Mathematical elaboration of the double sliding, free rotation model.” Arch. Mech., 29, 561–591.
Digby, P. J.(1981). “The effective elastic moduli of porous granular rock.” J. Appl. Mech., 48, 803–808.
Eringen, A. C. (1968). “Theory of micro-polar elasticity.” Fracture—An advanced treatise, H. Liebowitz, ed., Academic, New York, Vol. II, 621–693.
Geers, M. G. D. (1997). “Experimental analysis and computational modelling of damage and fracture.” PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
Hertz, H.(1881). “Über die berührung fester elastischer Körper.” J. Reine Angew. Math., 92, 156–171.
Heyliger, P. R., and McMeeking, R. M.(2001). “Cold plastic compaction of powders by a network model.” J. Mech. Phys. Solids, 49, 2031–2054.
Jenkins, J. T. (1988). “Volume change in small strain axisymmetric deformations of granular material.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, The Netherlands, 143–152.
Jenkins, J. T. (1997). “Inelastic behavior of random arrays of identical spheres.” IUTAM Symp. on Mechanics of Granular and Porous Materials, N. A. Fleck and A. C. F. Cocks, eds., Kluwer Academic, Dordrecht, The Netherlands, 11–22.
Johnson, K. L. (1985). Contact mechanics, Cambridge University Press, London.
Kim, M. K., and Lade, P.(1988). “Single hardening constitutive model for frictional materials: I. Plastic potential function.” Comput. Geotech., 5, 307–324.
Lade, P. V., and Duncan, J. M.(1975). “Elastoplastic stress-strain theory for cohesionless soil.” J. Geotech. Eng. Div., Am. Soc. Civ. Eng., 101(10), 1037–1053.
Liao, C. L., Chan, T. C., Suiker, A. S. J., and Chang, C. S.(2000). “Pressure-dependent elastic moduli of granular assemblies.” Int. J. Numer. Analyt. Meth. Geomech., 24, 265–279.
Liao, C. L., Chang, T. P., Young, D. H., and Chang, C. S.(1997). “Stress-strain relationships for granular materials based on the hypothesis of best-fit.” Int. J. Solids Struct., 34, 4087–4100.
Mehrabadi, M. M., and Cowin, S. C.(1978). “Initial planar deformation of dilatant granular materials.” J. Mech. Phys. Solids, 26, 269–284.
Mehrabadi, M. M., Nemat-Nasser, S., and Oda, M.(1982). “On statistical description of stress and fabric in granular materials.” Int. J. Numer. Analyt. Meth. Geomech., 6, 95–108.
Mindlin, R. D.(1964). “Micro-structure in linear elasticity.” Arch. Ration. Mech. Anal., 16, 51–78.
Misra, A., and Chang, C. S.(1993). “Effective elastic moduli of heterogeneous granular solids.” Int. J. Solids Struct., 30, 2547–2566.
Mühlhaus, H.-B., and Oka, F.(1996). “Dispersion and wave propagation in discrete and continuous models for granular materials.” Int. J. Solids Struct., 33, 2841–2858.
Satake, M. (1982). “Fabric tensor in granular materials.” Deformation and failure of granular materials, P. A. Vermeer and H. J. Luger, eds., Balkema, Rotterdam, The Netherlands, 63–68.
Spencer, A. J. M.(1964). “A theory of the kinematics of ideal soils under plane strain conditions.” J. Mech. Phys. Solids, 12, 337–351.
Suiker, A. S. J., Chang, C. S., De Borst, R., and Esveld, C.(1999a). “Surface waves in a stratified half space with enhanced continuum properties—Part 1—Formulation of the boundary value problem.” Eur. J. Mech. A/Solids, 18, 749–768.
Suiker, A. S. J., Chang, C. S., De Borst, R., and Esveld, C.(1999b). “Surface waves in a stratified half space with enhanced continuum properties—Part 2—Analysis of the wave characteristics in regard to high-speed railway tracks.” Eur. J. Mech. A/Solids, 18, 769–784.
Suiker, A. S. J., De Borst, R., and Chang, C. S.(2001a). “Micro-mechanical modelling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory.” Acta Mech., 149, 161–180.
Suiker, A. S. J., De Borst, R., and Chang, C. S.(2001b). “Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media.” Acta Mech., 149, 181–200.
Thornton, C.(2000). “Numerical simulations of deviatoric shear deformation of granular media.” Geotechnique, 50, 43–53.
Thornton, C., and Antony, S. J.(1998). “Quasi-static deformation of particulate media.” Philos. Trans. R. Soc. London, Ser. A, 356, 2763–2782.
Thornton, C., and Barnes, D. J.(1986). “Computer simulated deformation of compact granular assemblies.” Acta Mech., 64, 45–61.
Vardoulakis, I., and Sulem, J. (1995). Bifurcation analysis in geomechanics, Blackie Academic & Professional, London.
Walton, K.(1987). “The effective elastic moduli of a random packing of spheres.” J. Mech. Phys. Solids, 35, 213–226.
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Published In
Journal of Engineering Mechanics
Volume 130 • Issue 3 • March 2004
Pages: 283 - 293
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Sep 25, 2002
Accepted: Jul 30, 2003
Published online: Feb 19, 2004
Published in print: Mar 2004
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