메뉴 건너뛰기




Volumn 363, Issue 1836, 2005, Pages 2543-2580

Enhanced continua and discrete lattices for modelling granular assemblies

Author keywords

Discrete lattice models; Enhanced continuum models; Granular material; Homogenization; Micro structure; Wave propagation

Indexed keywords


EID: 27744434625     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2005.1586     Document Type: Review
Times cited : (29)

References (42)
  • 2
    • 0012716579 scopus 로고    scopus 로고
    • One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 2. Static and dynamic response
    • Askes, H. & Metrikine, A. V. 2002 One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 2. Static and dynamic response. Eur. J. Mech. A: Solids 21, 573-588.
    • (2002) Eur. J. Mech. A: Solids , vol.21 , pp. 573-588
    • Askes, H.1    Metrikine, A.V.2
  • 3
    • 0023983474 scopus 로고
    • Micromechanical aspects of isotropic granular assemblies with linear contact interactions
    • Bathurst, R. J. & Rothenburg, L. 1988 Micromechanical aspects of isotropic granular assemblies with linear contact interactions. J. Appl. Mech. 55, 17-23.
    • (1988) J. Appl. Mech. , vol.55 , pp. 17-23
    • Bathurst, R.J.1    Rothenburg, L.2
  • 7
    • 85023350349 scopus 로고
    • Micromechanical modelling of constitutive relations for granular material
    • (ed. M. Satake & J. T. Jenkins), Amsterdam: Elsevier
    • Chang, C. S. 1988 Micromechanical modelling of constitutive relations for granular material. In Micromechanics of granular material (ed. M. Satake & J. T. Jenkins), pp. 271-279. Amsterdam: Elsevier.
    • (1988) Micromechanics of Granular Material , pp. 271-279
    • Chang, C.S.1
  • 8
    • 0027640887 scopus 로고
    • Micromechanical modeling of deformation and failure for granulates with frictional contacts
    • doi:10.1016/0167-6636(93)90023-K
    • Chang, C. S. 1993 Micromechanical modeling of deformation and failure for granulates with frictional contacts. Mech. Mater. 16, 13-24. (doi:10.1016/0167-6636(93)90023-K.)
    • (1993) Mech. Mater. , vol.16 , pp. 13-24
    • Chang, C.S.1
  • 9
    • 0029357270 scopus 로고
    • Second-gradient constitutive theory for granular materials with random packing structure
    • doi:10.1016/0020-7683(94)00259-Y
    • Chang, C. S. & Gao, J. 1995 Second-gradient constitutive theory for granular materials with random packing structure. Int. J. Solids Struct. 32, 2279-2293. (doi:10.1016/0020-7683(94)00259-Y.)
    • (1995) Int. J. Solids Struct. , vol.32 , pp. 2279-2293
    • Chang, C.S.1    Gao, J.2
  • 10
    • 0029732155 scopus 로고    scopus 로고
    • Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation
    • doi:10.1007/BF01187439
    • Chang, C. S. & Gao, J. 1996 Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation. Acta Mech. 115, 213-229. (doi:10.1007/BF01187439.)
    • (1996) Acta Mech. , vol.115 , pp. 213-229
    • Chang, C.S.1    Gao, J.2
  • 11
    • 0007152323 scopus 로고    scopus 로고
    • Wave propagation in granular rod using high-gradient theory
    • doi:10.1061/(ASCE)0733-9399(1997)123:1(52)
    • Chang, C. S. & Gao, J. 1997 Wave propagation in granular rod using high-gradient theory. J. Eng. Mech. 123, 52-59. (doi:10.1061/(ASCE)0733- 9399(1997)123:1(52).)
    • (1997) J. Eng. Mech. , vol.123 , pp. 52-59
    • Chang, C.S.1    Gao, J.2
  • 12
    • 0025664180 scopus 로고
    • Constitutive relation for a particulate medium with the effect of particle rotation
    • doi:10.1016/0020-7683(90)90067-6
    • Chang, C. S. & Liao, C. L. 1990 Constitutive relation for a particulate medium with the effect of particle rotation. Int. J. Solids Struct. 29, 437-453. (doi:10.1016/0020-7683(90)90067-6.)
    • (1990) Int. J. Solids Struct. , vol.29 , pp. 437-453
    • Chang, C.S.1    Liao, C.L.2
  • 13
    • 0026692594 scopus 로고
    • Elastic material constants for isotropic granular solids with particle rotation
    • doi:10.1016/0020-7683(92)90071-Z
    • Chang, C. S. & Ma, L. 1992 Elastic material constants for isotropic granular solids with particle rotation. Int. J. Solids Struct. 29, 1001-1018. (doi:10.1016/0020-7683(92)90071-Z.)
    • (1992) Int. J. Solids Struct. , vol.29 , pp. 1001-1018
    • Chang, C.S.1    Ma, L.2
  • 14
  • 15
    • 0026226380 scopus 로고
    • Localisation in a Cosserat continuum under static and dynamic loading conditions
    • doi:10.1016/0045-7825(91)90185-9
    • De Borst, R. & Sluys, L. J. 1991 Localisation in a Cosserat continuum under static and dynamic loading conditions. Comput. Meth. Appl. Mech. Eng. 90, 805-827. (doi:10.1016/0045-7825(91)90185-9.)
    • (1991) Comput. Meth. Appl. Mech. Eng. , vol.90 , pp. 805-827
    • De Borst, R.1    Sluys, L.J.2
  • 16
    • 0001465340 scopus 로고
    • Stress-strain relations for a simple model of a granular medium
    • Deresiewicz, H. 1958 Stress-strain relations for a simple model of a granular medium. J. Appl. Mech. 25, 402-406.
    • (1958) J. Appl. Mech. , vol.25 , pp. 402-406
    • Deresiewicz, H.1
  • 17
    • 0019657872 scopus 로고
    • The effective elastic moduli of porous granular rock
    • Digby, P. J. 1981 The effective elastic moduli of porous granular rock. J. Appl. Mech. 48, 803-808.
    • (1981) J. Appl. Mech. , vol.48 , pp. 803-808
    • Digby, P.J.1
  • 18
    • 84986809104 scopus 로고
    • Stress-strain relations and vibrations of granular medium
    • Duffy, J. & Mindlin, R. D. 1957 Stress-strain relations and vibrations of granular medium. J. Appl. Mech. 24, 585-593.
    • (1957) J. Appl. Mech. , vol.24 , pp. 585-593
    • Duffy, J.1    Mindlin, R.D.2
  • 19
    • 0001244104 scopus 로고
    • Theory of micro-polar elasticity
    • (ed. H. Liebowitz), New York/London: Academic Press ch. 7
    • Eringen, A. C. 1968 Theory of micro-polar elasticity. In Fracture-an advanced treatise (ed. H. Liebowitz), vol. 2, pp. 621-693. New York/London: Academic Press ch. 7
    • (1968) Fracture-an Advanced Treatise , vol.2 , pp. 621-693
    • Eringen, A.C.1
  • 21
    • 0001198767 scopus 로고
    • On uniqueness and stability in the theory of finite elastic strain
    • doi:10.1016/0022-5096(57)90016-9
    • Hill, R. 1957 On uniqueness and stability in the theory of finite elastic strain. J. Mech. Phys. Solids 5, 229-241. (doi:10.1016/0022-5096(57)90016-9.)
    • (1957) J. Mech. Phys. Solids , vol.5 , pp. 229-241
    • Hill, R.1
  • 22
    • 0002581765 scopus 로고
    • Volume change in small strain axisymmetric deformations of granular material
    • (ed. M. Satake & J. T. Jenkins), Amsterdam: Elsevier
    • Jenkins, J. T. 1988 Volume change in small strain axisymmetric deformations of granular material. In Micromechanics of granular materials (ed. M. Satake & J. T. Jenkins), pp. 143-152. Amsterdam: Elsevier.
    • (1988) Micromechanics of Granular Materials , pp. 143-152
    • Jenkins, J.T.1
  • 25
    • 0031278490 scopus 로고    scopus 로고
    • Stress-strain relationships for granular materials based on the hypothesis of best-fit
    • doi:10.1016/S0020-7683(97)00015-2
    • Liao, C. L., Chang, T. P., Young, D. H. & Chang, C. S. 1997 Stress-strain relationships for granular materials based on the hypothesis of best-fit. Int. J. Solids Struct. 34, 4087-4100. (doi:10.1016/S0020-7683(97) 00015-2.)
    • (1997) Int. J. Solids Struct. , vol.34 , pp. 4087-4100
    • Liao, C.L.1    Chang, T.P.2    Young, D.H.3    Chang, C.S.4
  • 26
    • 0034002534 scopus 로고    scopus 로고
    • Pressure-dependent elastic moduli of granular assemblies
    • doi:10.1002/(SICI)1096-9853(200003)24:3<265::AID-NAG65>3.0.CO;2-X
    • Liao, C. L., Chan, T. C., Suiker, A. S. J. & Chang, C. S. 2000 Pressure-dependent elastic moduli of granular assemblies. Int. J. Numer. Anal. Meth. Geomech. 24, 265-279. (doi:10.1002/(SICI)1096-9853(200003)24:3<265:: AID-NAG65>3.0.CO;2-X.)
    • (2000) Int. J. Numer. Anal. Meth. Geomech. , vol.24 , pp. 265-279
    • Liao, C.L.1    Chan, T.C.2    Suiker, A.S.J.3    Chang, C.S.4
  • 28
    • 0012686118 scopus 로고    scopus 로고
    • One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 1. Generic formulation
    • Metrikine, A. V. & Askes, H. 2002 One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure. Part 1. Generic formulation. Eur. J. Mech. A: Solids 21, 555-572.
    • (2002) Eur. J. Mech. A: Solids , vol.21 , pp. 555-572
    • Metrikine, A.V.1    Askes, H.2
  • 29
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • doi:10.1007/BF00248490
    • Mindlin, R. D. 1964 Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51-78. (doi:10.1007/BF00248490.)
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 30
    • 0000095439 scopus 로고
    • Second gradient of strain and surface-tension in linear elasticity
    • doi:10.1016/0020-7683(65)90006-5
    • Mindlin, R. D. 1965 Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct. 1, 417-438. (doi:10.1016/0020-7683(65) 90006-5.)
    • (1965) Int. J. Solids Struct. , vol.1 , pp. 417-438
    • Mindlin, R.D.1
  • 31
    • 0030208823 scopus 로고    scopus 로고
    • Dispersion and wave propagation in discrete and continuous models for granular materials
    • doi:10.1016/0020-7683(95)00178-6
    • Mühlhaus, H.-B. & Oka, F. 1996 Dispersion and wave propagation in discrete and continuous models for granular materials. Int. J. Solids Struct. 33, 2841-2858. (doi:10.1016/0020-7683(95)00178-6.)
    • (1996) Int. J. Solids Struct. , vol.33 , pp. 2841-2858
    • Mühlhaus, H.-B.1    Oka, F.2
  • 32
    • 0023404291 scopus 로고
    • The thickness of shear bands in granular materials
    • Mühlhaus, H.-B. & Vardoulakis, I. 1987 The thickness of shear bands in granular materials. Geotechnique 37, 271-283.
    • (1987) Geotechnique , vol.37 , pp. 271-283
    • Mühlhaus, H.-B.1    Vardoulakis, I.2
  • 33
    • 0007456538 scopus 로고    scopus 로고
    • Micro-structure developed in shear bands of dense granular soils and its computer simulation-mechanism of dilatancy and failure
    • (ed. N. A. Fleck & A. C. F. Cocks). Dordrecht, The Netherlands: Kluwer Academic Publishers
    • Oda, M., Iwashita, K. & Kazama, H. 1997 Micro-structure developed in shear bands of dense granular soils and its computer simulation-mechanism of dilatancy and failure. In IUTAM Symposium on Mechanics of Granular and Porous Materials (ed. N. A. Fleck & A. C. F. Cocks), pp. 353-364. Dordrecht, The Netherlands: Kluwer Academic Publishers.
    • (1997) IUTAM Symposium on Mechanics of Granular and Porous Materials , pp. 353-364
    • Oda, M.1    Iwashita, K.2    Kazama, H.3
  • 34
    • 0000215584 scopus 로고
    • Micromechanical definition of the Cauchy stress tensor for particulate media
    • (ed. A. P. S. Selvadurai). Amsterdam: Elsevier
    • Rothenburg, L. & Selvadurai, A. P. S. 1981 Micromechanical definition of the Cauchy stress tensor for particulate media. In Mechanics of structured media (ed. A. P. S. Selvadurai), pp. 469-486. Amsterdam: Elsevier.
    • (1981) Mechanics of Structured Media , pp. 469-486
    • Rothenburg, L.1    Selvadurai, A.P.S.2
  • 36
    • 0033720253 scopus 로고    scopus 로고
    • Application of higher-order tensor theory for formulating enhanced continuum models
    • doi:10.1007/BF01190020
    • Suiker, A. S. J. & Chang, C. S. 2000 Application of higher-order tensor theory for formulating enhanced continuum models. Acta Mech. 142, 223-234. (doi:10.1007/BF01190020.)
    • (2000) Acta Mech. , vol.142 , pp. 223-234
    • Suiker, A.S.J.1    Chang, C.S.2
  • 37
    • 0033189450 scopus 로고    scopus 로고
    • Surface waves in a stratified half space with enhanced continuum properties. Part 1. Formulation of the boundary value problem
    • Suiker, A. S. J., Chang, C. S., De Borst, R. & Esveld, C. 1999 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.
    • (1999) Eur. J. Mech. A: Solids , vol.18 , pp. 749-768
    • Suiker, A.S.J.1    Chang, C.S.2    De Borst, R.3    Esveld, C.4
  • 38
    • 0034824728 scopus 로고    scopus 로고
    • Micro-mechanical modelling of granular material. Part 1. Derivation of a second-gradient micro-polar constitutive theory
    • doi:10.1007/BF01261670
    • Suiker, A. S. J., de Borst, R. & 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. (doi:10.1007/ BF01261670.)
    • (2001) Acta Mech. , vol.149 , pp. 161-180
    • Suiker, A.S.J.1    De Borst, R.2    Chang, C.S.3
  • 39
    • 0034821265 scopus 로고    scopus 로고
    • Micro-mechanical modelling of granular material. Part 2. Plane wave propagation in infinite media
    • doi:10. 1007/BF01261671
    • Suiker, A. S. J., de Borst, R. & Chang, C. S. 2001b Micro-mechanical modelling of granular material. Part 2. Plane wave propagation in infinite media. Acta Mech. 149, 181-200. (doi:10. 1007/BF01261671.)
    • (2001) Acta Mech. , vol.149 , pp. 181-200
    • Suiker, A.S.J.1    De Borst, R.2    Chang, C.S.3
  • 40
    • 0035253994 scopus 로고    scopus 로고
    • Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models
    • doi:10.1016/80020-7683(00)00104-9
    • Suiker, A. S. J., Metrikine, A. V. & de Borst, R. 2001c Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models. Int. J. Solids Struct. 38, 1563-1583. (doi:10.1016/80020-7683(00)00104-9.)
    • (2001) Int. J. Solids Struct. , vol.38 , pp. 1563-1583
    • Suiker, A.S.J.1    Metrikine, A.V.2    De Borst, R.3
  • 41
    • 0023209544 scopus 로고
    • The effective elastic moduli of a random packing of spheres
    • doi:10.1016/0022-5096(87)90036-6
    • Walton, K. 1987 The effective elastic moduli of a random packing of spheres. J. Mech. Phys. Solids 35, 213-226. (doi:10.1016/0022-5096(87)90036-6.)
    • (1987) J. Mech. Phys. Solids , vol.35 , pp. 213-226
    • Walton, K.1
  • 42
    • 0004109271 scopus 로고
    • Princeton, NY: Princeton University Press
    • Weyl, H. 1946 Classical groups. Princeton, NY: Princeton University Press.
    • (1946) Classical Groups
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.