One-dimensional localisation studied with a second grade model

European Journal of Mechanics, A/Solids

Volumn 17, Issue 4, 1998, Pages 637-656

  Chambon, R ^b   Caillerie, D ^b   El Hassan, N ^a  

^a LABORATOIRE SOLS SOLIDES STRUCTURES   (France)

^b NONE

Author keywords

Finite elements; Large strains; Localisation; Second grade model

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS;

SECOND GRADE MODELS; STRAIN LOCALIZATION;

STRAIN;

EID: 0032108333     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(99)80026-6     Document Type: Article

References (19)

1. AIFANTIS, 1984, On the microstructural origin of certain inelastic models, Transactions of ASME. J. Mat. Engng. Tech., 106, 326-330.
2. BAZANT et al., 1984, Continuum theory for strain softening, J. Eng. Mech. ASCE, 110, 1666-1692.
3. DE BORST, 1985, Non linear analysis of frictional materials. Dissertation, Delft University of Technology, Delft.
4. DE BORST R., MUHLHAUS H., Gradient dependent plasticity: formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering., 35, 521-539.
5. CHAMBON, 1989, Une classe de lois de comportement incrémentalement non linéaires pour les sols, résolution de quelques problèmes de cohérence, C.R.A.S., 308 Série II, 1571-1576.
6. CHAMBON et al., 1994, CLoE, a new rate type constitutive model for geomaterials, theoretical basis and implementation, International Journal for Numerical and Analytical Methods in Geomechanics, 18, 4, 253-278.
7. CHAMBON, CROCHEPEYRE, 1995, Loss of uniqueness of the solution in a boundary value problem, Proceedings of NUMOG V., 165-171 Rotterdam Balkema.
8. CHAMBON et al., 1996, Etude de la localisation unidimensionelle à l'aide d'un modèle de second gradient, C.R.A.S., 323, IIb, 231-238.
9. CHARLIER, 1987, Approche unifiée de quelques problèmes non linéaires de mécanique des milieux continus par la méthode des éléments finis, Thèse, Université de Liège, Liège.
10. FRANTZISKONIS, VARDOULAKIS, 1992, On the micro-structure of surface effects and related insatabilities, Eur. J. Mech. A/Solids, 11, 21-34.
11. FREMOND, NEDJAR, 1996, Damage gradient of damage and principle of virtual work, Int. J. Solids Structures, 33, 8, 1083-1103.
12. GERMAIN, 1973, La méthode des puissances virtuelle en mécanique des milieux continus: Première partie : théorie du second gradient, Journal de Mécanique, 12, 235-274.
13. MINDLIN, 1965, Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Structures., 1, 417-738.
14. MUHLHAUS, AIFANTIS, 1991, A variational principle for gradient plasticity, Int. J. Solids Structures, 28, 7, 845-857.
15. PAMIN, 1994, Gradient dependent plasticity in numerical simulation of localisation phenomena, Dissertation, Delft University of technology, Delft.
16. PEERLINGS et al., 1996, Gradient enhanced damage for quasi-brittle materials, Int. J. Numerical Methods Engng., 39, 3391-3403.
17. VARDOULAKIS, AIFANTIS, 1991, A gradient flow theory of plasticity for granular materials, Acta Mechanica, 87, 197-217.
18. VARDOULAKIS, FRANTZISKONIS 1992, Micro structure in kinematic hardening plasticity, Eur. J. Mech. A/Solids, 11, 467-486.
19. ZBIB, AIFANTIS, 1988, On the localisation and post localisation of plastic deformation, part I. On the initiation of shear bands. Part II. On the evolution and thickness of shear bands, Res Mechanica, 23, 261-277; 279-292. (Special Issue on Material Instabilities, Aifantis et al. eds).