Local second gradient models and damage mechanics: Application to concrete

11th International Conference on Fracture 2005, ICF11

Volumn 3, Issue , 2005, Pages 1800-1805

  Kotronis, P ^a   Chambon, R ^a   Mazars, J ^a   Collin, F ^b  

^a CNRS   (France)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUES; COMPUTATIONAL PERFORMANCE; CONCRETE SPECIMENS; CONTINUOUS DAMAGE MECHANICS; DAMAGE MECHANICS; DAMAGE MODEL; EQUILIBRIUM EQUATION; GRADIENT MODEL; ITERATIVE SOLVERS; LOCAL MODEL; MESH DEPENDENCE; MESH-INSENSITIVE; MESO SCALE; NONLINEAR BEHAVIOURS; NONLOCAL; NUMERICAL COMPUTATIONS; WITHOUT ENERGY DISSIPATION;

ENERGY DISSIPATION;

FRACTURE;

EID: 84869826773     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. Aifantis, E.C. On the mirostructural origin if certain inelastic models. Transaction of ASME, J. Mat. Engng. Tech., vol. 106, pp. 326-330, 1984.
2. Bazant, Z.P. Instability, ductility and size effect in strain softening concrete, J. Engng. Mech. ASCE, vol. 102, pp. 331-344, 1976.
3. Besuelle P. Implémentation d'un nouveau type d'élé ment fini dans le code LAGAMINE pour une classe de lois à longueur interne. Rapport d'activité pour le FNRS, Belgique, mai (2003).
4. Chambon R., Caillerie D., El Hassan N. Etude de la localisation unidimensionnelle à l'aide d'un modèle de second gradient, C.R.A.S-Série II b, vol. 323, pp. 231-238, 1996.
5. Chambon R., Caillerie D., El Hassan N. One dimensional localisation studied with a second grade model, European Journal of Mechanics A/Solids, vol. 17, no 4, pp. 637-656, 1998.
6. Chambon R., Caillerie D and Matsushima T. Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies, Int. J. Solids & Structures, vol. 38, pp 8503-8527, 2001.
7. Chambon R., Crochepeyre S. and Charlier R. An algorithm and a method to search bifurcation points in nonlinear problems, Int. J. Num. Meth. Engrg, vol. 51, pp 315-332, 2001.
8. Dragon, A., Mroz, Z. A continuum model for plastic-brittle behaviour of rock and concrete, Int. J. Engng. Sci., vol. 17, pp. 121-137, 1979.
9. Fichant, S., Pijaudier-Cabot, G. and La Borderie, C. Continuum damage modelling: approximation of crack induced anisotropy. Mech. Res. Comm., vol. 24, pp. 109-114, 1997.
10. Fichant, S., La Borderie, C. and Pijaudier-Cabot, G. Isotropic and anisotropic descriptions of damage in concrete structures. Int. J. Mech. of Cohes.-Frict. Mat, vol. 4, pp. 339-359, 1999.
11. Frémond M. and Nedjar B. Damage gradient of damage and principle of virtual work. Int. J. Solids Structures, vol. 33, 8, 1083-1103, 1996.
12. Gérard, B., Pijaudier-Cabot, G., and La Borderie, C. Coupled Diffusion-Damage Modelling and the Implications on Failure due to Strain Localisation, Int. J. Solids & Structures, Vol. 35, pp. 4107-4120, 1998.
13. Germain, P. The method of virtual power in continuum mechanics. Part 2 : Microstructure. SIAM J. Appl. Math. 25, 556-575, 1973.
14. Kachanov, L.M. Time of rupture process under creep conditions. Izvestia akademii nauk, USSR, 8, 26-31, 1958 (in Russian).
15. Krajcinovic, D. Constitutive equations for damaging material. J. Appl. Mech. ASME, vol. 50, 355-360, 1983.
16. La Borderie C.L. Phénomènes unilatéraux dans un matériau endommageable: modélisation et application à l'analyse des structures en béton. Thèse de doctorat, Université Paris 6, 1991.
17. Ladevèze, P. Sur une théorie de l'endommagement anisotrope. Int. Report n. 34, Laboratoire de Mécanique et Technologie, Cachan, France, 1983.
18. Lemaitre, J. and Chaboche, J.L. Mécanique des matériaux solides. Dunod-Bordas Ed. Paris, France, 1985.
19. Lemaitre, J. and Mazars J. Application de la théorie de l'endommagement au comportement non linéaire et à la rupture du béton de structures. Annales de l'ITBTP, 401, 1982.
20. Matsushima T., Chambon R. and Caillerie D. Second gradient models as a particular case of microstructured models: a large strain finite element analysis. C.R.A.S-Série II b, vol. 328, pp.179-186, 2000.
21. Mazars, J. Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure, Thèse de Doctorat ès Sciences, Université Paris 6, France, 1984.
22. Mazars, J. A description of micro and macroscale damage of concrete structures. Engrg. Fract. Mech., 25(5/6), 729-737, 1986.
23. Mazars, J., Pijaudier-Cabot, G. Continuum damage theory - application to concrete, J. Engng. Mech. ASCE, vol. 115, pp. 345-365, 1989.
24. Mindlin, R.D. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51-78, 1964.
25. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and de Vree, J.H.P. Gradient enhanced damage for quasi-brittle materials, Int. J. Num. Meth. Engrg., vol. 39, pp. 3391-3403, 1996.
26. Peerlings, R.H.J., Geers, M.G.D., de Borst, R., Brekelmans, W.A.M. A critical comparison of nonlocal and gradient-enhanced softening continua. Int. J. Solids & Structures, vol. 38, 7723-7746, 2001.
27. Pijaudier-Cabot, G. Continuum damage modelling. Numéro spécial de la Revue Française de Génie Civil, Ecole d'été ALERT, Constitutive Modelling of Geomaterials, Cambou and Di Prisco ed., vol. 4, no 5, pp. 33-57, 2000.
28. Pijaudier-Cabot, G. and Bazant, Z.P. Nonlocal damage theory, J. of Engrg. Mech. ASCE, vol. 113, pp. 1512-1533, 1987.
29. Pijaudier-Cabot, G., Burlion, N. Damage and localisation in elastic materials with voids, Int. J. Mech. of Cohes.-Frict. Mat., vol. 1, pp. 129-144, 1996.
30. Ragueneau F., La Borderie Ch., and Mazars J. Damage Model for Concrete Like Materials Coupling Cracking and Friction, Contribution towards Structural Damping: First Uniaxial Application. Mechanics Cohesive Frictional Materials, vol. 5, pp 607-625, 2000.