[en] The non linear behaviour of concrete is often simulated using local constitutive models based on the continuous damage mechanics theory. This approach however is not adequate for post-localisation studies with strain softening. It is well known that spurious mesh dependence appears in computations and cases of failure without energy dissipation. In order to improve computational performance second grade local models are chosen to include a meso scale in the continuous damage model. This approach differs from the nonlocal one in the sense that it is a local theory with higher order stresses depending only on the local cinematic history. 1D numerical computations with concrete specimens are presented. Using a random initialisation of the iterative solver of the equilibrium equation we search the existence of various solutions for the boundary value study and also to see if the second grade term regularise the problem giving results that are mesh insensitive and objective.
Aifantis, E.C., On the mirostructural origin if certain inelastic models (1984) Transaction of ASME, J. Mat. Engng. Tech., 106, pp. 326-330
Bazant, Z.P., Instability ductility and size effect in strain softening concrete (1976) J. Engng. Mech. ASCE, 102, pp. 331-344
Besuelle, P., Implémentation d'un nouveau type d'élément fini dans le code LAGAMINE pour une classe de lois à longueur interne (2003) Rapport D'activité Pour le FNRS, , Belgique, mai
Chambon, R., Caillerie, D., El Hassan, N., Etude de la localisation unidimensionnelle à l'aide d'un modèle de second gradient (1996) C.R.A.S-Série II B, 323, pp. 231-238
Chambon, R., Caillerie, D., El Hassan, N., One dimensional localisation studied with a second grade model (1998) European Journal of Mechanics A/Solids, 17 (4), pp. 637-656
Chambon, R., Caillerie, D., Matsushima, T., Plastic continuum with microstructure, local second gradient theories for geomaterials: Localization studies (2001) Int. J. Solids & Structures, 38, pp. 8503-8527
Chambon, R., Crochepeyre, S., Charlier, R., An algorithm and a method to search bifurcation points in nonlinear problems (2001) Int. J. Num. Meth. Engrg, 51, pp. 315-332
Dragon, A., Mroz, Z., A continuum model for plastic-brittle behaviour of rock and concrete (1979) Int. J. Engng. Sci., 17, pp. 121-137
Fichant, S., Pijaudier-Cabot, G., La Borderie, C., Continuum damage modelling: Approximation of crack induced anisotropy (1997) Mech. Res. Comm., 24, pp. 109-114
Fichant, S., La Borderie, C., Pijaudier-Cabot, G., Isotropic and anisotropic descriptions of damage in concrete structures (1999) Int. J. Mech. of Cohes.-Frict. Mat, 4, pp. 339-359
Frémond, M., Nedjar, B., Damage gradient of damage and principle of virtual work (1996) Int. J. Solids Structures, 33 (8), pp. 1083-1103
Gérard, B., Pijaudier-Cabot, G., La Borderie, C., Coupled diffusion-damage modelling and the implications on failure due to strain localisation (1998) Int. J. Solids & Structures, 35, pp. 4107-4120
Germain, P., The method of virtual power in continuum mechanics. Part 2 : Microstructure (1973) SIAM J. Appl. Math., 25, pp. 556-575
Kachanov, L.M., Time of rupture process under creep conditions (1958) Izvestia Akademii Nauk, USSR, 8, pp. 26-31. , in Russian
Krajcinovic, D., Constitutive equations for damaging material (1983) J. Appl. Mech. ASME, 50, pp. 355-360
La Borderie, C.L., (1991) Phénomènes Unilatéraux dans un Matériau Endommageable: Modélisation et Application À l'Analyse des Structures en Béton, , Thèse de doctorat, Université Paris 6
Ladevèze, P., Sur une théorie de l'endommagement anisotrope (1983) Int. Report N. 34, Laboratoire de Mécanique et Technologie, , Cachan, France
Lemaitre, J., Chaboche, J.L., (1985) Mécanique des Matériaux Solides, , Dunod-Bordas Ed. Paris, France
Lemaitre, J., Mazars, J., Application de la théorie de l'endommagement au comportement non linéaire et à la rupture du béton de structures (1982) Annales de L'ITBTP, 401
Matsushima, T., Chambon, R., Caillerie, D., Second gradient models as a particular case of microstructured models: A large strain finite element analysis (2000) C.R.A.S-Série II B, 328, pp. 179-186
Mazars, J., (1984) 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
Mazars, J., A description of micro and macroscale damage of concrete structures (1986) Engrg. Fract. Mech., 25 (5-6), pp. 729-737
Mazars, J., Pijaudier-Cabot, G., Continuum damage theory - Application to concrete (1989) J. Engng. Mech. ASCE, 115, pp. 345-365
Mindlin, R.D., Micro-structure in linear elasticity (1964) Arch. Ration. Mech. Anal., 16, pp. 51-78
Peerlings, R.H.J., De Borst, R., Brekelmans, W.A.M., De Vree, J.H.P., Gradient enhanced damage for quasi-brittle materials (1996) Int. J. Num. Meth. Engrg., 39, pp. 3391-3403
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 (2001) Int. J. Solids & Structures, 38, pp. 7723-7746
Pijaudier-Cabot, G., Continuum damage modelling (2000) Numéro Spécial de la Revue Française de Génie Civil, Ecole d'Été ALERT, Constitutive Modelling of Geomaterials, 4 (5), pp. 33-57. , Cambou and Di Prisco ed
Pijaudier-Cabot, G., Bazant, Z.P., Nonlocal damage theory (1987) J. of Engrg. Mech. ASCE, 113, pp. 1512-1533
Pijaudier-Cabot, G., Burlion, N., Damage and localisation in elastic materials with voids (1996) Int. J. Mech. of Cohes.-Frict. Mat., 1, pp. 129-144
Ragueneau, F., La Borderie, Ch., Mazars, J., Damage model for concrete like materials coupling cracking and friction, contribution towards structural damping: First uniaxial application (2000) Mechanics Cohesive Frictional Materials, 5, pp. 607-625
