zbMATH — the first resource for mathematics

Strain-based transient-gradient damage model for failure analyses. (English) Zbl 0938.74006
Summary: A transient-gradient enhanced damage model has been developed for the numerical modelling of the damage and fracture process within a continuum damage mechanics framework. Some deficiencies of existing gradient enhanced damage formulations for the simulation of macroscopic crack propagation are pointed out. The transient-gradient approach assumes a direct coupling between the material length parameter and the local strain state of the material, which leads to a transient behaviour of the nonlocal effect. Details of the method are presented and fully elaborated in an incremental-iterative solution scheme. Mesh objectivity and physical relevance of the method are analysed by one-dimensional and two-dimensional numerical examples.

74A45 Theories of fracture and damage
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI
[1] de Borst, R.; Mühlhaus, H.B., Continuum models for discontinuous media, (), 601-618
[2] Needleman, A., Material rate dependence and mesh sensitivity in localization problems, Comput. methods appl. mech. engrg., 67, 69-85, (1988) · Zbl 0618.73054
[3] de borst, R.; Carmeliet, J.; Pamin, J.; Sluys, L.J., New horizons in computer analysis of damage and fracture in quasi-brittle materials, (), 359-372
[4] Bažant, Z.P., Why continuum damage is nonlocal: micromechanics arguments, J. engrg. mech., 117, 5, 1070-1087, (1991)
[5] Bažant, Z.P.; Belytschko, T.; Chang, T.P., Continuum theory for strain-softening, J. engrg. mech., 110, 12, 1666-1692, (1984)
[6] Pijaudier-Cabot, G.; Bažant, Z.P., Nonlocal damage theory, J. engrg. mech., 113, 1512-1533, (1987)
[7] Bažant, Z.P.; Pijaudier-Cabot, G., Nonlocal continuum damage, localization instability and convergence, J. appl. mech., 55, 287-293, (1988) · Zbl 0663.73075
[8] Schreyer, H.L., Formulations for nonlocal softening in a finite zone with anisotropic damage, (), 426-439
[9] Aifantis, E.C., On the microstructural origin of certain inelastic models, J. engrg. mater. technol., 106, 326-334, (1984)
[10] Lasry, D.; Belytschko, T., Localization limiters in transient problems, Int. J. solids struct., 24, 581-598, (1988) · Zbl 0636.73021
[11] Mühlhaus, H.B.; Aifantis, E.C., A variational principle for gradient plasticity, Int. J. solids struct., 28, 845-858, (1991) · Zbl 0749.73029
[12] Vardoulakis, I.; Aifantis, E.C., A gradient flow theory of plasticity for granular materials, Acta mech., 87, 197-217, (1991) · Zbl 0735.73026
[13] de Borst, R.; Mühlhaus, H.B., Gradient-dependent plasticity: formulation and algorithmic aspects, Int. J. numer. methods engrg., 35, 521-539, (1992) · Zbl 0768.73019
[14] Pamin, J., Gradient-dependent plasticity in numerical simulation of localization phenomena, ()
[15] Triantafyllidis, N.; Aifantis, E.C., A gradient approach to localization of deformation, I. hyperelastic materials, J. elasticity, 16, 225-237, (1986) · Zbl 0594.73044
[16] Aifantis, E.C., On the role of gradients in the localization of deformation and fracture, Int. J. engrg. sci., 30, 1279-1299, (1992) · Zbl 0769.73058
[17] Mühlhaus, H.B.; de Borst, R.; Sluys, L.J.; Pamin, J., A thermodynamic theory for inhomogeneous damage evolution, (), 635-640
[18] Pijaudier-Cabot, G.; Burlion, N., Damage and localisation in elastic materials with voids, Mech. cohesive-frictional mater., 1, 129-144, (1996)
[19] Peerlings, R.H.J.; de Borst, R.; Brekelmans, W.A.M.; de Vree, J.H.P., Gradient-enhanced damage for quasi-brittle materials, Int. J. numer. methods engrg., 39, 3391-3403, (1996) · Zbl 0882.73057
[20] Peerlings, R.H.J.; de Borst, R.; Brekelmans, W.A.M.; de Vree, J.H.P.; Spee, I., Some observations on localisation in non-local and gradient damage models, Europ. J. mech., part A/solids, 15, 6, 937-953, (1996) · Zbl 0891.73055
[21] Frémond, M.; Nedjar, B., Damage, gradient of damage and principle of virtual power, Int. J. solids struct., 33, 8, 1083-1103, (1996) · Zbl 0910.73051
[22] de Borst, R.; Pamin, J.; Peerlings, R.H.J.; Sluys, L.J., On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials, Comput. mech., 17, 130-141, (1995) · Zbl 0840.73047
[23] de Borst, R.; Benallal, A.; Peerlings, R.H.J., On gradient-enhanced damage theories, (), 215-226
[24] R.H.J. Peerlings, R. de Borst, W.A.M. Brekelmans and M.G.D. Geers, Gradient-enhanced damage modelling of concrete fracture, Mech. Cohesive-Frictional Mat., in press. · Zbl 0995.74056
[25] Geers, M.G.D., Experimental analysis and computational modelling of damage and fracture, () · Zbl 0957.74034
[26] Rots, J.G., Removal of finite elements in strain-softening analysis of tensile fracture, (), 330-338
[27] Mazars, J., Application de la mécanique de l’endommagement au comportement non linéaire et á la rupture du béton de structure, ()
[28] Mazars, J.; Pijaudier-Cabot, G., Continuum damage theory—application to concrete, J. engrg. mech., 115, 2, 345-365, (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.