Summary
The present paper focusses on five phenomenological approaches in gradient-enhanced damage, several of which have been proposed in the literature to simulate material degradation. These different gradient-damage based nonlocal models are examined with respect to their ability to describe crack initiation and crack propagation. The models are applied to identical mechanical benchmark tests, where the material damage evolution law is taken as good as possible equal for each model. Interesting differences between the different models arise, and it is shown that care must be taken in the interpretation and application of these models. One-dimensional results cannot be extrapolated in a straightforward fashion to two dimensions, and the physical relevance of some results is in some cases debatable. Furthermore, it is shown that the response of some models is strongly influenced by small differences in the applied damage evolution law. A discussion is made on the use of two different types of such evolution laws, which are frequently applied in the literature.
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Ožbolt, J., Bažant, A. P.: Numerical smeared fracture analysis: nonlocal microcrack interaction approach. Int. J. Numer. Meth. Engng39, 635–661 (1996).
Drugan, W. J., Willis, J. R.: A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids44, 497–524 (1996).
Blechman, I.: Brittle solid under compression. Part I: Gradient mechanisms of microcracking. Int. J. Solids Structures34, 2563–2582 (1997).
Tvergaard, V., Needleman, A.: Nonlocal effects on localization in a void-sheet. Int. J. Solids Structures34, 2221–2238 (1997).
Eringen, A. C.: A unified theory of thermomechanical meterials. Int. J. Engng Sci.4, 179–202 (1966).
Maugin, G. A.: Nonlocal theories of gradient-type theories: a matter of convenience? Arch. Mech.31, 15–26 (1979).
Delaplace, A., Pijaudier-Cabot, G., Roux, S.: Progressive damage in discrete models and consequences on continuum modelling. J. Mech. Phys. Solids44, 99–136 (1996).
Geers, M. G. D., de Borst, R., Brekelmans, W. A. M., Peerlings, R. H. J.: Validation and internal length scale determination for a gradient damage model: Application to short glass-fibre-reinforced polypropylene. Int. J. Solids Sructures36, 2557–2583 (1998).
Geers, M. G. D., de Borst, R., Peijs, T.: Mixed numerical-experimental identification of nonlocal characteristics of random fibre reinforced composites. Composites Sci. Technology59, 1569–1578 (1999).
Peerlings, R. H. J., Geers, M. G. D., de Borst, R., Brekelmans W. A. M.: A critical comparison of nonlocal and gradient-enhanced continua. Int. J. Solids Structures (forthcoming).
Jirásek, M.: Nonlocal models for damage and fracture: comparison of approaches. Int. Journal Solids Structures35, 4133–4145 (1998).
Geers, M. G. D., de Borst, R., Brekelmans, W. A. M., Peerlings, R. H. J.: Strain-based transient-gradient damage model for failure analyses. Comp. Meth. Appl. Mech. Engng160, 133–154 (1998).
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. Meth. Engng39, 3391–3403 (1996).
de Borst, R., Benallal, A., Heeres, O. M.: A gradient-enhanced damage approach to fracture. J. de Physique IV,6, 491–502 (1996).
Geers, M. G. D.: Experimental analysis and computational modelling of damage and fracture. PhD thesis, Eindhoven University of Technology, The Netherlands (1997).
Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M., Geers, M. G. D.: Gradient-enhanced damage modelling of concrete fracture. Mech. Cohesive-Frictional Mater.3, 323–342 (1998).
Geers, M. G. D., de Borst, R., Peerlings, R. H. J.: Damage and crack modeling in single-edge and double-edge notched concrete beams. Eng. Fract. Mech. (forthcoming).
de Borst, R., Geers, M. G. D., Peerlings, R. H. J.: Computational damage mechanics. In: Computational fracture mechanics in concrete technology (Carpenteri, A., Aliabadi, M., eds.), chap. 2, pp. 33–69. WIT Press 1999.
Bažant, Z. P., Pijaudier-Cabot, G.: Nonlocal continuum damage, localization instability and convergence. J. Appl. Mech.55, 287–293 (1988).
Frémond, M., Nedjar, B.: Damage, gradient of damage and principle of virtual power. Int. J. Solids Structures33, 1083–1103 (1996).
Mühlhaus, H. B., de Borst, R., Sluys, L. J., Pamin, J.: A thermodynamic theory for inhomogeneous damage evolution. In: Computer methods and advances in geomechanics (Siriwardane, H. J., Zaman, M. M., eds.), pp. 635–640. Rotterdam and Boston: Balkema 1994.
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Geers, M.G.D., Peerlings, R.H.J., Brekelmans, W.A.M. et al. Phenomenological nonlocal approaches based on implicit gradient-enhanced damage. Acta Mechanica 144, 1–15 (2000). https://doi.org/10.1007/BF01181824
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DOI: https://doi.org/10.1007/BF01181824