Some remarks on gradient and nonlocal damage theories

Studies in Applied Mechanics

Volumn 46, Issue C, 1998, Pages 223-236

  de Borst, R ^a,b   Geers, M G D ^b,c   Peerlings, R H J ^b   Benallal, A ^d  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c ROYAL MILITARY ACADEMY   (Belgium)

^d Grande Voie des Vignes   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957088713     PISSN: 09225382     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0922-5382(98)80044-5     Document Type: Article

References (31)

1. Benallal A., Billardon R., and Geymonat G. Some mathematical aspects of the damage softening rate problem. In: Mazars J., and Bazant Z.P. (Eds). Cracking and Damage (1988), Elsevier, Amsterdam and London 247-258
2. Needleman A. Material rate dependence and mesh sensitivity in localization problems. Comp. Meth. Appl. Mech. Eng. 67 (1988) 69-86
3. Loret B., and Prévost J.H. Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. Comp. Meth. Appl. Mech. Eng. 83 (1990) 247-273
4. Sluys L.J. Wave propagation, localisation and dispersion in softening solids. Dissertation (1992), Delft University of Technology, Delft
5. Sluys L.J., and de Borst R. Wave propagation and localisation in a rate-dependent cracked medium - Model formulation and one-dimensional examples. Int. J. Solids Structures 29 (1992) 2945-2958
6. Sluys L.J., and de Borst R. Dispersive properties of gradient-dependent and rate-dependent media. Mech. Mater. 18 (1992) 131-149
7. Mühlhaus H.-B., and Vardoulakis I. The thickness of shear bands in granular materials. Geotechnique 37 (1987) 271-283
8. de Borst R. Simulation of strain localisation: A reappraisal of the Cosserat continuum. Engng. Comput. 8 (1991) 317-332
9. 2-flow theory for polar continua. Comp. Meth. Appl. Mech. Eng. 103 (1993) 347-362
10. Pijaudier-Cabot G., and Bazant Z.R. Nonlocal damage theory. J. Engng. Mech. 113 (1987) 1512-1533
11. Aifantis E.C. On the microstructural origin of certain inelastic models. J. Engng. Mater. Technol. 106 (1984) 326-334
12. Aifantis E.C. The physics of plastic deformation. Int. J. Plasticity 3 (1987) 211-247
13. Aifantis E.C. On the role of gradients in the localization of deformation and fracture. Int. J. Engng. Sci. 30 (1992) 1279-1299
14. Mühlhaus H.-B., and Aifantis E.C. A variational principle for gradient plasticity. Int. J. Solids Structures 28 (1991) 845-858
15. Vardoulakis I., and Aifantis E.C. A gradient flow theory of plasticity for granular materials. Acta Mechanica 87 (1991) 197-217
16. Schreyer H.L., and Chen Z. One-dimensional softening with localization. J. Appl. Mech. 53 (1986) 791-797
17. de Borst R., and Mühlhaus H.-B. Gradient-dependent plasticity: Formulation and algorithmic aspects. Int. J. Num. Meth. Eng. 35 (1992) 521-539
18. de Borst R., and Pamin J. Some novel developments in finite element procedures for gradient-dependent plasticity. Int. J. Num. Meth. Eng. 39 (1996) 2477-2505
19. de Borst R., and Pamin J. Gradient plasticity in numerical simulation of concrete cracking. Eur. J. Mechanics: A/Solids 15 (1996) 295-320
20. Sluys L.J., de Borst R., and Mühlhaus H.-B. Wave propagation, localization and dispersion in a gradient-dependent medium. Int. J. Solids Structures 30 (1993) 1153-1171
21. Mühlhaus H.-B., de Borst R., Sluys L.J., and Pamin J. A thermodynamic theory for inhomogeneous damage evolution. In: Siriwardane H.J., and Zaman M.M. (Eds). Computer Methods and Advances in Geomechanics (1994), Balkema, Rotterdam and Boston 635-640
22. de Borst R., Benallal A., and Heeres O.M. A gradient-enhanced damage approach to fracture. J. de Physique IV C6 (1996) 491-502
23. C. Comi, Computational modelling of gradient-enhanced damage in quasi-brittle materials, Mech. Coh.-frict. Mat., submitted for publication
24. 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. Eng. 39 (1996) 3391-3403
25. Peerlings R.H.J., de Borst R., Brekelmans W.A.M., de Vree J.H.P., and I. S. Some observations on localisation in non-local and gradient damage models. Eur. J. Mech./A: Solids 15 (1996) 937-954
26. Eindhoven. Geers M.G.D. Experimental Analysis and Computational Modelling of Damage and Fracture. Dissertation, Eindhoven University of Technology (1997)
27. M.G.D. Geers, R. de Borst, W.A.M. Brekelmans and R.H.J. Peerlings Strain-based transientgradient damage model for failure analyses, Comp. Meth. Appl. Mech. Eng., accepted for publication.
28. Simo J.C., and Ju J.W. Strain and stress-based continuum damage models: I. Formulation. Int. J. Solids Structures 23 (1987) 821-840
29. Lemaitre J., and Chaboche J.L. Mechanics of Solid Materials (1990), Cambridge University Press, Cambridge
30. Mazars J., and Pijaudier-Cabot G. Continuum damage theory-application to concrete. J. Eng. Mech. 115 (1989) 345-365
31. Huerta A., and Pijaudier-Cabot G. Discretization influence on the regularization by two localization limiters. J. Eng. Mech. 120 (1994) 1198-1218