Some observations on the regularizing field for gradient damage models

Acta Mechanica

Volumn 140, Issue 3, 2000, Pages 149-162

  Borino, G ^a   De Borst, R ^b  

^a UNIVERSITY OF PALERMO   (Italy)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; DEFORMATION; ELASTIC MODULI; PARTIAL DIFFERENTIAL EQUATIONS; PLASTICITY; TENSORS; THERMAL EXPANSION;

GRADIENT DAMAGE MODELS; PLASTIC STRAIN; STRAIN SOFTENING;

STRAIN MEASUREMENT;

EID: 0033684997     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01182507     Document Type: Article

References (30)

1. Lemaitre, J., Chaboche, J.-L.: Mechanics of solids materials. Cambridge: Cambridge University Press 1990.
2. Bažant, Z. P., Lin, F.-B.: Nonlocal yield limit degradation. Int. J. Num. Meths. Eng. 26, 1805-1823 (1988).
3. Benallal, A., Billarden, R., Geymonat, G.: Some mathematical aspects of the damage softening rate problem. In: Cracking and damage (Mazars, J., Bažant, Z. P., eds.), pp. 247-258. Amsterdam London: Elsevier 1988.
4. Pietruszczak, S., Mróz, Z.: Finite element analysis of deformation of strain-softening materials. Int. J. Num. Meth. Eng. 17, 327-334 (1981).
5. Eringen, A. C.: Theories of nonlocal plasticity. Int. J. Engng. Sci. 21, 741-751 (1983).
6. Bažant, Z. P., Belytschko, T. B., Chang, T. P.: Continuum theory for strain softening. J. Eng. Mech. ASCE 111, 381-389 (1984).
7. Pijaudier-Cabot, G., Bažant, Z. P.: Nonlocal damage theory. J. Eng. Mech. ASCE 113, 1512-1533 (1987).
8. Aifantis, E. C.: On the role of gradients in the localization of deformation and fracture. J. Eng. Sci. 30, 1279-1299 (1984).
9. Mühlhaus, H.-B., Aifantis, E. C.: A variational principle for gradient plasticity. Int. J. Solids Struct. 28, 845-858 (1991).
10. de Borst, R., Mühlhaus, H.-B.: Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Num. Meth. Eng. 35, 521-539 (1992).
11. de Borst, R., Sluys, L. J., Mühlhaus, H.-B., Pamin, J.: Fundamental issues in finite element analyses of localization of deformation. Engng Comp. 10, 99-121 (1993).
12. Fleck, N. A., Hutchinson, J. W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 12, 1825-1857 (1993).
13. Pamin, J.: Gradient-dependent plasticity in numerical solution of localization phenomena. Ph.D. Thesis, Delft University of Technology, Delft 1994.
14. Fleck, N. A., Muller, G. M., Ashby, M. F., Hutchinson, J. W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475-487 (1994).
15. Lutz, M. P., Zimmerman, R. W.: Thermal stresses in a functionally-graded cylinder. In: Thermal Stresses '97, (Hetnarski, R. B., Noda, N., Ghoneim, H., eds.), pp. 323-326. Rochester 1997.
16. Nemat-Alla, M., Noda, N.: Thermal stress intensity factor for edge cracked functionally graded strip with a two-dimensionally coefficient of thermal expansion. In: Thermal Stresses '97 (Hetnarski, R. B., Noda, N., Ghoneim, H., eds.), pp. 315-318. Rochester 1997.
17. Huerta, A., Pijaudier-Cabot, G.: Discretization influence on the regularization by two localization limiters. J. Eng. Mech. ASCE 120, 1198-1212 (1994).
18. Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M., de Vree, J. H. P., Spec, I.: Some observations on localization in nonlocal and gradient damage models. Eur. J. Mech. A/Solids 15, 937-953 (1996).
19. Svedberg, T., Runesson, K.: A thermodynamically consistent theory of gradient-regularized plasticity coupled with damage. Int. J. Plasticity 13, 669-696 (1997).
20. 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. Num. Meth. Eng. 39, 3391-3403 (1996).
21. de Borst, R., Heeres, O. M., Benallal, A.: A gradient enhanced damage model: theory and computation. In: Computational plasticity, fundamental and applications (Owen, D. R. J., Oñate. E., Hinton, E., eds.), pp. 373-380. Barcelona: CIMNE Press 1997.
22. Comi, C., Driemeier, L.: On gradient regularization for numerical analyses in the presence of damage. In: Material instabilities in solids (de Borst, R., van der Giessen, E., eds.), pp. 425-440. Chichester: Wiley 1998.
23. Carol, I., Willam, K.: Application of analytical solutions in elasto-plasticity to localization analysis of damage models. In: Computational plasticity, fundamental and applications (Owen, D. R. J., Oñate, E., Hinton, E., eds.), pp. 373-380. Barcelona: CIMNE Press 1997.
24. Kachanov, L. M.: Introduction to continuum damage mechanics. Dordrecht: Martinus Nijhoff 1986.
25. Simo, J. C., Ju, J. W.: Stress and strain based continuum damage models. Part I and II. Int. J. Solids Struct. 23, 375-400 (1987).
26. Ju, J. W.: On energy-based coupled elastoplastic damage theories: constitutive modelling and computational aspects. Int. J. Solids Struct. 25, 803-833 (1989).
27. Carol, I., Rizzi, E., Willam, K.: A unified theory of elastic degradation and damage based on a loading surface. Int. J. Solids Struct. 31, 2835-2865 (1994).
28. Geers, M. G. D.: Experimental analysis and computational modelling of damage and fracture. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven 1997.
29. 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. Int. J. Solids Struct. 36, 2557-2583 (1999).
30. Jirásek, M.: Nonlocal models for damage and fracture: comparison of approaches. Int. J. Solids Struct. 35, 4133-4145 (1998).