From the onset of damage to rupture: Construction of responses with damage localization for a general class of gradient damage models

Continuum Mechanics and Thermodynamics

Volumn 25, Issue 2-4, 2013, Pages 147-171

  Pham, Kim ^a   Marigo, Jean Jacques ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

Damage; Gradient theory; Localization; Variational approach

Indexed keywords

MECHANICAL PROPERTIES; MECHANICS;

CONSTRUCTION METHOD; DAMAGE; DAMAGE LOCALIZATION; GRADIENT THEORY; LOCALIZATION; MATERIAL CHARACTERISTICS; NUMERICAL INTEGRATIONS; VARIATIONAL APPROACHES;

DAMAGE DETECTION;

EID: 84878218341     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-011-0228-3     Document Type: Article

References (30)

1. Bažant Z.P., Belytschko T., Chang T.P.: Continuum theory for strain-softening. J. Eng. Mech. 110, 1666-1692 (1984)
2. Bažant Z.P., Pijaudier-Cabot G.: 'Non-local continum damage; localization instability and convergence'. J. Appl. Mech. ASME 55, 287-294 (1988)
3. Benallal, A., Billardon, R.,Geymonat, G.: Bifurcation and localization in rate independent materials. In: Nguyen, Q. C.S.I.M Lecture Notes on Bifurcation and Stability of Dissipative Systems, Springer, Berlin (1993)
4. Benallal A., Marigo J.-J.: Bifurcation and stability issues in gradient theories with softening. Modelling Simul. Mater. Sci. Eng. 15, 283-295 (2007)
5. Bourdin B., Francfort G., Marigo J.-J.: The variational approach to fracture. J. Elast. 91, 5-148 (2008)
6. Charlotte, M., Francfort, G., Marigo, J.-J., Truskinovsky, L.: 'Revisiting brittle fracture as an energy minimization problem: Comparisons of Griffith and Barenblatt surface energy models'. In: Benallal, A. (ed.) Continuous Damage and Fracture: Proceedings of the symposium, Cachan, France 23-27 octobre 2000. Elsevier. (2000)
7. Comi C.: On localisation in ductile-brittle materials under compressive loadings. Euro. J. Mech. A/Solids 14, 19-43 (1995)
8. Comi C.: A non-local model with tension and compression damage mechanisms. Euro. J. Mech. A/Solids 20, 1-22 (2001)
9. Comi C., Perego U.: Fracture energy based bi-dissipative damage model for concrete. Int J Solids Struct 38(36-37), 6427-6454 (2001)
10. de Borst R., Sluys L., Mühlhaus H.-B., Pamin J.: Fundamental issues in finite element analysis of localization of deformation. Eng. Comp. 10, 99-121 (1993)
11. DeSimone A., Marigo J.-J., Teresi L.: A damage mechanics approach to stress softening and its application to rubber. Euro. J. Mech. A/Solids 20(6), 873-892 (2001)
12. Francfort G., Marigo J.-J.: Stable damage evolution in a brittle continuous medium. Euro. J. Mech. A/Solids 12, 149-189 (1993)
13. Francfort G., Marigo J.-J.: Revisiting brittle fracture as an energy minimization. J. Mech. Phys. Solids 46, 1319-1342 (1998)
14. Lasry D., Lasry D.: Localization limiters in transient problems. Int. J. Solids Struct. 24, 581-587 (1988)
15. Lorentz E., Andrieux S.: Analysis of non-local models through energetic formulations. Int. J. Solids Struct. 40, 2905-2936 (2003)
16. Lorentz E., Cuvilliez S., Kazymyrenko K.: Convergence of a gradient damage model toward a cohesive zone model. Comptes Rendus Mécanique 339(1), 20-26 (2011)
17. Marigo J.-J.: Constitutive relations in plasticity, damage and fracture mechanics based on a work property. Nuclear Eng. Design 114, 249-272 (1989)
18. Marigo, J.-J.: From Clausius-Duhem and Drucker-Ilyushin inequalities to standard materials. In: Maugin, G.A., Drouot, R., Sidoroff, F. Continuum Thermodynamics: The Art and Science of Modelling Material Behaviour, vol. 76 of Solids Mechanics and Its Applications: Paul Germain's Anniversary, Kluwer, The Netherlands (2000)
19. Marigo J.-J., Truskinovsky L.: Initiation and propagation of fracture in the models of Griffith and Barenblatt. Contin. Mech. Thermodyn. 16(4), 391-409 (2004)
20. Mielke, A.: Evolution of rate-independent systems. In: Evolutionary equations, vol. II of Handb. Differ. Equ. Amsterdam: Elsevier/North-Holland, pp. 461-559 (2005)
21. Nguyen Q.: Bifurcation and postbifurcation analysis in plasticity and brittle fracture. J. Mech. Phys. Solids 35, 303-324 (1987)
22. Nguyen Q.S.: Stability and Nonlinear Solid Mechanics. Wiley, London (2000)
23. Peerlings R., de Borst R., Brekelmans W., de Vree J., Spee I.: Some observations on localisation in non-local and gradient damage models. Eur. J. Mech. A/Solids 15, 937-953 (1996)
24. Peerlings R., de Borst R., Brekelmans W., Geers M.: Wave propagation and localisation in nonlocal and gradient-enhanced damage models. J. de Physique IV 8, 293-300 (1998)
25. Pham K., Amor H., Marigo J.-J., Maurini C.: Gradient damage models and their use to approximate brittle fracture. Int. J. Damage Mech. 20(4), 618-652 (2011)
26. Pham K., Marigo J.-J.: Approche variationnelle de l'endommagement: I. Les concepts fondamentaux. Comptes Rendus Mécanique 338(4), 191-198 (2010)
27. Pham K., Marigo J.-J.: Approche variationnelle de l'endommagement: II. Les modèles à gradient'. Comptes Rendus Mécanique 338(4), 199-206 (2010)
28. Pham K., Marigo J.-J., Maurini C.: 'The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models'. J. Mech. Phys. Solids 59(6), 1163-1190 (2011)
29. Pijaudier-Cabot G., Bažant Z.P.: Non-local damage theory. J. Eng. Mech. 113, 1512-1533 (1987)
30. Pijaudier-Cabot G., Benallal A.: Strain localization and bifurcation in a non-local continuum. Int. J. Solids Struct. 30, 1761-1775 (1993)