A new path-following constraint for strain-softening finite element simulations

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 2, 2004, Pages 499-526

  Lorentz, E ^a   Badel, P ^a,b  

^a EDF R AND D   (France)

^b INSTITUT JEAN LE ROND D ALEMBERT   (France)

Author keywords

Damage; Finite element; Instability; Path following method; Strain softening

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; FAILURE (MECHANICAL); FINITE ELEMENT METHOD; STRUCTURES (BUILT OBJECTS);

STRAIN-SOFTENING;

ENGINEERING;

FINITE ELEMENT ANALYSIS;

EID: 2442473234     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.971     Document Type: Article

References (31)

1. Nguyen QS. Bifurcation and stability of time-independent standard dissipative systems. In Bifurcation and Stability of Dissipative Systems, Nguyen QS (ed.), vol. CISM 327, Springer: Berlin, 1993.
2. Marigo JJ. L'endommagement et la rupture: hier, aujourd'hui et demain. In Comportement non linéaire des matériaux. Cours de l'Institut pour la Promotion des Sciences de l'Ingénieur (IPSI): Paris, 2000.
3. Crisfield MA. Snap-through and snap-back response in concrete structures and the dangers of under-integration. International Journal for Numerical Methods in Engineering 1986; 22:751-767.
4. Bosco C, Carpinteri A. Discontinuous constitutive response of brittle matrix fibrous composites. Journal of the Mechanics and Physics of Solids 1995; 43(2):261-274.
5. Alfano G, Crisfield MA. Finite element interface models for the delamination analysis of laminated composites: mechanical and Computational issues. International Journal for Numerical Methods in Engineering 2001; 50(7):1701-1736.
6. Argyris JH. Continua and discontinua. In Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics, Wright-Patterson A.F.B. OH, 1965: 11-189.
7. Batoz J-L, Dhatt G. Incremental displacement algorithms for nonlinear problems. International Journal for Numerical Methods in Engineering 1979; 14:1262-1267.
8. de Borst R. Computation of post-bifurcation and post-failure behaviour of strain-softening solids. Computers and Structures 1987; 25(2):211-224.
9. Riks E. The application of Newton's method to the problem of elastic stability. Journal of Applied Mechanics 1972; 39:1060-1066.
10. Wempner GA. Discrete approximations related to non linear theories of solids. International Journal of Solids and Structures 1971; 7:1581-1599.
11. Crisfield MA. A fast incremental-iterative solution procedure that handles snap-through. Computers and Structures 1981; 13:55-62.
12. Ramm E. Strategies for tracing the non-linear response near limit points. Non-linear Finite Element Analysis in Structural Mechanics, Wunderlich W (ed.). Springer: Berlin, 1981: 63-89.
13. Hellweg HB, Crisfield MA. A new arc-length method for handling sharp snap-backs. Computer and Structures 1998; 66(5):704-709.
14. Geers MGD. Enhanced solution control for physically and geometrically non linear problems. International Journal for Numerical Methods in Engineering 1999; 46:177-230.
15. Crisfield MA. Nonlinear Finite Element Analysis of Solids and Structures, vol. 1. Wiley: Chichester, 1996.
16. Bathe KJ. Finite Element Procedures in Engineering Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1982; 110-111, 182-185.
17. Nguyen QS, Bui HD. Sur les matériaux élastoplastiques à écrouissage positif ou négatif. Journal de Mécanique 1974: 13(2):321-342.
18. Marigo JJ. Formulation d'une loi d'endommagement d'un matériau élastique. Compte-rendu de l'Académie des Sciences, Paris 1981; Série II, 292(19):1309-1312.
19. Zhilong Zhou, Murray DW. An incremental solution technique for unstable equilibrium paths of shell structures. Computers and Structures 1994; 55(5):749-759.
20. Barenblatt GI. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 1962; 7:55-129.
21. Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy minimization problem. Journal of the Mechanics̀ and Physics of Solids 1998; 46(8):1319-1342.
22. Laverne J, Lorentz E, Marigo JJ. Un modèle de rupture avec énergie de Barenblatt: considérations théoriques et implantation numérique. Accepté au 16è Congrès Français de Mécanique, 2003.
23. GMSH meshing software, open source on www.geuz.org/gmsh.
24. Finite element Codeter, Analyses de Structures Thermo-élastiques pour des Etudes et des Recherches, EDF 2001, open source on www.code-aster.org.
25. Benallal A, Billardon R, Geymonat G. Bifurcation and localization in rate-independent materials. Some general considerations. In Bifurcation and Stability of Dissipative Systems. Nguyen QS (ed.), vol. CISM 327, Springer: Berlin, 1993.
26. Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP. Gradient-enhanced damage for quasi- brittle materials. International Journal for Numerical Methods in Engineering 1996; 39:3391-3403.
27. Godard V. Modélization mécanique non locale des matériaux fragiles: délocalization de la déformation. Rapport de DEA, université Paris 6, France, 2001.
28. Lorentz E, Andrieux S. Analysis of non-local models through energetic formulations. International Journal of Solids and Structures 2003; 40:2905-2936.
29. Peerlings RHJ. Enhanced damage modelling for fracture and fatigue. Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 1999.
30. Drucker DC, Prager W. Soil mechanics and plastic analysis in limit design. Quarterly of Applied Mathematics 1952; 10:157-165.
31. Chavant C, Cirée B. Modèle de comportement plastique avec double critère de Drucker-Prager. Documentation de référence du Code Aster (www.code-aster.org) 2001;