Numerical simulation of ductile fracture with the Rousselier constitutive law

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 21-24, 2008, Pages 1965-1982

  Lorentz, E ^a   Besson, J ^b   Cano, V ^a  

^a EDF R AND D   (France)

^b PSL RESEARCH UNIVERSITY   (France)

Author keywords

Constitutive law; Ductile fracture; Mixed finite element; Nonlocal model; Plasticity; Rousselier

Indexed keywords

COMPUTER SIMULATION; CONSTITUTIVE EQUATIONS; DAMAGE DETECTION; DEFORMATION; FINITE ELEMENT METHOD; PLASTIC FLOW; STRAIN RATE;

NONLOCAL MODEL; ROUSSELIER CONSTITUTIVE LAW; VOLUMETRIC LOCKING;

DUCTILE FRACTURE;

COMPUTER SIMULATION; CONSTITUTIVE EQUATIONS; DAMAGE DETECTION; DEFORMATION; DUCTILE FRACTURE; FINITE ELEMENT METHOD; PLASTIC FLOW; STRAIN RATE;

EID: 40249098498     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.12.015     Document Type: Article

References (40)

1. Xia L., Shih C.F., and Hutchinson J.W. A computational approach to ductile crack growth under large scale yielding conditions. J. Mech. Phys. Solids 43 3 (1995) 389-413
2. Scheider I., and Brocks W. Simulation of cup-cone fracture using the cohesive model. Engrg. Fract. Mech. 70 (2003) 1943-1961
3. Rudnicki J., and Rice J. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23 (1975) 371-394
4. Benallal A., Billardon R., and Geymonat G. Bifurcation and localization in rate-independent materials. Some general considerations. In: Nguyen Q.S. (Ed). Bifurcation and Stability of Dissipative Systems CISM Courses and Lectures vol. 327 (1993), Springer-Verlag 1-44
5. Besson J., Steglich D., and Brocks W. Modeling of crack growth in round bars and plane strain specimens. Int. J. Solids Struct. 38 (2001) 8259-8284
6. S. Forest, E. Lorentz, Localization and regularization, in: J. Besson (Ed.), Local Approach to Fracture, Presses de l'Ecole des Mines de Paris, 2004.
7. Tvergaard V., and Needleman A. Analysis of cup-cone fracture in a round tensile bar. Acta Metall. 32 (1984) 157-169
8. Gurson A.L. Continuum theory of ductile rupture by void growth: part I - yield criterion and flow rules for porous ductile media. J. Engrg. Mater. Technol. 99 (1977) 2-15
9. Rousselier G. Finite deformation constitutive relations including ductile fracture damage. In: Nemat-Nasser (Ed). Three Dimensional Constitutive Relations and Ductile Fracture (1987), North Holland Publishing Company 331-355
10. Rousselier G. Ductile fracture models and their potential in local approach of fracture. Nucl. Engrg. Des. 105 (1987) 97-111
11. Rousselier G. Dissipation in porous metal plasticity and ductile fracture. J. Mech. Phys. Solids 49 (2001) 1727-1746
12. Besson J., Steglich D., and Brocks W. Modeling of plane strain ductile rupture. Int. J. Plasticity 19 (2003) 1517-1541
13. Halphen B., and Nguyen Q.S. Sur les matériaux standard généralisés. J. de Mécanique 14 (1975) 39-63
14. Germain P., Nguyen Q.S., and Suquet P. Continuum thermodynamics. J. Appl. Mech. 50 12 (1983) 1010-1020
15. Lee E. Elastic-plastic deformation at finite strains. J. Appl. Mech. 36 (1969) 1-6
16. Simo J.C., and Armero F. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Methods Engrg. 33 (1992) 1413-1449
17. de Souza Neto E.A., Andrade Pires F.M., and Owen D.R.J. F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking. Int. J. Numer. Methods Engrg. 62 (2005) 353-383
18. Taylor R.L. A mixed-enhanced formulation for tetrahedral finite elements. Int. J. Numer. Methods Engrg. 47 (2000) 205-227
19. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. fifth ed. Solid Mechanics vol. 2 (2000), Butterworth-Heinemann, Oxford pp. 328-332
20. Germain P. The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J. Appl. Math. 25 (1973) 556-575
21. BardenHagen S., and Triantafyllidis N. Derivation of higher order gradient continuum theories in 2, 3-D nonlinear elasticity from periodic lattice models. J. Mech. Phys. Solids 42 1 (1994) 111-139
22. Chambon R., Caillerie D., and Matsuchima T. Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies. Int. J. Solids Struct. 38 (2001) 8503-8527
23. Fleck N.A., and Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41 12 (1993) 1825-1857
24. M. Gologanu, J.-B. Leblond, G. Perrin, J. Devaux, Recent extensions of Gurson's model for porous ductile metals, in: INRIA, Ecole EDF-CEA-INRIA, Fracture et fatigue, Rocquencourt, France, 1998.
25. Lorentz E., and Andrieux S. Analysis of non-local models through energetic formulations. Int. J. Solids Struct. 40 (2003) 2905-2936
26. Francfort G., and Mielke A. Existence results for a class of rate-independent material models with nonconvex elastic energies. J. Reine Angew. Math. 595 (2004) 55-91
27. Nguyen Q.S. Bifurcation and stability in dissipative media (plasticity, friction, fracture). Appl. Mech. Rev. 47 1 (1994) 1-31
28. Simo J.C., and Miehe C. Associative coupled thermoplasticity at finite strains formulation, numerical analysis and implementation. Comput. Methods Appl. Mech. Engrg. 98 (1992) 41-104
29. Lorentz E., and Cano V. A minimisation principle for finite strain plasticity: incremental objectivity and immediate implementation. Commun. Numer. Methods Engrg. 18 (2002) 851-859
30. Baaser H., and Tvergaard V. A new algorithmic approach treating nonlocal effects at finite rate-independent deformation using the Rousselier damage model. Comput. Methods Appl. Mech. Engrg. 192 (2003) 107-124
31. Simo J.C., and Hughes T.J.R. Computational Inelasticity (1998), Springer-Verlag, New York
32. Zhang Z.L. On the accuracies of numerical integration algorithms for Gurson-based pressure-dependent elastoplastic constitutive models. Comput. Methods Appl. Mech. Engrg. 121 (1995) 15-28
33. V. Cano, E. Lorentz Modèle de Rousselier en grandes déformations. Documentation de Code_Aster R5.03.06. , 2002.
34. Simo J.C., and Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Engrg. 48 (1985) 101-118
35. A. Parrot, Instrumental Charpy test "Group of the SF2M": summary of the numerical Round Robin on the simulation of simplified compact tension specimen in the transition. EDF internal report HT-26/02/022/A, 2003.
36. G. Rousselier, R. Masson, G. Barbier, Modèle de Rousselier pour la rupture ductile. Documentation de Code_Aster R5.03.07. , 2004.
37. S. Michel-Ponnelle, E. Lorentz, Eléments finis adaptés aux comportements quasi-incompressibles. Documentation de Code_Aster R3.06.08, forthcoming on , 2006.
38. J. Besson, E. Lorentz, Calcul de dommages: simuler et prédire le vieillissement mécanique des installations de production et de transport d'énergie. CdM - Ecole des Mines de Paris, rapport annuel ACI/ARMINES 042240, 2006.
39. Code_Aster. Opensource finite element software , courtesy of EDF.
40. Drabek T., and Böhm H.J. Damage models for studying ductile matrix fracture in composites. Comput. Mater. Sci. 32 (2005) 329-336