Yield criteria for porous media in plane strain: Second-order estimates versus numerical results

Comptes Rendus - Mecanique

Volumn 330, Issue 11, 2002, Pages 741-747

  Pastor, Joseph ^a   Ponte Castañeda, Pedro ^b  

^a ESIGEC   (France)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Homogenization; Limit analysis; Optimization; Porous media

Indexed keywords

POROUS MEDIUM;

CALCULATION; FLOW; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; POROSITY; REVIEW;

EID: 0036855336     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-0721(02)01526-7     Document Type: Article

References (20)

1. P. Francescato, J. Pastor, H. Thai-The, Étude du critère de plasticité des matériaux poreux, C. R. Acad. Sci. Paris, Série IIb 329 (2001) 753-760.
2. P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I - Theory, J. Mech. Phys. Solids 50 (2002) 737-757.
3. P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. II - Applications, J. Mech. Phys. Solids 50 (2002) 759-782.
4. A. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I. Yield criteria and flow rules for porous ductile media, J. Engrg. Math. Tech. 99 (1977) 1-15.
5. N. Bilger, F. Auslender, M. Bornert, R. Masson, New bounds and estimates for porous media with rigid perfectly plastic matrix, C. R. Mécanique 330 (2002) 127-132.
6. P. Ponte Castañeda, Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, J. Mech. Phys. Solids 44 (1996) 827-862.
7. P. Ponte Castañeda, The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids 39 (1991) 45-71.
8. H. Thai-The, P. Francescato, J. Pastor, Limit analysis of unidirectional porous media, Mech. Res. Comm. 25 (1998) 535-542.
9. J.C. Michel, H. Moulinec, P. Suquet, Effective properties of composite materials with periodic microstructure: A computational approach, Comput. Methods Appl. Mech. Engrg. 172 (1999) 109-143.
10. G. Rousselier, Ductile fracture model and their potential in local approach of fracture, Nuclear Engrg. Design 105 (1987) 97-111.
11. W.A. Spitzig, R.E. Smelser, O. Richmond, The evolution of damage and fracture in iron compacts with various initial porosities, Acta Metall. 36 (1988) 1201-1211.
12. Y.-P. Pellegrini, Plasticity criterion for porous medium with cylindrical void, C. R. Mécanique 330 (2002), submitted.
13. P. Suquet, On bounds for the overall potential of power-law materials containing voids with an arbitrary shape, Mech. Res. Comm. 19 (1992) 51-58.
14. J. Pastor, H. Thai-The, P. Francescato, New bounds of the height limit of a vertical slope, Internat. J. Numer. Anal. Methods Geomech. 24 (2000) 165-182.
15. A. Ben-Tal, A. Nemirovski, On polyhedral approximations of the second-order cone, Math. Oper. Res. 26 (2001) 193-205.
16. F. Glineur, Topics in convex optimization, Thèse de la Faculté Polytechnique de Mons, Belgique, 2001.
17. P. Ponte Castañeda, P. Suquet, Nonlinear composites, Adv. Appl. Mech. 34 (1998) 171-302.
18. S. Turgeman, J. Pastor, Comparaison des charges limites d'une structure réelle et homogénéisée, J. Méc. Théor. Appl. 6 (1987) 121-143.
19. G. Bouchitté, P. Suquet, Charges limites, plasticité et homogénéisation: Le cas d'un bord chargé, C. R. Acad. Sci. Paris, Série I 305 (1987) 441-444.
20. P. Suquet, Private communication, 2001.