A homogenization-based constitutive model for two-dimensional viscoplastic porous media

Comptes Rendus - Mecanique

Volumn 336, Issue 1-2, 2008, Pages 79-90

  Danas, Kostas ^a,b   Idiart, Martin I ^a,b   Ponte Castañeda, Pedro ^a,b  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Gurson criterion; Homogenization; Nonlinear composites; Porous media

Indexed keywords

MATHEMATICAL MODELS; POROUS MATERIALS; VISCOPLASTICITY;

COMPARATIVE STUDY; ESTIMATION METHOD; HYDROSTATICS; ISOTROPY; MICROSTRUCTURE; POROUS MEDIUM; STRESS; VISCOPLASTICITY;

EID: 38949179127     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2007.10.017     Document Type: Short Survey

References (27)

1. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth. J. Engrg. Mater. Technol. 99 (1977) 2-15
2. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. (1962) 143-150
3. Leblond J.B., Perrin G., and Suquet P. Exact results and approximate models for porous viscoplastic solids. Int. J. Plasticity 10 (1994) 213-235
4. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39 (1991) 45-71
5. Willis J.R. On methods for bounding the overall properties of nonlinear composites. J. Mech. Phys. Solids 39 (1991) 73-86
6. Michel J.C., and Suquet P. The constitutive law of nonlinear viscous and porous materials. J. Mech. Phys. Solids 40 1992 (1991) 783-812
7. Hashin Z., and Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11 (1963) 127-140
8. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory. J. Mech. Phys. Solids 50 (2002) 737-757
9. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. II. Applications. J. Mech. Phys. Solids 50 (2002) 759-782
10. Pastor J., and Ponte Castañeda P. Yield criteria for porous media in plane strain: second-order estimates versus numerical results. C. R. Mecanique 330 (2002) 741-747
11. Despois J.F., Mueller R., and Mortensen A. Uniaxial deformation of microcellular metals. Acta Mater. 54 (2006) 4129-4142
12. deBotton G., and Ponte Castañeda P. On the ductility of laminated materials. Int. J. Solids Struct. 29 (1992) 2329-2353
13. deBotton G., and Hariton I. High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior. J. Mech. Phys. Solids 50 (2002) 2577-2595
14. M.I. Idiart, Macroscopic behavior and field statistics in viscoplastic composites, Ph.D. thesis, University of Pennsylvania, 2006
15. Francfort G., and Murat F. Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94 (1986) 307-334
16. Milton G.W. The Theory of Composites (2002), Cambridge University Press
17. Hill R. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids A 11 (1963) 127-140
18. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44 (1996) 827-862
19. Levin V.M. Thermal expansion coefficients of heterogeneous materials. Mekh. Tverd. Tela 2 (1967) 83-94
20. Willis J.R. Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids 25 (1977) 185-202
21. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241 (1957) 376-396
22. Idiart M.I., Danas K., and Ponte Castañeda P. Second-order estimates for nonlinear composites and application to isotropic constituents. C. R. Mecanique 334 (2006) 575-581
23. Idiart M.I., and Ponte Castañeda P. Field statistics in nonlinear composites. I: Theory. Proc. R. Soc. A 463 (2007) 183-202
24. Idiart M.I., and Ponte Castañeda P. Second-order estimates for nonlinear isotropic composites with spherical pores and rigid particles. C. R. Mecanique 333 (2005) 147-154
25. Bilger N., Auslender F., Bornert M., Michel J.-C., Moulinec H., Suquet P., and Zaoui A. Effect of a nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis. Int. J. Solids Struct. 29 (2005) 517-538
26. Ponte Castañeda P. Bounds and estimates for the properties of nonlinear heterogeneous systems. Philos. Trans. Roy. Soc. London A 340 (1992) 531-567
27. Idiart M.I. Nonlinear sequential laminates reproducing hollow sphere assemblages. C. R. Mecanique 335 7 (2007) 363-368