Infinite-contrast periodic composites with strongly nonlinear behavior: Effective-medium theory versus full-field simulations

International Journal of Solids and Structures

Volumn 46, Issue 18-19, 2009, Pages 3365-3382

  Idiart, M I ^a,b   Willot, F ^b,c   Pellegrini, Y P ^c   Ponte Castaneda P ^a,b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^c DIF   (France)

Author keywords

Homogenization; Porous media; Reinforced composites; Viscoplasticity

Indexed keywords

COMPUTATION THEORY; FAST FOURIER TRANSFORMS; HOMOGENIZATION METHOD; NUMERICAL METHODS; NUMERICAL MODELS; POROSITY; POROUS MATERIALS; REINFORCEMENT; RIGIDITY; SHEAR FLOW; STRESS INTENSITY FACTORS; VISCOPLASTICITY;

EFFECTIVE MEDIUM THEORIES; FAST FOURIER TRANSFORM ALGORITHM; IN-PLANE SHEAR LOADINGS; LOCAL FIELD DISTRIBUTION; MACROSCOPIC BEHAVIORS; NONLINEAR HOMOGENIZATION; REINFORCED COMPOSITES; STRAIN RATE SENSITIVITY;

STRAIN RATE;

EID: 67649662184     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2009.05.009     Document Type: Article

References (47)

1. 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. 42 (2005) 517-538
2. Bouchitté, G., Suquet, P., 1991. Homogenization, plasticity and yield design. In: Proceedings of the Workshop on Composite Media and Homogenization Theory, pp. 107-133.
3. Chenchiah I.V., and Bhattacharya K. Examples of non-linear homogenization involving degenerate energies. I. Plane strain. Proc. Roy. Soc. Lond. A 461 (2005) 3681-3703
4. Danas K., Idiart M.I., and Ponte Castañeda P. Homogenization-based constitutive model for isotropic viscoplastic porous media. Int. J. Solids Struct. 45 (2008) 3392-3409
5. Drucker D.C. The continuum theory of plasticity on the macroscale and the microscale. J. Mater. 1 (1966) 873-910
6. Duva J.M., and Hutchinson J.W. Constitutive potentials for dilutely voided nonlinear materials. Mech. Mater. 3 (1984) 41-54
7. Duxbury P.M., McGarrity E.S., and Holm E.A. Critical manifolds in non-linear response of complex materials. Mech. Mater. 38 (2006) 757-771
8. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. Lond. A 241 (1957) 376-396
9. Fleck N.A., and Hutchinson J.W. Void growth in shear. Proc. Roy. Soc. Lond. A 407 (1986) 435-458
10. Francfort G.A., and Suquet P. Duality relations for nonlinear incompressible two dimensional elasticity. Proc. Roy. Soc. Edimb. A 131 (2001) 351-369
11. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13 (1965) 89-100
12. Hutchinson J.W. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. Roy. Soc. Lond. A 348 (1976) 101-127
13. Idiart M.I., and Ponte Castañeda P. Field statistics in nonlinear composites. I - theory. Proc. Roy. Soc. Lond. A 463 (2007) 183-202
14. Idiart M.I., and Ponte Castañeda P. Field statistics in nonlinear composites. II - applications. Proc. Roy. Soc. Lond. A 463 (2007) 203-222
15. Idiart M.I., Danas K., and Ponte Castañeda P. Second-order theory for nonlinear composites and application to isotropic constituents. C.R. Mecanique 334 (2006) 575-581
16. Idiart M.I., Moulinec H., Ponte Castañeda P., and Suquet P. Macroscopic behavior and field fluctuations in viscoplastic composites: second-order estimates vs. full-field simulations. J. Mech. Phys. Solids 54 (2006) 1029-1063
17. Kachanov L.M. Fundamentals of the Theory of Plasticity (2004), Dover, New York
18. Lebensohn R.A., Liu Y., and Ponte Castañeda P. Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates. Proc. Roy. Soc. Lond. 460 (2004) 1381-1405
19. Lebensohn R.A., Liu Y., and Ponte Castañeda P. On the accuracy of the self-consistent approximation for polycrystals: comparisons with full-field numerical simulations. Acta Mater. 52 (2004) 5347-5361
20. Lebensohn R.A., Tomé C.N., and Ponte Castañeda P. Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philos. Mag. 87 (2007) 4287-4322
21. Lee B.J., and Mear M.E. Effective properties of power-law solids containing elliptical inhomogeneities. Part I: rigid inclusions. Mech. Mater. 13 (1992) 313-335
22. Maghous, S., 1991. Détermination du Critère de Résistance Macroscopique d'un Matériau Hétérogène à Structure Périodique. Ph.D. Thesis, École Nationale des Ponts et Chaussées.
23. Michel J.-C., Moulinec H., and Suquet P. A computational scheme for linear and non-linear composites with arbitrary phase contrast. Int. J. Numer. Meth. Eng. 52 (2001) 139-158
24. Moulinec H., and Suquet P. A fast numerical method for computing the linear and nonlinear properties of composites. C.R. Acad. Sci. Paris II 318 (1994) 1417-1423
25. Moulinec H., and Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Meth. Appl. Mech. Eng. 157 (1998) 69-94
26. Moulinec H., and Suquet P. Intraphase strain heterogeneity in nonlinear composites: a computational approach. Eur. J. Mech. A 22 (2003) 751-770
27. Moulinec H., and Suquet P. Homogenization for nonlinear composites in the light of numerical simulations. In: Ponte Castañeda P., et al. (Ed). Nonlinear Homogenization and its Applications to Composites. Polycrystals and Smart Materials (2004), Kluwer Academic Publishers, The Netherlands 193-223
28. 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
29. Pellegrini Y.P. Self-consistent effective-medium approximation for strongly non-linear media. Phys. Rev. B 64 (2001) 134211
30. Pellegrini, Y.P., 2001b. Unpublished work.
31. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39 (1991) 45-71
32. Ponte Castañeda P. New variational principles in plasticity and their application to composite materials. J. Mech. Phys. Solids 40 (1992) 1757-1788
33. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44 (1996) 827-862
34. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I - theory. J. Mech. Phys. Solids 50 (2002) 737-757
35. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. II - applications. J. Mech. Phys. Solids 50 (2002) 759-782
36. Ponte Castañeda P., and Suquet P. Nonlinear composites. Adv. Appl. Mech. 34 (1998) 171-302
37. Rekik A., Auslender F., Bornert M., and Zaoui A. Objective evaluation of linearization procedures in nonlinear homogenization: a methodology and some implications on the accuracy of micromechanical schemes. Int. J. Solids Struct. 44 (2007) 3468-3496
38. Salençon J. Calcul à la rupture et analyse limite (1983), Presses École Nationale des Ponts et Chaussées, Paris
39. Suquet P. Sur les équations de la plasticité: existence et régularité des solutions. J. Mécanique 20 (1981) 3-39
40. Suquet P. Overall properties of nonlinear composites: a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure. C.R. Acad. Sci. Paris II 320 (1995) 563-571
41. Taliercio A. Lower and upper bounds for the macroscopic strength domain of a fiber-reinforced composite material. Int. J. Plasticity 8 (1992) 741-762
42. Willis J.R. Variational and related methods for the overall properties of composites. Adv. Appl. Mech. 21 (1981) 1-78
43. Willis J.R. The overall response of nonlinear composite media. Eur. J. Mech. A 19 (2000) S165-S184
44. Willot, F., 2007. Contribution à l'étude théorique de la localisation plastique dans les poreux. Ph.D. thesis, École Polytechnique and Commissariat à l'Énergie Atomique, France.
45. Willot, F., Pellegrini, Y.P., 2008. Numerical FFT computations in 2D perfectly plastic pixel wise disordered porous media. In: Proceedings of the 11th International Symposium on Continuum Models and Discrete Systems (July 30-August 3, Paris, 2007) (École des Mines, Paris, 2008), pp. 443-449. Also, arXiv:0802.2488v1.
46. Willot F., Pellegrini Y.P., Idiart M.I., and Ponte Castañeda P. Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior. Phys. Rev. B 78 (2008) 104111
47. Willot F., Pellegrini Y.P., and Ponte Castañeda P. Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions. J. Mech. Phys. Solids 56 (2008) 1245-1268