Apparent and effective mechanical properties of linear matrix-inclusion random composites: Improved bounds for the effective behavior

International Journal of Solids and Structures

Volumn 49, Issue 10, 2012, Pages 1195-1211

  Salmi, Moncef ^a   Auslender, François ^a   Bornert, Michel ^b   Fogli, Michel ^a  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

Apparent behavior; Bounds; Effective behavior; Linear elasticity; Matrix inclusion composites; Random microstructure

Indexed keywords

APPARENT BEHAVIOR; BOUNDS; EFFECTIVE BEHAVIOR; LINEAR ELASTICITY; RANDOM MICROSTRUCTURE;

ELASTICITY; MICROSTRUCTURE;

MATRIX ALGEBRA;

EID: 84859753275     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2012.01.018     Document Type: Article

References (46)

1. M. Beran Statistical Continuum Theories 1968 John Wiley New York
2. N. Bilger, F. Auslender, M. Bornert, J.-C. Michel, H. Moulinec, P. Suquet, and A. Zaoui Effect of a non uniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis Int. J. Solids Struct. 42 2005 517 538
3. M. Bornert Homogénéisation des milieux aléatoires: bornes et estimations M. Bornert, T. Bretheau, P. Gilormini, Homogénéisation en mécanique des matériaux 1: Matériaux aléatoires élastiques et milieux périodiques 2001 Hrmes Science Publication pp 133 221
4. M. Bornert, C. Stolz, and A. Zaoui Morphologically representative pattern-based bounding in elasticity J. Mech. Phys. Solids 44 1996 307 331
5. G. Casella, and R. Berger Statistical Inference 2001 Duxbury United States
6. CEA, 2003. Cast3m. http://www-cast3m.cea.fr/.
7. R.M. Christensen, and K.H. Lo Solution for effective shear properties in three phase sphere and cylinder models J. Mech. Phys. Solids 27 1979 315 330 (Pubitemid 10433797)
8. M. Danielsson, D. Parks, and M. Boyce Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers J. Mech. Phys. Solids 55 2007 533 561 (Pubitemid 46108823)
9. I. Doghri, L. Adam, and N. Bilger Mean-field homogenization of elasto-viscoplastic composites based on a general incrementally affine linearization method Int. J. Plast. 26 2010 219 238
10. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. R. Soc. Lond. A A421 1957 376 396
11. I. Gitman, H. Askes, and L. Sluys Representative volume: existence and size determination Eng. Fracture Mech. 74 2007 2518 2534 (Pubitemid 47177169)
12. A. Gusev Representative volume element size for elastic composites: a numerical study J. Mech. Phys. Solids 45 9 1997 1449 1459 (Pubitemid 127412533)
13. Z. Hashin The elastic moduli of heterogeneous materials J. Appl. Mech. 29 1962 143 150
14. Z. Hashin, and B.W. Rosen The elastic moduli of fiber-reinforced materials J. Appl. Mech. 31 1964 223 232
15. Z. Hashin, and S. Shtrikman A variational approach to the theorie of the elastic behavior of multiphase material J. Mech. Phys. Solids 11 1963 127 140
16. C. Huet Application of variational concepts to size effects in elastic heterogeneous bodies J. Mech. Phys. Solids 38 1990 813 841
17. M. Jiang, K. Alzebdeh, I. Jasiuk, and M. Ostoja-Starzewski Scale and boundary conditions effects in elastic properties of random composites Acta Mech. 148 1-4 2001 63 78 (Pubitemid 32694191)
18. T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin Determination of the size of the representative volume element for random composites: statistical and numerical approach Int. J. Solids Struct. 40 2003 3647 3679 (Pubitemid 36659117)
19. E. Kroner Berechnung der elastischen konstanten des vielkrilstalls aus den konstanten des einkristalls Z. Phys. 151 1958 504 518
20. N. Lahellec, and P. Suquet Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide C.R. Mec. 332 2004 693 700 (Pubitemid 38950668)
21. N. Lahellec, and P. Suquet On the effective behavior of nonlinear inelastic composites: I Incremental variational principles J. Mech. Phys. Solids 55 2007 1932 1963 (Pubitemid 47021156)
22. R. Masson, and A. Zaoui Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials J. Mech. Phys. Solids 47 1999 1543 1568
23. T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall. 21 1973 597 629
24. S. Nemat-Nasser, and M. Hori Micromechanics: overall Properties of Heterogenous Materials 1993 North Holland Amsterdam
25. M. Ostoja-Starzewski Random field models of heterogeneous materials Int. J. Solids Struct. 35 1998 2429 2455 (Pubitemid 128368533)
26. M. Ostoja-Starzewski Material spatial randomness: from statistical to representative volume element Prob. Eng. Mech. 21 2006 112 132
27. G. Papanicolaou, and S. Varadhan Boundary Value Problems with Rapidly Oscillating Random Coefficients 1978 North-Holland Amsterdam pp. 835-873
28. C. Pelissou, J. Baccou, Y. Monerie, and F. Perales Determination of the size of the representative volume element for random quasi-brittle composites Int. J. Sol. Struct. 46 14-15 2009 2842 2855
29. P. Ponte Castañeda Second-order homogeneisation estimates for nonlinear composites incorporating field fluctuations: I- theory J. Mech. Phys. Solids 50 2002 737 757 (Pubitemid 34201320)
30. Ponte Castañeda, P., Suquet, P., 1997. Nonlinear composites. Advances in Applied Mechanics 34, 171-212, 212a, 212b, 212c, 212d, 213-302.
31. P. Ponte Castañeda, and J. Willis The effect of spatial distribution on the effective behavior of composite materials and cracked media J. Mech. Phys. Solids 43 12 1995 1919 1951
32. S. Ranganathan, and M. Ostoja-Starzewski Scaling function, anisotropy and the size of RVE in elastic random polycrystals J. Mech. Phys. Solids 56 2008 2773 2791
33. A. Reuss Calculation of the flow limits of mixed crystals on the basis of the plasticity of mono-crystals Z. Angew. Math. Mech 9 1929 49 58
34. M. Rintoul, and S. Torquato Reconstruction of the structure of dispersions J. Colloid Interface Sci. 186 2 1997 467 476 (Pubitemid 27468850)
35. K. Sab On the homogenization and the simulation of random materials Eur. J. Mech. A/Solids 11 1992 585 607 (Pubitemid 23559661)
36. Salmi, M., 2011. Homogénéisation des composites linéaires: étude de la variabilité des comportements. Ph.D. thesis, Université Blaise Pascal. Clermont-Ferrand (France).
37. Salmi, M., Auslender, F., Bornert, M., Fogli, M., 2012. Various estimates of representative volume element sizes based on a statistical analysis of the apparent behavior of random linear composites. Comptes Rendus Mécanique, in press.
38. E. Sanchez-Palencia, and A. Zaoui vol. 272 1987 Springer-Verlag New York
39. Schoberl, J., Gerstmayr, H., Gaisbauer, R., 2003. Netgen - Automatic mesh generator. http://www.hpfem.jku.at/netgen/.
40. C. Stolz, and A. Zaoui Analyse morphologique et approches variationnelles du comportement d'un milieu élastique hétérogne C.R. Acad. Sci. Paris, II 312 1991 143 150
41. W. Voigt über die beziehung zwischen den beiden elasticitä tsconstanten isotroper körper Ann. Phys. (Leipzig) 38 1889 573 587
42. L. Walpole Elastic Behavior of Composite Materials: Theoretical Foundations. vol. 21 1981 Academic Press New York pp. 160-242
43. J. Willis Bounds and self-consistent estimates for the overall properties of anisotropic composites J. Mech. Phys. Solids 25 1977 185 202 (Pubitemid 8551428)
44. J. Willis Variational and related methods for the overall properties of composites Adv. Appl. Mech. 21 1981 1 78 (Pubitemid 12465507)
45. F. Willot, and Jeulin Elastic behavior of composites containing boolean random sets of inhomogeneities Int. J. Eng. Sci. 47 2009 313 324
46. F. Willot, Y.-P. Pellegrini, and P. Ponte Castañeda Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions J. Mech. Phys. Solids 56 4 2008 1245 1268 (Pubitemid 351410521)