Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media

International Journal of Solids and Structures

Volumn 44, Issue 7-8, 2007, Pages 2225-2243

  Pensee V ^a   He, Q C ^a  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

Micromechanics; Particle reinforced composites; Representative volume element; Shear modulus; Size effects

Indexed keywords

ELASTIC MODULI; INCLUSIONS; MATHEMATICAL MODELS; OPTIMIZATION; PORE SIZE;

ELASTIC ISOTROPIC INCLUSIONS; GENERALIZED SELF CONSISTENT MODEL (GSCM); PARTICLE REINFORCED COMPOSITES; REPRESENTATIVE VOLUME ELEMENTS;

COMPOSITE MICROMECHANICS;

EID: 33846928707     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.07.003     Document Type: Article

References (37)

1. Balendrana B., and Nemat-Nasser S. Bounds on elastic moduli of composites. J. Mech. Phys. Solids 43 (1995) 1825-1853
2. Bornert, M., 1996. Morphologie microstructurale et comportement mécanique; caractérisations expérimentales, approches par bornes et estimations autocohérentes généralisées. Ph.D. Thesis, Ecole Nationale des Ponts et Chaussées, France (in French).
3. Christensen R.M. A critical evaluation for a class of micromechanics models. J. Mech. Phys. Solids 38 (1990) 379-404
4. Christensen R.M. Two theoretical elasticity micromechanics models. J. Elasticity 50 (1998) 15-25
5. Christensen R.M., and Lo K.H. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27 (1979) 315-330
6. Drugan W.J. Micromechanics-based variational estimates for a high order nonlocal constitutive equation and optimal choice of effective moduli for elastic composites. J. Mech. Phys. Solids 48 (2000) 1359-1387
7. Drugan W.J., and Willis J.R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids 44 4 (1996) 497-524
8. Eshelby J.D. The force on an elastic singularity. Philos. Trans. R. Soc. Lond. A 244 (1951) 87-112
9. Guidoum, A., 1994. Simulation numérique 3D des comportements des bétons en tant que composites granulaires. Doctoral dissertation No. 1310, Ecole Polytechnique Fédérale de Lausanne, Switzerland (in French).
10. Gusev A.A. Representative volume element size for elastic composites: a numerical study. J. Mech. Phys. Solids 45 (1997) 1419-1459
11. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
12. Hazanov S. On micromechanics of imperfect interfaces in heterogeneous bodies smaller than the representative volume. Int. J. Engng. Sci. 37 (1999) 847-861
13. Hazanov S. On apparent properties of elastic heterogeneous bodies smaller than the representative volume. Acta Mech. 134 (1999) 123-134
14. Hazanov S., and Amieur M. On overall properties of elastic heterogeneous bodies smaller than the representative volume. Int. J. Engng. Sci. 33 (1995) 1289-1301
15. Hazanov S., and Huet C. Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. J. Mech. Phys. Solids 42 (1994) 1995-2011
16. He Q.-C. Effects of size and boundary conditions on the yield strength of heterogeneous materials. J. Mech. Phys. Solids 49 (2001) 2557-2575
17. He Q.-C., and Benveniste Y. Exactly solvable spherically anisotropic thermoelastic microstructures. J. Mech. Phys. Solids 52 (2004) 2661-2682
18. He Q.-C., and Pensée V. A spherically anisotropic microstructure model for fluid-saturated poroelastic isotropic materials. Int. J. Fracture 136 (2005) L19-L26
19. Hervé E., and Zaoui A. n-layered inclusion-based micromechanical modelling. Int. J. Engng. Sci. 31 1 (1993) 1-10
20. Huet Ch. Application of variational concepts to size-effects in elastic heterogeneous bodies. J. Mech. Phys. Solids 38 (1990) 813-841
21. Huet Ch. Coupled size and boundary-conditions effects in viscoelastic heterogeneous and composite bodies. Mech. Mater. 31 (1999) 787-829
22. Jiang M., Ostoja-Starzewski M., and Jasiuk I. Scale dependent bounds on effective elastoplastic response of random composites. J. Mech. Phys. Solids 49 (2001) 655-673
23. Kanit T., Forest S., Galliet I., Mounoury V., and Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40 (2003) 3647-3679
24. Kerner E.H. The elastic and thermo-elastic properties of composite media. Proc. Phys. Soc. Lond. B 69 (1956) 808-813
25. Le Quang H., and He Q.-C. Micromechanical estimation of the shear modulus of a composite consisting of anisotropic phases. J. Mater. Sci. Tech. 20 (2004) 6-10
26. Le Quang, H., He, Q.-C., submitted for publication. A one-parameter generalized self-consistent model for isotropic multiphase composites. Int. J. Solids Struct.
27. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity (1944), Dover, New York
28. Nemat-Nasser S., and Hori M. Micromechanics: Overall Properties of Heterogeneous Materials (1999), North-Holland, Amsterdam
29. Ostoja-Starzewski M. Bounding of effective thermal conductivities of multiscale materials by essential and natural boundary conditions. Phys. Rev. B 54 (1996) 278-285
30. Ostoja-Starzewski M. Random field model of heterogeneous materials. Int. J. Solids Struct. 35 (1998) 2429-2455
31. Ostoja-Starzewski M. Microstructural disorder mesoscale finite elements and macroscopic response. Proc. Royal Soc. Lond. A 455 (1999) 3189-3199
32. Pecullan S., Gibiansky L.V., and Torquato S. Scale effects on the elastic behavior of periodic and hierarchical two dimensional composites. J. Mech. Phys. Solids 47 (1999) 1509-1542
33. Ren Z.-Y., and Zheng Q.-S. A quantitative study on minimum sizes of representative volume elements of cubic polycrystals - numerical experiments. J. Mech. Phys. Solids 50 (2002) 881-893
34. Ren Z.-Y., and Zheng Q.-S. Effects of grain sizes, shapes and distribution on minimum sizes of representative volume elements of cubic polycrystals. Mech. Mater. 36 (2004) 1217-1229
35. Sab K. On the homogenization and the simulation of random materials. Eur. J. Mech. Solids 11 (1992) 585-607
36. Sab K., and Nedjar B. Periodization of random media and representative volume element size for linear composites. C.R. Mecanique 333 (2005) 187-195
37. Zohdi T.I., Oden J.T., and Rodin G.J. Hierarchical modeling of heterogeneous bodies. Comput. Methods Appl. Mech. Engng. 138 (1996) 273-398