Variational methods for the homogenization of periodic heterogeneous media

European Journal of Mechanics, A/Solids

Volumn 17, Issue 4, 1998, Pages 599-617

  Luciano, R ^a   Sacco, E ^a  

^a UNIVERSITY OF CASSINO AND SOUTHERN LAZIO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; MICROSTRUCTURE; STRESS CONCENTRATION; VARIATIONAL TECHNIQUES;

PERIODIC HETEROGENEOUS MEDIA;

COMPOSITE MATERIALS;

EID: 0032108065     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(99)80024-2     Document Type: Article

References (31)

1. ABOUDI J., 1991, Mechanics of Composite Materials, Elsevier.
2. ANTHOINE A., 1995, Derivation of the in-plane elastic characteristics of masonry through homogenization theory, Int. J. Solids and Structures, 32, 137-163.
3. BARBERO E. J., LUCIANO R., 1995, Micromechanical formulas for the relaxation tensor of linear viscoelastic composites with transversally isotropic filters, Int. J. Solids Structures, 32, 1859-1872.
4. BISEGNA P., LUCIANO R., 1996, Bounds on the off-diagonal coefficients of the homogenized constitutive tensor of a composite material, Mech. Res. Comm., 23, 239-245.
5. BENVENISTE Y., 1987, A new approach to the application of Mori-Tanaka's theory in composite materials, Mech. Mater., 6, 147-157.
6. BREZZI F., FORTIN M., 1991, Mixed and Hybrid Finite Element Method, Springer-Verlag.
7. BUDIANSKY B., O'CONNELL R. J., 1976, Elastic moduli of a cracked solid, Int. J. Solids Structures, 12, 81-97.
8. ESHELBY J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London, A241, 376-396.
9. HALLEN D. H., JONES R. H., BOYD J. G., 1994, Micromechanical analysis of a continuous fiber metal matrix composite including the effect of matrix viscoplasticity and evolving damage, J. Mech. Phys. Solids, 42, 505-529.
10. HASHIN Z., SHTRIKMAN S., 1963, A variational approach to the theory of the elastic behaviour of polycrystals, J. Mech. Phys. Solids, 10, 335-342.
11. HILL R., 1965, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 227-240.
12. KRALJ B., PANDE G. N., MIDDLETON J., 1991, On the mechanics of frost damage to brick masonry, Comp. & Struct., 41, 53-66.
13. LAWS N., DVORAK G. J., HEJAZI M., 1983, Stiffness changes in unidirectional composites caused by crack systems, Mech. Mater., 2, 123-137.
14. LUCIANO R., BARBERO E. J., 1994, Formulas for the stiffness of composites with periodic microstructure, Int. J. Solids Structures, 31, 2933-2944.
15. LUCIANO R., BARBERO E. J., 1995, Analytical expressions for the relaxation moduli of linear viscoelastic composites with periodic microstructure, J. Appl. Mechanics, 62, 786-793.
16. LUCIANO R., SACCO E., 1997, Homogenization technique and damage model for old masonry material, Int. J. Solids Structures, 34, 3191-3208.
17. MOULINEC H., SUQUET P., 1994, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, C. R. Acad. Sci. Paris, 318, Serie II, 1417-1423.
18. ODEN J. T., REDDY J. N., 1976, An Introduction to Mathematical Theory of Finite Elements, John Wiley and Sons.
19. MORI T., TANAKA K., 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21, 571-574.
20. NEMAT-NASSER S., YU N., HORI M., 1993, Bounds and estimates of overall moduli of composites with periodic microstructure, Mechanics of Materials, 15, 163-181.
21. PANDE G. N., LIANG J. X., MIDDLETON J., 1989, Equivalent elastic moduli for brick masonry, Comput. Geotech., 8, 243-265.
22. PONTE CASTAñEDA P., SUQUET P. M., 1995. On the effective behavior of weakly inhomogeneous nonlinear materials, Eur. J. Mech. A/Solids, 14, 205-236.
23. SANCHEZ-HUBERT J., SANCHEZ-PALENCIA E., 1992, Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson.
24. SUQUET P. M., 1987, Elements of homogenization for inelastic solid mechanics. In Homogenization Techniques for Composite Media, (Edited by E. Sanchez-Palencia and A. Zaoui), Lecture Notes in Physics Vol. 272, Springer-Verlag.
25. SUQUET P. M., 1990, Une méthode simplifiée pour le calcul des propriétés élastiques de matériaux hétérogènes à structure pérodique, C. R. Acad. Sci. Paris, 311, Serie II, 769-774.
26. TEPLY J. L., DVORAK G. J., 1988, Bound on overall instantaneous properties of elastic-plastic composites, J. Mech. Phys. Solids, 36, 29-58.
27. TVERGAARD V., 1993, Model studies of fibre breakage and debonding in a metal reinforced by short fibres, J. Mech. Phys. Solids, 41, 1309-1326.
28. WASHIZU K., 1982, Variational Methods in Elasticity and Plasticity, Pergamon Press.
29. WENG G. J., 1992, Explicit evaluation of Willis' bounds with ellipsoidal inclusions, Int. J. Engng Sci., 30, 83-92.
30. WILLIS J. R., 1977, Bounds and self-consistent estimates for the overall moduli of anisotropic composites, J. Mech. Phys. Solids, 25, 185-202.
31. WILLIS J. R., 1983, The overall response of composite materials, ASME J. Appl. Mech., 50, 1202-1209.