Exact results for the homogenization of elastic fiber-reinforced solids at finite strain

Journal of Elasticity

Volumn 83, Issue 2, 2006, Pages 153-177

  He, Q C ^a   Le Quang, H ^a   Feng, Z Q ^b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b University of Evry Paris Saclay   (France)

Author keywords

Fiber reinforced composites; Homogeneous strain fields; Homogenization; Large deformations; Microstructure; Porous materials

Indexed keywords

DEFORMATION; ELASTIC MODULI; FUNCTION EVALUATION; MICROSTRUCTURE; POROUS MATERIALS; STRAIN; STRESS ANALYSIS;

HOMOGENEOUS STRAIN FIELDS; HOMOGENIZATION; LARGE DEFORMATIONS;

FIBER REINFORCED MATERIALS;

EID: 33645659764     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-006-9049-1     Document Type: Article

References (34)

1. R. Abeyaratne and N. Triantafyllidis, An investigation of localization in a porous elastic material using homogenization theory. ASME J. Appl. Mech. 51 (1984) 481-486.
2. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977) 337-403.
3. R.B. Borden, A Course in Advanced Calculus. Dover, New York (1998).
4. P. Chadwick and R.W. Ogden, A theorem of tensor calculus and its application to Isotropic elasticity. Arch, Rational Mech. Anal. 44 (1971) 54-68.
5. P.G. Ciarlet, Mathematical Elasticity - Volume I: Three-Dimensional Elasticity. North-Holland, Amsterdam (1988).
6. A. Curnier, Computational Methods in Solid Mechanics. Kluwer, Dordrecht (1994).
7. G.J. Dvorak, On uniform fields in heterogeneous media. Proc. R. Soc. Lond. A 431 (1990) 89-110.
8. G. Geymonat, S. Müller and N. Triantafyllidis, Homogenization of nonlinear elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Rational Mech. Anal. 122 (1993) 231-290.
9. M.E. Gurtin, An Introduction to Continuum Mechanics. Academic, Boston (1981).
10. Z. Hashin, Large isotropic elastic deformations of composite and porous media. Int. J. Solids Structures 21 (1985) 711-720.
11. Q.C. He, Effects of size and boundary conditions on the yield strength of heterogeneous materials. J. Mech. Phys. Solids 49 (2001) 2557-2575.
12. Q.C. He, Uniform strain fields and microstructure-independent relations in nonlinear elastic fibrous composites. J. Mech. Phys. Solids 47 (1999) 1781-1793.
13. Q.C. He and A. Curnier, A more fundamental approach to damaged elastic stress-strain relations. Int. J. Solids Structures 32 (1995) 1433-1457.
14. R. Hill, Theory of mechanical properties of fiber-strengthened materials - I. Elastic behavior. J. Mech. Phys. Solids 12 (1964) 199-212.
15. R. Hill, On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. London A 326 (1972) 131-147.
16. G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, Chichester (2000).
17. C. Hurt, Application of variational concepts to size effects in elastic heterogeneous bodies. J. Mech. Phys. Solids 38 (1990) 813-841.
18. O. Lopez-Pamies and P.P Castañeda, Second-order estimates for the large-deformation response of particle-reinforced rubbers. C. R. Mecanique 331 (2003) 1-8.
19. O. Lopez-Pamies and P.P. Castañeda, Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations. J. Elasticity 76 (2004) 247-287.
20. C. Miehe, Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput. Methods. Appl. Mech. Eng. 192 (2003) 559-591.
21. C. Miehe, J. Schröder and M Becker, Computational homogenization analysis in finite elasticity: Material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction. Comput. Methods. Appl. Mech. Eng. 191 (2002) 4971-5005.
22. G.W. Milton, The Theory of Composites. Cambridge University Press, Cambridge (2002).
23. G.W. Milton and S.K. Serkov, Bounding the current in nonlinear conducting composites. J. Mech. Phys. Solids 48 (2000) 1295-1324.
24. S. Müller, Homogenization of nonconvex integral functional and cellular elastic materials. Arch. Rational Mech. Anal. 99 (1987) 189-212.
25. S. Nemat-Nasser, Averaging theorems in finite deformation plasticity. Mech. Mater. 31 (1999) 493-523.
26. S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, Amsterdam (1999).
27. R.W. Ogden, On the overall moduli of non-linear elastic composite materials. J. Mech. Phys. Solids 22 (1974) 541-553.
28. R.W. Ogden, Extremum principles in non-linear elasticity and their application to composites - I. Theory. Int. J. Solids Structures 14 (1978) 265-282.
29. R.W. Ogden, Nonlinear Elastic Deformations. Ellis Horwood and Wiley, Chichester (1984).
30. P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory. J. Mech. Phys. Solids 50 (2002) 737-757.
31. P.P. Castañeda and P. Suquet, Nonlinear composites. In: E. van der Giessen and T.W. Wu (eds.). Advances in Applied Mechanics, vol. 34, Academic, San Diego (1998) pp. 171-302.
32. S. Torquato, Random Heterogeneous Media: Microstructure and Macroscopic Properties. Springer, Berlin Heidelberg New York (2001).
33. N. Triantafyllidis and B.N. Maker, On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. ASME J. Appl. Mech. 52 (1985) 794-800.
34. C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics. Springer, Berlin Heidelberg New York (1992).