A new derivative on the shift property of effective elastic compliances for planar and three-dimensional composites

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 457, Issue 2011, 2001, Pages 1675-1684

  Hu, G K ^a   Weng, G J ^b  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Composites; Effective compliances; Shift properties; Universal relations

Indexed keywords

EID: 57249097749     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2001.0783     Document Type: Article

References (26)

1. Bobeth, M. & Diener, G. 1987 Static elastic and thermoelastic field fluctuation in multiphase composites. J. Mech. Phys. Solids 35, 137-149.
2. Chen, T. 1995 Further results on invariant properties of the stress in plane elasticity and its extension to piezoelasticity. Mech. Res. Commun. 22, 251-256.
3. Cherkaev, A. V., Lurie, K. A. & Milton, G. W. 1992 Invariant properties of the stress in plane elasticity and equivalence classes of composites. Proc. R. Soc. Lond. A438, 519-529.
4. Day, A. R. Snyder, K. A., Garboczi, E. J. & Thorpe, M. F. 1992 The elastic moduli of a sheet containing circular holes. J. Mech. Phys. Solids 40, 1031-1051.
5. Dundurs, J. 1967 Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1, 310-322.
6. Dundurs, J. & Jasiuk, I. 1997 Effective elastic moduli of composite materials: reduced parameter dependence. Appl. Mech. Rev. 50, S39-S43.
7. Dundurs, J. & Markenscoff, X. 1993 Invariance of stresses under a change in elastic compliance. Proc. R. Soc. Land. A443, 289-300.
8. Francfort, G. A. & Murat, F. 1986 Homogenization and optimal bounds in linear elasticity. Arch. Ration. Mech. Analysis 94, 307-334.
9. Hashin, Z. 1965 On elastic behavior of reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids 13, 119-134.
10. Hashin, Z. & Shtrikman, S. 1963 A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11, 127-140.
11. Hill, R. 1963 Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11, 357-372.
12. Hu, G. K. 1996 A method of plasticity for general aligned spheroidal void or fiber reinforced composites. Int. J. Plasticity 12, 439-449.
13. Kreher, W. & Pompe, W. 1989 Internal stresses in heterogeneous solids. Berlin: Akademie.
14. Michell, J. H. 1899 On the direct determination of stress in an elastic solid, with application to the theory of plates. Proc. Land. Math. Soc. 31, 100-125.
15. Milgrom, M. 1990 Linear response of general composite systems to many coupled fields. Phys. Rev. B41, 12484-12494.
16. Milton, G. W. 1986 Modeling the properties of composites by laminates. In Homogenization and effective moduli of materials and media (ed. J. L. Ericksen, D. Kinderlehrer, R. Kohn & J. L. Lions), vol. I, pp. 150-174. IMA Volumes in Mathematics and Applications. Springer.
17. Moran, B. & Gosz, M. 1994 Stress invariance in plane anisotropic elasticity. Modelling Simul. Mater. Sci. Engng 2, 677-688.
18. Nemat-Nasser, S. & Hori, M. 1993 Micromechanics: overall properties of heterogeneous materials. Elsevier.
19. Norris, A. N. 1985 A differential scheme for the effective moduli of composites. Mech. Mater. 4, 1-16.
20. Norris, A. N. 1999 Stress invariance and redundant moduli in three-dimensional elasticity. Proc. R. Soc. Lond. A455, 4097-4116.
21. Ostoja-Starzewski, M. & Jasiuk, I. 1995 Stress invariance in planar Cosserat elasticity. Proc. R. Soc. Land. A451, 453-470.
22. Thorpe, M. F. & Jasiuk, I. 1992 New results in the theory of elasticity for two-dimensional composites. Proc. R. Soc. Lond. A438, 531-544.
23. Zheng, Q. S. & Chen, T. 1999a Generalized plane deformation of electromagnetic thermoelastic solids. I. Correspondence and invariance shifts. Proc. R. Soc. Land. A455, 1283-1299.
24. Zheng, Q. S. & Chen, T. 1999b Generalized plane deformation of electromagnetic thermoelastic solids. II. Further results on invariance shifts and reduced dependences. Proc. R. Soc. Land. A455, 1301-1314.
25. Zheng, Q. S. & Hwang, K. C. 1996 Reduced dependence of defect compliance on matrix and inclusion elastic properties in two-dimensional elasticity. Proc. R. Soc. Land. A452, 2493-2507.
26. Zheng, Q. S. & Hwang, K. C. 1997 Two-dimensional elastic compliances of materials with holes and microcracks. Proc. R. Soc. Land. A453, 353-364.