Improved bounds for the overall properties of a nonlinear composite dielectric

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

Volumn 457, Issue 2007, 2001, Pages 587-597

  Talbot, D R S ^a  

^a Institute for Clean Growth and Future Mobility   (United Kingdom)

Author keywords

Bounds; Dielectrics; Effective properties; Energy methods; Nonlinear composites

Indexed keywords

EID: 57249090233     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0683     Document Type: Article

References (24)

1. Astala, K. 1994 Area distortion of quasiconformal mappings. Acta Math. 173, 37-60.
2. Astala, K. & Miettinen, M. 1998 On quasiconformal mappings and 2-dimensional G-closure problems. Arch. Ration. Mech. Analysis 143, 207-240.
3. Bañuelos, R. & Wang, G. 1995 Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms. Duke Math. J. 80, 575-600.
4. Eremenko, A. & Hamilton, D. H. 1995 On the area distortion by quasiconformal mappings. Proc. Am. Math. Soc. 123, 2793-2797.
5. Hashin, Z. & Shtrikman, S. 1962 A variational approach to the theory of the elastic behaviour of polycrystals. J. Mech. Phys. Solids 10, 343-352.
6. Hashin, Z. & Shtrikman, S. 1963 A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127-140.
7. John, F. & Nirenberg, L. 1961 On functions of bounded mean oscillation. Commun. Pure Appl. Math. 14, 415-426.
8. Milton, G. W. 1981 Bounds on the electromagnetic, elastic, and other properties of two-component composites. Phys. Rev. Lett. 46, 542-545.
9. Milton, G. W. & Nesi, V. 1999 Optimal G-closure bounds via stability under lamination. Arch. Ration. Mech. Analysis 150, 191-207.
10. Nesi, V. 1996 Quasiconformal mappings as a tool to study certain two-dimensional G-closure problems. Arch. Ration. Mech. Analysis 134, 17-51.
11. Nesi, V. 1997 Reverse Holder's inequality in nonlinear conductivity. Nonlinear Diff. Eqns Appl. 4, 283-303.
12. Ponte Castañeda, P. 1991 The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39, 45-71.
13. Ponte Castañeda, P. 1992 Bounds and estimates for the properties of nonlinear heterogeneous systems. Phil. Trans. R. Soc. Lond. A 340, 531-567.
14. Stein, E. M. 1979 Singular integrals and differentiability properties of functions. Princeton University Press.
15. Talbot, D. R. S. 1999 Bounds which incorporate morphological information for a nonlinear composite dielectric. Proc. R. Soc. Lond. A 455, 3017-3628.
16. Talbot, D. R. S. & Willis, J. R. 1985 Variational principles for inhomogeneous nonlinear media. IMA J. Appl. Math. 35, 39-54.
17. Talbot, D. R. S. & Willis, J. R. 1994 Upper and lower bounds for the overall properties of a nonlinear composite dielectric. I. Random microgeometry. Proc. R. Soc. Lond. A 447, 365-384.
18. Talbot, D. R. S. & Willis, J. R. 1995 Upper and lower bounds for the overall properties of a nonlinear elastic composite. In Proc. IUTAM and ISIMM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics (ed. D. F. Parker & A. H. England), pp. 409-414. Dordrecht: Kluwer Academic.
19. Talbot, D. R. S. & Willis, J. R. 1996 Three-point bounds for the overall properties of a nonlinear composite dielectric. IMA J. Appl. Math. 57, 41-52.
20. Talbot, D. R. S. & Willis, J. R. 1997 Bounds of third order for the overall response of nonlinear composites. J. Mech. Phys. Solids 45, 87-111.
21. Talbot, D. R. S. & Willis, J. R. 1998 Upper and lower bounds for the overall response of an elastoplastic composite. Mech. Mater. 28, 1-8.
22. Toland, J. F. & Willis, J. R. 1989 Duality for families of natural variational principles in nonlinear electrostatics. SIAM J. Math. Analysis 20, 1283-1292.
23. Willis, J. R. 1986 Variational estimates for the overall response of an inhomogeneous nonlinear dielectric. In Homogenization and effective moduli of materials and media (ed. J. L. Eriksen, D. Kinderlehrer & J.-L. Lions), pp. 247-263. Springer.
24. Willis, J. R. 1989 The structure of overall constitutive relations for a class of nonlinear composites. IMA J. Appl. Math. 43, 231-242.