Three-point bounds for the overall properties of a nonlinear composite dielectric

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 57, Issue 1, 1996, Pages 41-52

  Talbot, D R S ^a   Willis, J R ^b  

^a Faculty of Engineering and Computing   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE MATERIALS; DIELECTRIC MATERIALS; GEOMETRY; OSCILLATIONS; VARIATIONAL TECHNIQUES;

BOUNDED MEAN OSCILLATION; COMPARISON MEDIUM; ENERGY DENSITY FUNCTION; MICROGEOMETRY; NONLINEAR COMPOSITE DIELECTRIC; THREE POINT BOUNDS;

NONLINEAR EQUATIONS;

EID: 0030206382     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/57.1.41     Document Type: Article

References (16)

1. BERAN, M. J., 1965. Use of the variational approach to determine bounds for the effective permittivity of a random medium. Nuovo Cim. 38, 771-82.
2. HASHIN, Z., & SHTRIKMAN, S., 1962. A variational approach to the theory of the elastic behaviour of polycrystals. J. Mech. Phys. Solids 10, 343-52.
3. HASHIN, Z., & SHTRIKMAN, S., 1963. A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127-40.
4. JOHN, F., & NIRENBERG, L., 1961. On functions of bounded mean oscillation. Commun. Pure Appl. Math. 14, 415-26.
5. MILTON, G. W., 1981. Bounds on the electromagnetic, elastic, and other properties of two-component composites. Phys. Rev. Lett. 46, 542-5.
6. PONTE CASTAÑEDA, P., 1991. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39, 45-71.
7. PONTE CASTAÑEDA, P., 1992. Bounds and estimates for the properties of nonlinear heterogeneous systems. Phil. Trans. R. Soc. Lond. A 340, 531-67.
8. PONTE CASTAÑEDA, P., & WILLIS, J. R., 1993. The effective behaviour of nonlinear composites: A comparison between methods. In: Continuum Models of Discrete Systems CMDS7 (K.-H. Anthony and H.-J. Wagner, eds.), pp. 351-60. Trans Tech Publications.
9. TALBOT, D. R. S., & WILLIS, J. R., 1985. Variational principles for inhomogeneous nonlinear media. IMA J. Appl. Math. 35, 39-54.
10. TALBOT, D. R. S., & WILLIS, J. R., 1992. Some simple explicit bounds for the overall behaviour of nonlinear composites. Int. J. Solids Structures 29, 1981-7.
11. TALBOT, D. R. S., & WILLIS, J. R., 1994a. Upper and lower bounds for the overall properties of a nonlinear composite dielectric. I. Random microgeometry. Proc. R. Soc. Lond. A 447, 365-84.
12. TALBOT, D. R. S., & WILLIS, J. R., 1994b. Upper and lower bounds for the overall properties of a nonlinear composite dielectric. II. Periodic microgeometry. Proc. R. Soc. Lond. A 447, 385-96.
13. 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 (D. F. Parker & A. H. England, eds.), pp. 409-14. Kluwer Academic.
14. WILLIS, J. R., 1983. The overall elastic response of composite materials. J. Appl. Mech. 50, 1202-9.
15. WILLIS, J. R., 1986. Variational estimates for the overall response of an inhomogeneous nonlinear dielectric. In: Homogenization and Effective Moduli of Materials and Media (J. L. Ericksen, D. Kinderlehrer, R. V. Kohn, & J.-L. Lions, eds.), pp. 247-63. New York: Springer-Verlag.
16. WILLIS, J. R., 1991. On methods for bounding the overall properties of nonlinear composites. J. Mech. Phys. Solids 39, 73-86.