The effect of the interface on the dc transport properties of nonlinear composite materials

Journal of Applied Physics

Volumn 86, Issue 3, 1999, Pages 1480-1487

  Lipton, Robert ^a   Talbot, D R S ^b  

^a United States   (United States)

^b Faculty of Health and Life Sciences   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE MATERIALS; CRITICAL CURRENTS; CURRENT DENSITY; ELECTRIC CONTACTS; ELECTRIC FIELDS; ELECTRIC POTENTIAL; ELECTRIC PROPERTIES; ELECTRON TRANSPORT PROPERTIES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PHASE INTERFACES; VARIATIONAL TECHNIQUES;

POISSON EQUATION;

ELECTRIC CONDUCTORS;

EID: 0032621307     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.370917     Document Type: Article

References (25)

1. R. Eizinger, Annu. Rev. Mater. Sci. 17, 299 (1987).
2. G. A. Niklasson, Physica A 157, 482 (1989).
3. C. C. Liang, J. Electrochem. Soc. 120, 1289 (1973).
4. K. Shahi and J. B. Wagner, J. Electrochem. Soc. 128, 6 (1981).
5. A. Bundle, W. Deterich, and E. Roman, Phys. Rev. Lett. 55, 5 (1985).
6. D. L. Johnson, J. Koplik, and L. M. Schwartz, Phys. Rev. Lett. 57, 2564 (1986).
7. E. J. Garboczi, D. P. Bentz, and L. M. Schwartz, Journal of Advanced Cement-Based Materials 2, 169 (1995).
8. L. M. Schwartz, E. J. Garboczi, and D. P. Bentz, J. Appl. Phys. 78, 5898 (1995).
9. H. Pham Huy and E. Sanchez-Palencia, J. Math. Anal. Appl. 47, 284 (1974).
10. R. Holm, Electric Contacts (Springer, Berlin, 1967).
11. K. W. Garret and H. M. Rosenberg, J. Phys. D 7, 1247 (1974).
12. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
13. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
14. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
15. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
16. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
17. Macroscopic energies without the surface energy term were proposed in the classic work of R. Hill, J. Mech. Phys. Solids 11, 357 (1963); the general structure, starting from a variational formulation, has been examined in J. R. Willis, IMA J. Appl. Math. 43, 231 (1989); J. F. Toland and J. R. Willis, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 1283 (1989). Bounding the properties of nonlinear composites was initiated by J. R. Willis, J. Appl. Mech. 50, 1202 (1983); J. R. Willis, in Homogenization and Effective Properties of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. L. Lions (Springer, New York, 1986), pp. 245-263; D. R. S. Talbot and J. R. Willis, IMA J. Appl. Math. 35, 39 (1985).
18. In the absence of a surface energy term, P. Ponte Castañeda and J. R. Willis, Proc. R. Soc. London, Ser. A 416, 217 (1998) proved that the overall energy of a nonlinear viscous composite is convex. Application of similar arguments shows that the overall macroscopic energies W̃(Ē) and C̃(Ē) are convex.
19. R. Lipton, Institute for Mathematics and Its Applications Preprint Series, 1995 (unpublished), Preprint Number 1339; SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 57, 347 (1997).
20. R. Lipton, Institute for Mathematics and Its Applications Preprint Series, 1995 (unpublished), Preprint Number 1339; SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 57, 347 (1997).
21. S. Torquato and M. D. Rintoul, Phys. Rev. Lett. 75, 4067 (1995).
22. R. Lipton and B. Vernescu, Proc. R. Soc. London, Ser. A 452, 325 (1996).
23. We mention, in the context of linear two-phase composites, the recent and relevent work of Y. Benveniste and T. Miloh, J. Appl. Phys. (submitted) Motivated by the results given in Lipton and Vernescu Ref. 16 and in Lipton Ref. 14, they have developed a method for choosing a nonconstant interfacial conductivity so that the field external to the inclusion remains undisturbed when linear boundary conditions for the electric potential are given. Their results apply to a large class of inclusion shapes.
24. R. Lipton J. Mech. Phys. Solids 45, 361 (1997).
25. Z. Hashin, J. Mech. Phys. Solids 40, 767 (1992).