Translation and related bounds for the response of a nonlinear composite conductor

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

Volumn 455, Issue 1990, 1999, Pages 3687-3707

  Nesi, V ^a   Talbot, D R S ^a   Willis, J R ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Dielectric breakdown; Nonlinear composite; Translation method

Indexed keywords

EID: 0003158484     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0472     Document Type: Article

References (16)

1. Bhattacharya, K. & Kohn, R. V. 1997 Elastic energy minimization and the recoverable strain of polycrystalline shape-memory materials. Arch. Ration. Mech. Analysis 139, 99-180.
2. Dal Maso, G. 1993 An introduction to F-convergence. Boston, MA: Birkhäuser.
3. Hashin, Z. & Shtrikman, S. 1962 A variational approach to the theory of effective magnetic permeability of multiphase materials. J. Appl. Phys. 33, 3125-3131.
4. Jikov, V. V., Kozlov, S. M. & Oleinik, O. A. 1991 Homogenization of differential operators and integral functionals. Berlin: Springer.
5. Kohn, R. V. & Little, T. D. 1998 Some model problems of polycrystal plasticity with deficient basic crystals. SIAM Jl Appl. Math. 59, 172-197.
6. Kohn, R. V. & Milton, G. W. 1986 On bounding the effective conductivity of anisotropic composites. In Homogenization and effective moduli of materials and media. The IMA volumes in mathematics and its applications (ed. J. L. Ericksen, D. Kinderlehrer, R. Kohn & J.-L. Lions), vol. 1. New York: Springer.
7. Lurie, K. A. & Cherkaev, A. V. 1984 Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportions. Proc. R. Soc. Edinb. A 99, 71-87.
8. Marcellini, P. 1978 Periodic solutions and homogenization of nonlinear variational problems. Ann. Mat. Pura Appl. 117, 139-152.
9. Milton, G. W. 1990 On characterizing the set of possible effective tensors of composites: the variational method and the translation method. Commun. Pure Appl. Math. XLIII, 63-125.
10. Murat, F. & Tartar, L. 1985 Calcul des variations et homogénéisation. In Les methodes d'homogénéisation: theorie et applications en physique, pp. 319-369. Coll. de la Dir. des Etudes et Recherches d'Electricité de France, Eyrolles, Paris.
11. Nesi, V. 1995 Bounds on thé effective conductivity of 2D composites made of n 3 isotropic phases: the weighted translation method. Proc. R. Soc. Edinb. A125, 1219-1239.
12. Ponte Castaneda, P. 1991 The effective mechanical properties of nonlinear isotropic composites. J. Alech. Phys. Solids 39, 45-71.
13. Ponte Castaneda, P. 1992 A new variational principle and its application to nonlinear heterogeneous systems. SIAM Jl Appl Math. 52, 1321-1341.
14. Ponte Castaneda, P. & Willis, J. R. 1993 The effective behavior of nonlinear composites: a comparison between two methods. In Continuum models and discrete systems (CMDS7) (ed. K. H. Anthony & H.-H. Wagner), pp. 351-360. Aedermannsdorf: Trans. Tech.
15. Talbot, D. R. S. & Willis, J. R. 1985 Variational principles for inhomogeneous nonlinear media. IAM Jl Appl. Math. 35, 39-54.
16. Tartar, L. 1985 Estimations fines des coefficients homogénéises. In Ennio De Giorgi's Colloquium (ed. P. Kree). Research notes in Mathematics, vol. 125, pp. 168-175. London: Pitman.