On Hashin-Shtrikman-type bounds for nonlinear conductors

For linear composite conductors, it is known that the celebrated Hashin-Shtrikman bounds can be recovered by the translation method. We investigate whether the same conclusion extends to nonlinear composites in two dimensions. To that purpose, we consider two-phase composites with perfectly conducting inclusions. In that case, explicit expressions of the various bounds considered can be obtained. The bounds provided by the translation method are compared with the nonlinear Hashin-Shtrikman-type bounds delivered by the Talbot-Willis (1985) [2] and the Ponte Castañeda (1991) [3] procedures.