Bounds for the effective conductivity of a composite with an imperfect interface

The problem of bounding the effective conductivity of a two-phase composite with an imperfect interface is considered. The interface can be either highly conducting or resistive, and both the material properties and geometric arrangement of the phases can be anisotropic. The problem is formulated variationally and by choosing appropriate trial fields, new bounds are obtained in terms of upper and lower bounds on the effective conductivity of a composite with the same microgeometry in which the phases are perfectly bonded. The methodology also applies to composites with a nonlinear interface, and a particular example is described