Variational methods, bounds, and size effects for composites with highly conducting interface

摘要

New variational principles are developed for the effective conductivity tensor for anisotropic two-phase electric conductors. Here the interface between phases is assumed to be highly conducting. Extra geometric information is encoded into the principles through the solution operators of simpler transport problems. These operators can be expressed as gradients of simple layer potentials with densities supported on phase interfaces or in terms of simple Dirichlet problems inside each phase region.