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We investigate the problem of planar conductivity inclusion with imperfectinterface conditions. We assume that the inclusion is simply connected. Thepresence of the inclusion causes a perturbation in the incident backgroundfield. This perturbation admits a multipole expansion of which coefficients wecall the generalized polarization tensors (GPTs), extending the previousterminology for inclusions with perfect interfaces. We derive explicit matrixexpressions for the GPTs in terms of the incident field, material parameters,and geometry of the inclusion. As an application, we construct GPT-vanishingstructures of general shape that result in negligible perturbations for alluniform incident fields. The structure consists of a simply connected core withan imperfect interface. We provide numerical examples of GPT-vanishingstructures obtained by our proposed scheme.

Construction of inclusions with vanishing generalized polarization tensors by imperfect interfaces