Design of neutral elastic inhomogeneities in plane elasticity in the case of non-uniform loading

We use the concept of imperfect interface to design a (stress) neutral elastic inhomogeneity in the case when the inhomogeneity-matrix system is subjected to plane deformations. Of particular interest is the fact that the prescribed stress field inside the matrix is assumed to be non-uniform. Using complex variable techniques, we derive conditions on the functions describing the (imperfect) interface to ensure neutrality in several cases of practical interest.