We study the internal stress state of an ( \(N+\) 1)-phase composite in which the internal elastic rectangular inhomogeneity is bonded to an infinite elastic matrix through \(N-\) 1 arbitrary coatings. The matrix is subjected to uniform remote in-plane normal stresses. The N interfaces of the composite are described by an ( \(N+\) 1)-term conformal mapping function. All of the \(N-\) 1 coatings have a common shear modulus but have distinct Poisson’s ratios. We prove that the internal stress state within the rectangular inhomogeneity can still remain uniform and hydrostatic provided that the plane-strain bulk modulus of the rectangular inhomogeneity and the Poisson’s ratios of the outer \(N-\) 2 coatings are uniquely determined for given elastic properties of the innermost coating and the matrix and given geometry of the composite by solving a set of \(N-\) 1 coupled linear algebraic equations while the remote loading is required to satisfy a particular restriction.
