A circular inhomogeneity subjected to non-uniform remote loading in finite plane elastostatics

We consider an inhomogeneity–matrix system from a particular class of compressible hyperelastic materials of harmonic-type undergoing finite plane deformations. We obtain the complete solution for a perfectly bonded circular inhomogeneity when the system is subjected to non-uniform remote stress characterized by stress functions described by general polynomials of order n⩾1n⩾1 in the corresponding complex-variable zz used to describe the matrix.