Abstract
We consider a composite material containing an elastic elliptic inhomogeneity which is assumed to be perfectly bonded to a surrounding matrix of similar elastic material. In fact, both the inhomogeneity and the matrix belong to the same class of compressible hyperelastic materials of harmonic-type but each has its own distinct material properties. We consider finite plane deformations of the inhomogeneity-matrix system and obtain the complete solution when the system is subjected to classes of nonuniform remote (Piola) stress characterized by stress functions described by general polynomials of order n ≥ 1 in the corresponding complex variable z used to describe the matrix.
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