Closed-form solution for the composite sphere subject to quadratic eigenstrains with radial symmetry

This paper contains the closed-form solution for the problem of a biphase sphere, in the presence of a polar symmetric eigenstrain field, represented by a quadratic polynomial in each phase. In general, the determination of the residual stress field generated in composite structures during service, as well as during deposition and forming procedures, is essential for failure analysis and for an effective design of these procedures. In particular, the present problem is relevant in the analysis of glass-fiber-reinforced polymers with an inhomogeneous matrix moisture absorption, and of plasma-sprayed ceramic coatings on metallic substrates.