Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution

Abstract In the present work, solutions are recapitulated according to theory of elasticity for deformations an adhesive spherical inhomogeneity in infinite matrix under remote uniform axial and axial-symmetrical radial tension. Stress fields at interface provided, too. It is shown that sphere deformed a spheroid any loading cases considered. Due axial-symmetric setup problem, deformation fully described by two displacement values line segments on principal axes spheroid. The displacements depend applied load traction inhomogeneity-matrix interface. For combination stiffness, condition compatibility yields system linear equations with magnitudes tractions as unknowns. Thus, problem reduced formulation solving twofold statically indetermined structure. solved exact solution general differing stiffness terms Young’s moduli Poisson’s ratios inclusion presented.