Using the Stroh sextic formalism, we study the problem of an anisotropic elastic
inhomogeneous elliptical inclusion undergoing uniform eigenstrains embedded in an
infinite anisotropic elastic matrix. The inhomogeneous inclusion and the matrix have
separate elastic properties. A real-form solution of the internal uniform elastic
field characterizing stresses, total strains and rigid-body rotation within the
inhomogeneous elliptical inclusion is obtained in terms of the fundamental elasticity
matrix for the elliptical inclusion and the Barnett–Lothe tensors for the matrix. Also
obtained in real-form are the constant fourth-rank Eshelby’s tensor inside the
elliptical inclusion, the hoop stress vectors and hoop stresses along the elliptical
interface on both the matrix and inclusion sides, as well as the strain energy per unit
height of the composite.
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