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A three-phase anisotropic elastic elliptical inhomogeneity with internal linear stress and strain distributions

### Xu Wang and Peter Schiavone

Vol. 17 (2022), No. 5, 489–501
##### Abstract

We use the Stroh sextic formalism to examine the internal elastic field of stresses and strains inside an anisotropic elastic elliptical inhomogeneity which is bonded to an infinite anisotropic elastic matrix through an intermediate isotropic elastic interphase layer with two confocal elliptical interfaces when the matrix is subjected to nonuniform remote stresses and strains assumed to be linear functions of the two in-plane coordinates. We prove that for given geometric and material parameters characterizing the composite, linear internal stress and strain distributions inside the elliptical inhomogeneity remain possible when two specific conditions are satisfied for the remote loading. In addition, the internal linear elastic field inside the elliptical inhomogeneity is determined in real-form in terms of the two $6×6$ fundamental elasticity matrices for the inhomogeneity and the matrix and the three Barnett–Lothe tensors for the matrix.

##### Keywords
three-phase elliptical inhomogeneity, anisotropic elasticity, isotropic elasticity, Stroh sextic formalism, real-form solution, nonuniform loading