Using the Stroh sextic formalism, we analyze the generalized plane strain
problem associated with an elliptical incompressible liquid inclusion in an
infinite anisotropic elastic matrix subjected to a uniform loading at infinity. A
real-form solution of the internal uniform hydrostatic stresses, strains and
rigid body rotation within the liquid inclusion is obtained in terms of the
Barnett–Lothe tensors and the fundamental elasticity matrix for the surrounding
matrix. Real-form expressions for the hoop stress vector and hoop stress
along the elliptical interface on the matrix side are also obtained. Explicit
results are derived for an orthotropic elastic matrix with isotropy as a special
case.