We study the state of stress inside an elliptical elastic inhomogeneity which is bonded
to an infinite matrix through an intermediate confocal interphase layer undergoing
uniform in-plane eigenstrains. A simple condition is found that ensures that the
internal stress state is uniform but in general nonhydrostatic. This condition can be
considered as a restriction on the imposed eigenstrains for given geometric and
material parameters of the three-phase composite. Once this condition is met,
the corresponding stress distributions are obtained in elementary form. In
particular, the mean stress is found to be uniform within the interphase
layer.
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