Three-phase piezoelectric inclusions of arbitrary shape with internal uniform electroelastic field

We investigate the internal electroelastic field within a three-phase piezoelectric inclusion of arbitrary shape when the piezoelectric matrix is subjected to remote uniform electroelastic loadings. It is observed that in the presence of the intermediate interphase layer, the internal electroelastic field within an inclusion of non-elliptical shape can be conditionally or unconditionally uniform. In order to ensure that the internal electroelastic field is conditionally uniform, the thickness of the interphase layer should be properly designed for given electroelastic constants of the three-phase piezoelectric composite, and the remote uniform electric displacements should be dependent on the applied remote uniform stresses. To ensure an unconditionally uniform internal electroelastic field, the electroelastic constants of the interphase layer can be uniquely determined by given thickness of the interphase layer and given electroelastic constants of both the internal inclusion and the surrounding matrix. Interestingly, our analysis indicates that even in the absence of the interphase layer, the internal electroelastic field within a piezoelectric inclusion of arbitrary shape can still be conditionally uniform if the electroelastic constants of the two-phase composite satisfy a restriction.