In this paper we present an analytical solution to calculate the stress concentrations around an elliptical void in a piezoelectric medium subjected to electrical loading. We show that the stress concentrations can be eliminated if the material properties satisfy a certain mathematical relation. While a trivial solution exists for this problem, we demonstrate that other families of solutions exist (optimal) to minimize/eliminate the stresses. The optimal families are shown to be independent of geometry and therefore are universally applicable to a specific material system. The optimal families do not limit the deformation profile and represent admissible solutions to the problem. Numerical studies demonstrate that the entire stress field in the medium vanishes and not just at the critical locations as dictated by the mathematics. Finally, we numerically demonstrate that the optimal properties are also applicable to the crack problem.

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