CIRCULAR INCLUSION PROBLEM IN ANTIPLANE PIEZOELECTRICITY

A circular piezoelectric inclusion embedded in an infinite piezoelectric matrix is analysed in the framework of linear piezoelectricity. A closed-form solution is obtained for the case of a far-field antiplane mechanical load and a far-field inplane electrical load. It is shown that in modeling cavities, imposing an impermeable boundary condition is a good approximation provided that the piezoelectric material has high dielectric constant and strong electro-elastic coupling. Stress and electric field concentrations are also studied. It is shown that a high electric field can be induced in the inclusion under a mechanical load when the matrix and the inclusion are poled in the opposite directions. The path-independent M-integral of elastostatics. generalized to take piezoelectric effect into account, is used to study the energetics of a self-similarly expanding piezoelectric inclusion.