Abstract
Exact closed-form solutions are obtained for the stress and induction field of a spheroidal piezo-electric inclusion in an infinite piezo-electric matrix subjected to spatially homogeneous mechanical and electrical loadings far away from the inclusion. Three types of loading are considered: axisymmetric, in-plane and out-of-plane shear. A limiting case of this solution allows us to determine the stress and induction field of a penny-shaped crack in a piezo-electric material. Closed-form expressions for the stress and induction intensity factors of a penny-shaped crack are obtained.
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