Abstract
I start with the theory of small deformations and fields superposed on large static deformations and fields, given by Eringen and Maugin ( Electrodynamics of Continua, Vol. 1, Foundations and Solid Media. Springer, New York (1990); Section 7.14). The considered body is an elastic dielectric and the quasi-static approximation is used. In the paper are given conditions in which the stability of the equilibrium state of a prestressed piezoelectric crystal is assured. Also established are conditions in which non-uniqueness, internal instability or resonance can occur. Finally, results are presented concerning the asymptotic behavior of the incremental fields near the tips of a crack in a prestressed piezoelectric crystal. It is proven that the stress singularity is the same as in an initial stress free body. The analysis is based on the use of complex potentials in order to represent the incremental fields.
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