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IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):39-52; doi:10.1093/imamat/hxh060
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IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

General solution in terms of complex potentials for incremental antiplane states in prestressed and prepolarized piezoelectric crystals: application to Mode III fracture propagation*

Eduard-Marius Craciun1, Eveline Baesu2 § and Eugen Soós3 ¶

1 Faculty of Mathematics and Informatics, Ovidius University, Constanta, Romania, 2 Department of Engineering Mechanics, University of Nebraska, Lincoln, NE, 68588, USA, 3 Institute of Mathematics of the Romanian Academy, Bucharest, Romania  §

The problem considered is the antiplane deformation in prestressed and prepolarized piezoelectric crystals in equilibrium. The representation of the general solution is derived in terms of complex potentials for all piezoelectric crystal classes in which an antiplane state is possible. This generalizes earlier results obtained in respect of a specific crystal class. The general formulae are specialized to find the antiplane state generated by a Mode-III crack.

Keywords: antiplane; fracture; initial fields; prepolarized; prestressed; piezoelectricity.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday

§ Corresponding author.

Deceased.


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