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

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.