Arbitrarily loaded circular crack in a piezoelectric solid of the symmetry class 6

Abstract

The paper focuses on the problem of evaluating analytically the electric and elastic fields in a piezoelectric material of the symmetry class 6 containing a penny-shaped crack loaded by both normal and tangential tractions and by electric charges. A solution of this kind has been developed for symmetry class 6 mm by Karapetian et al. (Arch. Appl. Mech. 70: 201–229, 2000). To the best of our knowledge, it has never been derived for a material of class 6. The research is motivated by needs in evaluation of damage accumulated in bone tissue, which possesses such a symmetry. The problem is solved by the method of potential functions developed by Fabrikant (Applications of Potential Theory in Mechanics: Selection of New Results. Kluwer, Dordrecht,1989). Closed form solutions are obtained for the full electric and elastic fields. The approach is first verified by comparison with the results of Karapetian et al. (Arch. Appl. Mech. 70: 201–229, 2000) for the limiting case of piezoceramic of class 6 mm (PZT-6B) and then applied to calculation of the electroelastic fields associated with a penny-shaped crack in cortical bone (material of class 6).