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).

本文关注的问题是分析性地评估对称类别6的压电材料中的电场和弹性场，该压电材料包含一个由法向和切向牵引力以及电荷加载的便士形裂纹。Karapetian等人针对对称性等级为6 mm的这种类型的解决方案进行了开发。（Arch。Appl。Mech。70：201-229，2000）。据我们所知，它从未衍生出第6类材料。该研究的动机是需要评估具有这种对称性的骨组织中累积的损伤。通过Fabrikant开发的势函数方法解决了该问题（势理论在力学中的应用：新结果的选择。Kluwer，Dordrecht，1989）。对于完整的电场和弹性场，可以获得封闭形式的解决方案。首先通过与Karapetian等人的结果进行比较来验证该方法。（Arch。Appl。Mech。70：201–229，2000）用于6mm类压电陶瓷的极限情况（PZT-6B），然后应用于计算与皮骨中的一分钱形裂缝相关的电弹性场（第6类的材料）。