A penny-shaped crack in piezoelectrics: resolved

This paper reconsiders the problem of a penny-shaped crack in a piezoelectric medium under uniform mechanical as well as electric loadings applied at infinity (mode I). The analysis is based on the general solution of three-dimensional piezoelasticity, which is represented by four quasi-harmonic displacement functions. It is shown that these harmonics can be expressed in terms of two potentials of a simple layer. By using the previous results in potential theory, exact solution of the mode I crack is obtained. In particular, the solution is complete and in terms of elementary functions.