Mode I fracture analysis of a piezoelectric strip based on real fundamental solutions

In existing papers, mode I crack problems of piezoelectric ceramics are generally solved in complex domain because of the complex fundamental solutions of in-plane piezoelectric governing equations. In fact, these problems can alternatively be analyzed in real number field by recasting the solutions in real form instead. The main purpose of the present work is to develop such real fundamental solutions by detailed eigenvalue and eigenvector analyses. As an example of application, the widely studied fracture problem of a piezoelectric strip with a center-situated crack under mode I loading condition is then revisited based on the real fundamental solutions. Mixed boundary value conditions of the crack are transformed into Cauchy singular integral equations, which are then solved numerically to get fracture parameters including the energy release rate and intensity factors. Convergence behaviors of the kernel functions are surveyed. Theoretical derivation and computation are validated by the exact solution in a special case. The effect of a combined geometrical parameter on the crack is also investigated.