XFEM for semipermeable crack in piezoelectric material with Maxwell stress

In this work, extended finite element method (XFEM) is implemented to model the semipermeable cracks in the piezoelectric material with Maxwell stresses. This Maxwell stress is induced due to the presence of an electric field at the crack faces and boundary of the piezoelectric material. To model the semipermeable crack with Maxwell stress, the crack tip is enriched with six-fold enrichment functions. The electro-mechanical interaction integral is modified and implemented for several crack configurations to compute the stress intensity factor (SIF). The accuracy of the XFEM-based semipermeable crack model in the presence of Maxwell stresses is demonstrated by validating with the analytical solution. The effects of crack length, far-field loading, Maxwell stress, and poling direction are investigated on the normalized SIF.

Automated summary

In this study, the extended finite element method (XFEM) is used to model semipermeable cracks in piezoelectric materials subjected to Maxwell stresses induced by an electric field. The crack tip is enriched with six-fold enrichment functions to accurately represent the semipermeable crack with Maxwell stress. The electro-mechanical interaction integral is modified and implemented for different crack configurations to calculate the stress intensity factor (SIF). The accuracy of the XFEM-based semipermeable crack model is demonstrated through validation with analytical solutions and the effects of various factors on the normalized SIF are investigated.