Complex variable solution for mode-III quadratically varying PS model in piezoelectric media

Complex variable technique and extended Stroh formalism approach are applied to develop the closed-form solutions for mode-III quadratically varying polarization saturation (PS) model in an infinite piezoelectric media. A semipermeable centre crack problem is considered for study under the influence of out of plane far-field mechanical loading and in-plane electrical displacement loading. Similar to PS model, the electrical yielding zones or saturated zones are considered just infront of the crack-tips in the form of a strip. But in place of constant PS condition imposed on yielding zones, the quadratically varying PS condition is considered for study. Mathematically, this problem reduces into simultaneous non-homogeneous Riemann-Hilbert problems which are solved by finding the solutions of involved singular integrals. Hence, some standard fracture parameters are derived in explicit forms such as saturated zone lengths, crack sliding displacement, crack potential drop and local stress intensity factor. Also, the comparative studies for quadratically varying PS model and PS model are presented graphically.