Complex variable solution for mode-III linearly varying polarization saturation model in piezoelectric media

Abstract

Analytical solution for mode-III linearly varying polarization saturation (PS) model in semipermeable piezoelectric me- dia is presented. An infinite arbitrary polarized piezoelectric domain weakened by a center crack is considered for the study based on linearly varying polarization saturation model. For the analysis, an out of plane mechanical and in-plane electric displacement loadings are applied on the boundaries of the infinite domain. After mathematical formulation using complex variable and ex- tended Stroh's formalism approach, the problem is reduced into simultaneous non-homogeneous Riemann-Hilbert (R-H) problems in terms of complex variable functions. Explicit solutions for fracture parameters such as saturated zone length, crack sliding dis- placement (CSD), crack opening potential (COP), local stress intensity factor (LSIF), electric displacement intensity factor (EDIF) and normalize energy release rate (G∗) are derived after obtaining the solution for the R-H problems.