The limited electrically permeable crack model in linear piezoelasticity

The problem of a crack in a piezoelectric material under electromechanical loading is considered. The exact solution, obtained in this work, includes the unknown a priori normal component of the electric displacement inside the crack. Several different physical assumptions associated with limited electric permeability of the crack are utilized to determine those unknown electric fluxes through the crack boundaries. Analytical formulae for the stress and electric intensity factors are derived. The effects of electric boundary conditions (limited permeability) at the crack surface on the basic parameters of fracture mechanics are analyzed and some features of the solution are discussed. If the permeability of the medium inside the crack tends to zero or is very large the extreme results i.e. impermeable or permeable crack solution are obtained.