Hf. Tiersten et Tl. Sham, ON THE NECESSITY OF INCLUDING ELECTRICAL-CONDUCTIVITY IN THE DESCRIPTION OF PIEZOELECTRIC FRACTURE IN REAL MATERIALS, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 45(1), 1998, pp. 1-3
Because no real material is a perfect insulator, but has some small el
ectrical conductivity, under static circumstances the piezoelectric eq
uations are not applicable to any real material and, hence, have no ph
ysical significance. On account of the existence of real current, when
the time-dependence is sufficiently slow, the zero charge equation of
electrostatics does not apply and must be replaced by the equation of
the continuity of electric charge.