On the necessity of including electrical conductivity in the description of piezoelectric fracture in real materials

Because no real material is a perfect insulator, but has some small electrical conductivity, under static circumstances the piezoelectric equations are not applicable to any real material and, hence, have no physical 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.