Phase field model for electrically induced damage using microforce theory

In this paper, we present a consistent derivation of the phase field model for electrically induced damage. The derivation is based on Gurtin’s microstress and microforce theory and the Coleman–Noll procedure. The resulting model accounts for Ohmic currents, includes charge conservation law and allows for finite electric permittivity and conductivity distribution in the medium. Special attention is devoted to the case when the damaged region is a codimension-two object, i.e., a curve in three dimensions. It is shown that in this case the free energy of the model necessarily includes a high-order term, which ensures the well-posedness of the problem. A special problem setting is proposed to account for the prescribed charge distribution. Local features of the phase field distribution are illustrated with one-dimensional axisymmetric numerical experiments.