Dielectric breakdown model for conductor-loaded and insulator-loaded composite materials

In the present work we generalize the dielectric breakdown model to describe dielectric breakdown patterns in both conductor-loaded and insulator-loaded composites. The present model is an extension of a previous one [F. Peruani , Phys. Rev. E 67, 066121 (2003)] presented by the authors to describe dielectric breakdown patterns in conductor-loaded composites. Particles are distributed at random in a matrix with a variable concentration p. The generalized model assigns different probabilities P(i,k-->i('),k(')) to breakdown channel formation according to particle characteristics. Dielectric breakdown patterns are characterized by their fractal dimension D and the parameters of the Weibull distribution. Studies are carried out as a function of the fraction of inhomogeneities, p.