When an electric field is applied to an inhomogeneous material, the resulting current and power densities may have strong spatial variations. Areas where the dissipated Joule heat is much higher than in neighboring regions are called hot spots. It is natural to assume that the conductivity in these spots is altered as a result of the large Joule heat dissipation . One may ask where hot spots occur in the material, and how they will develop when the material properties change. We use a resistor network model to study the occurrence and evolution of hot spots in inhomogeneous materials, which are two dimensional, two phase, and statistically isotropic. We show that the stability to resistive breakdown of such materials depends upon the concentration of hot spots. When the spots are concentrated, the interaction between the spots makes the evolution of the material rapid. The material is then considered to be unstable to resistive breakdown. The development is in general faster when the spots are made well conducting than when they are made poorly conducting.

• Received 21 March 1986

DOI:https://doi.org/10.1103/PhysRevB.35.352