Electrical and Dielectric Breakdown: The Discrete Approach

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 23)


Discrete models of electrical and dielectric breakdown of composite solids have provided very useful insights into the properties of these important phenomena, by demonstrating the significant role that defects of heterogeneities play in them. In particular, they have provided the important prediction that the statistics of these breakdown phenomena depend critically on the volume fraction of the defects or the broadness of the distribution of the heterogeneities. If the volume fraction of the defects is low, then, the probability distribution of the failure fields (voltage or current) is of Gumble type, rather than the classical Weibull distribution. Moreover, the discrete models have enabled us to obtain important predictions for the effect of sample size on breakdown properties of heterogeneous materials.


Percolation Threshold Discrete Model Linear Size Electrical Breakdown Effective Conductivity 
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© Springer-Verlag New York, Inc. 2003

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