In the study of heterogeneous materials, the preponderance
of work has been devoted to finding the effective transport,
electromechanical, and mechanical properties of the
material,1 which amounts to knowing only the first moment
of the local field. When composites are subjected to constant
applied fields, the associated local fields exhibit strong spatial
fluctuations. The analysis and evaluation of the distribution
of the local field has received far less attention. Nonetheless,
the distribution of the local field is of great
fundamental and practical importance in understanding many
crucial material properties such as breakdown phenomenon2
and the nonlinear behavior of composites.3 Much of the work
on field distributions has been carried out for lattice models
using numerical4,5 and perturbation methods.6 Recently, continuum
models have been also addressed using numerical
techniques.7
In the study of heterogeneous materials, the preponderanceof work has been devoted to finding the effective transport,electromechanical, and mechanical properties of thematerial,1 which amounts to knowing only the first momentof the local field. When composites are subjected to constantapplied fields, the associated local fields exhibit strong spatialfluctuations. The analysis and evaluation of the distributionof the local field has received far less attention. Nonetheless,the distribution of the local field is of greatfundamental and practical importance in understanding manycrucial material properties such as breakdown phenomenon2and the nonlinear behavior of composites.3 Much of the workon field distributions has been carried out for lattice modelsusing numerical4,5 and perturbation methods.6 Recently, continuummodels have been also addressed using numericaltechniques.7
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