Homogenized Maxwell’s Equations; a Model for Varistor Ceramics
نویسندگان
چکیده
A model for a semiconducting ceramic material used in devices to protect electrical equipment against overvoltages is presented. The fine structure in the material induces highly oscillating coefficients in the Maxwell equation. Maxwell equations are homogenized to obtain a coupled system. The fine scales in the model yield a local problem coupled with the homogenized Maxwell’s equations. In the electrostatic case upper and lower bounds are obtained for the effective conductivity in the varistor. These two bounds are associated with two types of failures in varistor ceramics. The upper bound corresponds two thermal heating and the puncture failure due to localization of strong currents. The lower bound corresponds to fracturing of the varistor, due to charge build up at the grain boundaries resulting in stress caused by the piezoelectric property of the varistor.
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