A Model Problem: Dielectrics Undergoing Multifield Processes
An important issue that this monograph addresses is the modeling and simulation of strongly coupled electromagnetic and thermodynamic fields that arise in particulate-doped dielectrics using an adaptive staggered FDTD (Finite Difference Time Domain) method. Of particular interest is to provide a straightforward modular approach to finding the effective dielectric (electromagnetic) response of a material, incorporating thermal effects arising from Joule heating which alter the pointwise dielectric properties such as the electric permittivity, magnetic permeability, and electric conductivity. This is important for “thermal (damage) management” of materials used in electromagnetic applications. Because multiple field coupling is present, a staggered, temporally-adaptive scheme is developed to resolve the internal microstructural electric, magnetic and thermal fields, accounting for the simultaneous pointwise changes in the material properties. Numerical examples are provided to illustrate the approach. Extensions to coupled chemical and mechanical fields are also provided. Here, we follow an approach found in Zohdi .
KeywordsRelative Permeability Model Problem Representative Volume Element Magnetic Permeability Joule Heating
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