Electromagnetic properties of multiphase dielectrics

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Recently, applications driven by microtechnology have emerged that require materials with tailored electromagnetic properties for successful design. These properties are achieved by combining a moldable base matrix with particles selected for their dielectric characteristics. Analyzing such materials often involves simulating both macroscopic and microscopic electromagnetic responses, along with their coupled thermal responses, which are crucial for identifying potential failures in "hot spots." This process requires stress analysis, as these interactions can trigger degradatory chemical processes, necessitating models for these effects as well. The main objective of this work is to provide foundational models and numerical solution strategies for analyzing the coupled responses of these materials through direct simulation on standard laptop or desktop equipment. The content includes: (1) Foundations of Maxwell's equations, (2) Basic homogenization theory, (3) Coupled systems (electromagnetic, thermal, mechanical, and chemical), (4) Numerical methods, and (5) An introduction to select biological problems. This monograph serves as a research resource suitable for upper-division undergraduate or first-year graduate courses aimed at students in applied sciences, mechanics, and mathematics interested in particulate material analysis.