Electromagnetic Properties of Multiphase Dielectrics

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Recently, several applications driven by microtechnology have emerged, necessitating materials with tailored electromagnetic (dielectric) properties for effective design. These tailored properties result from combining a moldable base matrix with particles selected to achieve desired effective characteristics. Analyzing such materials often requires simulating both macroscopic and microscopic electromagnetic responses, along with their coupled thermal responses, which are crucial for identifying potential failures in "hot spots." This analysis also demands stress evaluations. Additionally, since these processes can trigger degradatory chemical reactions, incorporating models for these processes is often essential. A central goal of this work is to provide foundational models and numerical solution strategies for analyzing the coupled responses of these materials through direct simulation using 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 text serves as a research monograph suitable for upper-division undergraduate or first-year graduate courses aimed at students in applied sciences, mechanics, and mathematics interested in the analysis of particulate materials.