Inclusions, Fibers, and Fractures: Micromechanics of Heterogenous Materials and Composites - 535.733

This course introduces core concepts in the micromechanics of heterogeneous materials and composites. Micromechanics is the study of the relationship between macroscopic material behavior and properties of its constituents. The course begins with fundamental concepts in mechanics such as tensor and matrix algebra, stress and strain, balance laws, isotropic and anisotropic linear elasticity, and boundary value problems. The course then focuses heavily on micromechanics topics including representative volume elements, Voigt and Reuss bounds, Eshelby’s equivalent inclusion method, dilute distribution and self-consistent methods, Hashin-Shtrikman bounds, Mori-Tanaka theory, and microstructure characterization and generation. Applications of these topics are provided for particulate and matrix-based composites, fiber-reinforced composites (e.g., laminates), materials with microcracks, and materials with periodic microstructures. Students will leave the course able to make property predictions for a broad range of heterogeneous materials. Prerequisite: A prior course on the mechanics of materials at the advanced undergraduate level or above.