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The usage of materials is the backbone of engineering practice. Yet, advances in materials have stagnated due to overly conservative approaches, trial-and-error testing, and long qualification times. Material modeling offers tremendous opportunities to address these issues. This class offers advanced modeling strategies at the intersection of mechanics and materials science for both polycrystalline and composite materials. The course topics are defined as follows: First, advanced micromechanics analysis of modern engineering materials with emphasis on relating elastic microstructural phenomena to the mechanics of material behavior, via the Eshelby inclusion problem and its application to fiber reinforced composites. Second, classical plasticity is summarized via phenomenological and mathematical formulation of the constitutive laws, including yielding, yield surface; von Mises, Tresca yield criteria; Drucker's stability postulate; strain or work hardening, normality rule, perfect plasticity, and stress-strain law. Third, crystal plasticity is discussed, specifically physical and mathematical foundation for plasticity in crystalline materials, with a detailed description of the Bishop and Hill implementation of the Taylor model for deformation of polycrystals. Lastly, concepts of dislocations leading to strengthening mechanisms in metals are discussed: (i) by studying the anisotropy of material and elastoplastic properties at crystal level, microstructural basis for deformation in metals, polymers, and ceramics and (ii) failure mechanisms and toughening in metals, with primary emphasis on work/strain hardening, solid solution hardening, precipitate hardening, and grain boundaries. The course will be comprised of three projects, where the student chooses the topic of the third and final project. Prerequisite: AAE 55300 or equivalent.

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