Introduction and review of mathematical principles and continuum mechanics. Homogenization methods for heterogeneous materials- averaging and mean-field theories, Eshelby and Mori-Tanaka approaches, self-consistent methods, cell methods, effective and apparent properties for inelastic solids, computational homogenization for highly nonlinear solids. Plasticity and microplasticity in metals - macroscale plasticity, crystal plasticity, scale size effects: strain gradient plasticity, discrete dislocation plasticity. Micromechanics of polymers and composites. Micromechanics of cellular, granular and porous materials. Multi-phase microstructures- discrete & lattice models: fundamentals, elasticity and fracture, martensitic phase transformations, microstructure evolution. Mechanics of nanostructures e.g., carbon nanotubes, graphene, polymer nanocomposites, DNA, nanoscale metallic multilayers. Practical application of micromechanics- micromechanics of manufacturing process, micromechanics of electronics systems. Discrete Dislocation Dynamics, Molecular Dynamics, Monte Carlo methods
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