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This lecture covers the fundamental concepts of elasticity and plasticity in materials science, exploring topics such as the linear elasticity origin at the atomic level, the Poisson's ratio, energy storage and release in elastic materials, the behavior of metals, ceramics, and polymers under stress, and the criteria for material selection based on Young's modulus and density. The lecture also delves into the theoretical and practical aspects of material elasticity limits, defects in crystalline materials, and the presence of multiple phases in polycrystalline materials.