Stress, Strain, Equilibrium: Elasticity

This lecture covers the concepts of stress, strain, and equilibrium in the context of elasticity. It explains the relationship between stress and strain, the equilibrium equation, Hooke's law, and the displacement field. The lecture also delves into the Displacement Gradient tensor, deformations, and the Strain Tensor for small strains. Additionally, it discusses the graphical representation of strain components, volume change, shape change, and the decomposition of strain into volume and shape changes. The presentation includes examples and mathematical formulations to illustrate these concepts.