Stress and Strain: Generalization to 3D

This lecture covers stress equilibrium, strain, and the generalization of stress to 3D. It explains the concepts of stress and strain beyond 1D, introducing Hooke's Law and analyzing structures with axial loads. The lecture delves into stress and traction vectors, defining equilibrium on surfaces and the direction of the unit normal. It discusses the stress tensor, symmetric stress components, and the equilibrium of deformable structures. The lecture also explores the concept of tensors, the state of stress at a point, and the definition of a tensor. Additionally, it covers displacement vectors, the gradient matrix, and small displacements. The lecture concludes with the definition of the strain tensor.