Continuum Mechanics: Forces and Deformation

This lecture covers the fundamental concepts of continuum mechanics, focusing on the transmission of forces in continua, energy conservation, governing equations, material vs. spatial frame, solid deformation, kinematics, and tensor calculus. It also delves into the analysis of solid deformation, the polar decomposition theorem, and the geometric interpretation of eigen vectors in deformation. The instructor emphasizes the symmetry of principle strains and the diagonalization of the strain tensor, ensuring at least three mutually perpendicular eigen vectors. The lecture concludes with the geometric interpretation of eigen vectors in deformation, highlighting the purely elongational or contractile nature of deformation.