Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics

This lecture introduces the fundamental concepts of Continuum Mechanics, focusing on the application of conservation laws to continuous media, the description of continuum mechanics through tensor objects, and the study of fluid motion. The course covers topics such as the deformation gradient, stress tensors, objectivity in tensor objects, and the velocity gradient tensor. It also explores the interplay between geometry and mechanics, fracture of rock with fluid pressure, stability of turbulent fluid flows, and vortex dynamics. Additionally, it addresses the stability of dynamic fracture, small-scale oscillators, and the study of friction and fracture with numerical methods.