Mechanics of Continuous Media

This lecture covers the fundamental concepts of the relationship between stress tensors and strain vectors, the equilibrium of forces, and the interpretation of equations of motion in the context of continuous media mechanics. The instructor explains the importance of stress-strain relationships, the geometric interpretation of these concepts, and the use of Cauchy's relation to determine unknown constants. The lecture also delves into the properties of isotropic and anisotropic materials, the homogeneity of materials, and the significance of symmetry in elasticity. The discussion concludes with a detailed exploration of the linear relationship between stress and strain, highlighting the essential coefficients and their symmetries in the context of elastic solids.