Continuum Mechanics: Deformation and Compatibility Equations

This lecture covers the concept of deformation in continuum mechanics, focusing on the equations of compatibility. It explains how to calculate the strain tensor from the displacement field and vice versa, highlighting the importance of the compatibility equations. The instructor demonstrates how these equations ensure a unique displacement field corresponding to a given deformation. Additionally, the lecture delves into stress analysis, introducing the concept of stress tensors and the Cauchy stress hypothesis. It concludes by discussing principal stresses and the transformation of stress tensors to principal stress directions, providing insights into material behavior under different loading conditions.