Chapter 10.11, Problem 9MP

If $u$ is a vector specifying the displacement under stress of each point of a deformable medium, then $\nabla u$ is a $2^{\text{nd }}$-rank Cartesian tensor (see Problem 11 ) which describes the strain at each point. Display the components of $\nabla u$ as a matrix. Write $\nabla u$ as the sum of a symmetric tensor and an antisymmetric tensor [see (3.5)].Comment: The symmetric part of $\nabla u$ is called the stress tensor and the antisymmetric part the rotation tensor.