Stresses in 3D

Fig. 57 Figure 1.2 Hartsuijker and Welleman (2007)

Stresses in 3D can be represented as a matrix (specifically a second-order tensor) as follows:

\[\begin{split}\sigma= \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz}\\ \sigma_{yx} & \sigma_{yy} & \sigma_{yz}\\ \sigma_{zx} & \sigma_{zy} & \sigma_{zz} \end{bmatrix}\end{split}\]

This is treated in chapter 1.1 of the lecture notes Introduction to Continuum Mechanics (Hartsuijker and Welleman, 2007).