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2. Cauchy stress

Cutting a body reveals the internal forces acting within it. Let us consider a particular point of the cutting surface with the unit normal $\nb$ and the stress vector (i.e. areal density of force) $\tb$ . Both vectors are connected by the linear transformation $\Tb$ :

$\begin{eqnarray*}\tb=\Tb \nb. \end{eqnarray*}$

$\Tb$ is the CAUCHY stress tensor. By lack of couple stresses the stress tensor $\Tb$ is symmetric.

The components of $\Tb$ are denoted by T_ij:

$\begin{eqnarray*}\left( \begin{array}{ccc} T_{11} & T_{12} & T_{13} \cr T_{21} &... ...} & T_{23} \cr T_{31} & T_{32} & T_{33} \end{array} \right) \, . \end{eqnarray*}$

Wolfgang Fellin
1999-10-01