Stress

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The stress is given by

{\mathbf F} = \sigma_{ij} {\mathbf A}

where {\mathbf F} is the force, {\mathbf A} is the area, and \sigma_{ij} is the stress tensor, given by

\sigma_{ij} \equiv \left[{\begin{matrix}
   \sigma _x & \tau _{xy} & \tau _{xz} \\
   \tau _{yx} & \sigma _y & \tau _{yz} \\
   \tau _{zx} & \tau _{zy} & \sigma _z \\
  \end{matrix}}\right]

where where \ \sigma_{x}, \ \sigma_{y}, and \ \sigma_{z} are normal stresses, and \ \tau_{xy}, \ \tau_{xz}, \ \tau_{yx}, \ \tau_{yz}, \ \tau_{zx}, and \ \tau_{zy} are shear stresess.

References

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