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For a given surface element with nor normal vector | LaTeX Math Inline |
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| body | {\bf n} =(n_1x, \, n_2y, \, n_3z), \quad |{\bf n} | = \sqrt{n_1^2 x^2 +n_2^2 y^2 +n_3^2z^2} =1 |
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the stress is represented by a vector | LaTeX Math Inline |
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| body | {\bf T} = (T_1x, \, T_2y, \, T_3z) |
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, showing direction and the value of forces exerted across a given surface element : 
Image Removed
| LaTeX Math Block |
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\begin{bmatrix}
T_x \\
T_y \\
T_z
\end{bmatrix} =
\begin{bmatrix}
\sigma_x & \tau_{xy} & \tau_{xz} \\
\tau_{xy} & \sigma_y & \tau_{yz} \\
\tau_{xz} & \tau_{yz} & \sigma_z
\end{bmatrix}
\begin{bmatrix}
n_x \\
n_y \\
n_z
\end{bmatrix} |
where
| Normal stress | Shear stress |
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| LaTeX Math Inline |
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| body | \{ \sigma_x, \, \sigma_y, \, \sigma_z \} |
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| | LaTeX Math Inline |
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| body | \{ \tau_{xy} \, \tau_{xz}, \, \tau_{yz} \} |
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|
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See also
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Physics / Mechanics / Continuum mechanics
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