A tensor measure of internal forces that neighbouring particles of a continuum body exert on each other per unit area across which the force is applied.

Symbol

SI units

Oil metric units

Oil field units

Additional

$\begin{array}{l}\sigma\end{array}$

M L^-1 T^-2

Pa

kPa = 10³ Pa = 0.145038 psi

MPa = 10³ Pa = 145.038 psi

GPa = 10⁶ Pa = 145,038 psi

psi = 6894.76 Pa = 6.89476 kPa

bar = 10⁵ Pa = 100 kPa = 14.5038 psi

atm = 101,325 Pa = 101.325 kPa = 14.6959 psi

For a given surface element $\begin{array}{l}dS_{\bf n}\end{array}$ with nor normal vector $\begin{array}{l}{\bf n} =(n_x, \, n_y, \, n_z), \quad |{\bf n} | = \sqrt{n_x^2 +n_y^2 +n_z^2} =1\end{array}$ the stress is represented by a vector $\begin{array}{l}{\bf T} = (T_x, \, T_y, \, T_z)\end{array}$ , showing direction and the value of forces exerted across a given surface element $\begin{array}{l}dS_{\bf n}\end{array}$ :

(1)	$\begin{array}{l}\begin{bmatrix} T_x \\ T_y \\ T_z \end{bmatrix} = \begin{bmatrix} \sigma_x & \tau_{xy} & \tau_{xz} \\ \tau_{xy} & \sigma_y & \tau_{yz} \\ \tau_{xz} & \tau_{yz} & \sigma_z \end{bmatrix} \begin{bmatrix} n_x \\ n_y \\ n_z \end{bmatrix}\end{array}$

where

Normal stress	Shear stress
$\begin{array}{l}\{ \sigma_x, \, \sigma_y, \, \sigma_z \}\end{array}$	$\begin{array}{l}\{ \tau_{xy} \, \tau_{xz}, \, \tau_{yz} \}\end{array}$

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See also

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Stress

See also