Difference between revisions of "Stress"

From SklogWiki
Jump to: navigation, search
(New page: The '''stress''' is given by :<math>{\mathbf F} = \sigma_{ij} {\mathbf A}</math> where <math>{\mathbf F}</math> is the force, <math>{\mathbf A}</math> is the area, and <math>\sigma_{ij}...)
 
m (Added a paper)
Line 13: Line 13:
  
 
where where <math>\ \sigma_{x}</math>, <math>\ \sigma_{y}</math>, and <math>\ \sigma_{z}</math> are normal stresses, and  <math>\ \tau_{xy}</math>, <math>\ \tau_{xz}</math>, <math>\ \tau_{yx}</math>, <math>\ \tau_{yz}</math>, <math>\ \tau_{zx}</math>, and <math>\ \tau_{zy}</math> are shear stresess.
 
where where <math>\ \sigma_{x}</math>, <math>\ \sigma_{y}</math>, and <math>\ \sigma_{z}</math> are normal stresses, and  <math>\ \tau_{xy}</math>, <math>\ \tau_{xz}</math>, <math>\ \tau_{yx}</math>, <math>\ \tau_{yz}</math>, <math>\ \tau_{zx}</math>, and <math>\ \tau_{zy}</math> are shear stresess.
 +
==References==
 +
<references/>
 +
'''Related reading'''
 +
*[http://dx.doi.org/10.1063/1.3245303 Aidan P. Thompson, Steven J. Plimpton, and William Mattson "General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions", Journal of Chemical Physics '''131''' 154107 (2009)]
 
[[category: classical mechanics]]
 
[[category: classical mechanics]]

Revision as of 15:45, 20 October 2009

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

Related reading