# Editing Stress

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β | + | 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}</math> is the stress tensor, given by | ||

+ | |||

+ | :<math>\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]</math> | ||

+ | |||

+ | 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)] | ||

+ | *[http://dx.doi.org/10.1063/1.3316134 G. C. Rossi and M. Testa "The stress tensor in thermodynamics and statistical mechanics", Journal of Chemical Physics '''132''' 074902 (2010)] | ||

+ | *[http://dx.doi.org/10.1063/1.3582905 Nikhil Chandra Admal and E. B. Tadmor "Stress and heat flux for arbitrary multibody potentials: A unified framework", Journal of Chemical Physics '''134''' 184106 (2011)] | ||

+ | [[category: classical mechanics]] |