Stress

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \sigma _{x}} , $\ \sigma _{y}$, and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \sigma _{z}} are normal stresses, and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{xy}} , Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{xz}} , Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{yx}} , Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{yz}} , Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{zx}} , and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ \tau _{zy}} are shear stresess.

References

Related reading

• 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)
• G. C. Rossi and M. Testa "The stress tensor in thermodynamics and statistical mechanics", Journal of Chemical Physics 132 074902 (2010)
• 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)