# Stanch Snap-Stress Tensor

The Stanch Snap-Stress Tensor is a measure of the Stanch snap that microstructures can undergo when put under extreme stress.

The Stanch Snap-Stress Tensor (SSST), ${\displaystyle S}$ is defined by:

${\displaystyle S=c_{m}\partial _{\mu }(g^{\mu \nu }{B^{p}}_{n}f_{p\nu })}$

where ${\displaystyle c_{m}}$ are climbing factors, ${\displaystyle g}$ is the metric, ${\displaystyle B}$ are the so-called bottle paths and ${\displaystyle f}$ is the fracture trajectory over the bottle path.

The SSST can be integrated over spacetime to give a numerical stress factor, ${\displaystyle s}$:

${\displaystyle s={\frac {\int \partial _{B}S(x,t,c)\,dt\,d^{3}x}{\int g\,dt\,d^{3}x}},}$

where here we have expressed the stress as a ratio ${\displaystyle 0.

At ${\displaystyle s=0}$, the system is not Stanch snap susceptible, but at ${\displaystyle s=B/h\approx 0.6}$ (for most materials), the system is gaining stress. It has been speculated that ${\displaystyle s\neq 1}$ under any situation since the Stanch snap-stresses will realign the material, but it has been proposed that under certain Alexian conditions, ${\displaystyle s\rightarrow 1}$ can be observed.

The tensor was defined by Agellio Stanch.