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), $S$ is defined by:

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

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

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

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

where here we have expressed the stress as a ratio $0<s<1$.

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

The tensor was defined by Agellio Stanch.