Has anyone measured Flux Friction for different materials?

I was reading this question: What happens when a force is applied to a flux pinned superconductor?

And the answer to it basically suggests that for a flux pinned object to move it from some physical location to another requires an amount of work proportional to the energy required to destroy the original flux tubes and then create the new flux tubes that support the new location.

It would appear that the energy required to create these tubes is a physical property of the superconducting material and could vary from material to material.

I.E. There should be some kind of experimental quantity that I’d like to call "Flux Coefficient of Friction" that can be defined for different superconducting materials.

Does this have a standard name and has it been studied/measured/found-or-refuted?

To be more concrete for those interested:

A starting definition could be: $text{Flux_Friction_Energy}_{text{Material}}(t,d,x,y,M)$ is the Energy required to move a $t$-meter thick rectangular block of width and length $x,y$ at a height $d$ above a much larger flat magnetic surface with field strength $M$, 1 meter to the right. And one could define $text{Flux_Friction_Energy}/M$ as a coefficient of "flux friction" as it divides out the dependence on the magnetic field strength.