Ah, springiness is something I hadn't considered!
Don't think engineers can't quantify that, though.
We deal with stiffness (spring rate - k) and "springiness" (effectively, damping ratio (c) in concert with spring rate) all the time.
I bet I could create a fixture that measured the damping factor of rods. Just need a decent DAC and pressure sensor..... Hmmm, lots to think about!