I am starting working on damping in metamaterials, and I found the following statement that caught my attention:
"Dissipation engineering at the macroscopic level is additive; it builds on what may be achieved at the microscopic level. Furthermore, it enables increased, or decreased, dissipation at very low frequencies, i.e., frequencies far lower than what can be accessed by microscopic mechanisms."
My question, is why microscopic mechanisms, such as microstructure atomic configuration, defects or rheological properties (hysteresis), are constrained by low frequencies?.
I wonder is an explanation from the Materials Science approach and probably the filtering behavior of them at certain range of frequencies, but I don't know the exact reaction of these.
This largely has to do with statistics and the fact that length scale is deeply connected to time scale in most materials phenomena. In other words, as you move from the macro-scale to the atomic scale, the time taken for relevant phenomena keeps decreasing.
Consider the simple example of boiling water. At the macro-scale, it takes minutes for vapour pressure to surpass atmospheric pressure and boiling to visibly start. At the microscopic scale, it would take much less time bubbles to nucleate within water (but only a few of them will grow and survive). At the atomic/molecular scale, individual water molecules might jump between liquid and vapour phases in pico- (or even femto-) seconds. So to observe the relevant phenomenon at atomic scale (molecular jumps) you need a very small time-step. At the macroscale, the relevant phenomenon (vapour formation) can be observed at much larger time-steps. If you apply long time-steps to atomic phenomena, you won't see much, because many individual jumps will be timed such that they cancel each other out (~ out of phase). So statistically, the effects will get smeared out. A more academic and materials-centric explanation of this interlinking of length/time scales can be found here:
https://www.mpg.de/36458/cpt01_MultiscaleModeling-basetext.pdf
Applying this to your example of damping, it is easy to see how a low frequency (hence long time) damping structure/mechanism could work at macro-scale, but get averaged out and yield nothing at micro-scale. In fact, as the linked study shows, even a small change in frequency (1-2 orders of magnitude) can occasion 3 distinct damping behaviours (this is all at micro-scale):
Article Effect of hypoeutectic boron modification on the dynamic pro...
Great explanation Aashranth! Thanks a lot! I hope it helps to César too.
Let alone atomic jumping and focus on plastic (dislocation) role in damping.Dislocation velocity cannot exceed the sound velocity in the solid (kind of analogy to special relativity). actually the needed stress becomes too high when the Dislocation velocity reaches say 100m/s. At typical cm dimensions this suggests time of about 10^-4 s I.e frequency of ten kHz- rather low (sound range). Note, this is rough UPPER bound.
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