Can a block or thick plate be idealized as an axial spring?

[hootrpootr]

Hello, I want to drop a heavy mass onto a "pad", or thick plate (potentially even a block if the thickness is great enough). I am trying to determine an effective axial stiffness with which to apply to the pad. I know that for a rod for example, the stiffness could be worked out to be k = EA/L, where A is the cross-sectional area and L is the length of the rod.

Is it even an assumption worth making that if I drop a mass (A = length x width) onto a thick plate/block of a similar area (so that the edges don't behave nonlinearly or flare up), I could derive the through thickness axial stiffness of the pad as:

k = EA/t, where A is essentially the impact area, and t is the thickness of the pad?

Of course you might get effects where the pad expands outward as well as compresses, but for now I just want to focus on the axial stiffness of the pad.

 

[IRstuff]

It seems to me that your "heavy mass" is also contributory to the total spring of the "system"

TTFN (ta ta for now)
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[ClearCalcs]

If both your blocks/masses are of similar area then k = EA/t is the solution per Hooke's law. If your contact areas vary greatly you will get some effects from triaxiality but these effects will almost certainly be negligible in the noise of the impact if you're doing an actual test.

Things can get weird when you're dealing with dynamic loads like this. Your measured load and deflections are going to be greatly amplified by the impact nature of your load (which will affect your "effective" stiffness). I'd recommend looking at "Design of Welded Structures" by Omar Blodgett - it's an old book but its short section on impact loads has a derivation of exactly your case, I think. Two formulas are given which would be useful for you:

and

These are developed based on energy balance. Using K = EA/t with those equations should give you the appropriate peak load / deflection from which you can then calculate an "effective" stiffness for your case.

-Laurent

http://www.ClearCalcs.com

 

[XR250]

HootrPootr,

I think your handle could be construed as sexist and/or offensive depending on how it is interpreted.