The 9/11 Forum

OneWhiteEye wrote:The first two connections in both the upper and lower block break, then it is crush down exclusively ...

That is a fine demonstaration! Did you just remove one connector between the two blocks, so that some small crush-up occurred?

David B. Benson wrote:

OneWhiteEye wrote:The first two connections in both the upper and lower block break, then it is crush down exclusively ...

That is a fine demonstaration!

Thank you!

Did you just remove one connector between the two blocks, so that some small crush-up occurred?

Yes, the functional equivalent: the joint is omitted and the simulation started. Actually, two structures are created according to identical processes with the desired number of stories and nearest neighbor joins, with one positioned above the other. This allows the initial height of the upper block to be set independently, though unit story height is all I've done.

Given the input parameters, that's all there is to it. Whatever the relative proportions of crush up/down are, when and where they occur, is then dictated by the simulation. Changing the parameters, of course, gives different results. I was surprised at how easy it was to converge on the general behavior exhibited above, where crush down dominates after some early crush-up, only a few trials. Such behavior is seen, so far, over quite a range of parameters.

In fact, I do believe a challenge would be to create a system with sustained equal proportion of crush up and down.

OneWhiteEye wrote:In fact, I do believe a challenge would be to create a system with sustained equal proportion of crush up and down.

Let me clarify. It's trivial if you remove the gravitational field and impart equal and opposite initial velocities to the two blocks:



This is like two ships colliding in space. I think it's more like two ships in water, and moving horizontally, than any dominoes I've seen. Equal and opposite, as expected. Nice validation of the model.

In empty space, it wouldn't matter if the respective blocks had velocities v and -v or 0 and -2v. It matters in this simulation space because there is an unseen immutable ground plane upon which the lower block rests. Some interesting behavior can be zeen in zero-g scenarios which have the upper block smash into the lower stationary block which is placed against the ground plane, but not fixed to it in any way. With the upper block moving at a similar velocity as the combined velocities from above, crush up dominates at first, but the lower block is more damaged at the end:




Double the speed and the lower block is totally destroyed, the upper only half destroyed:




Double the speed again and now both blocks are totally destroyed, simultaneously, with equal crush up/down:




In the last you can see the crush front moves roughly with the geometric center of the system, which is about the center of mass for the system; indeed, I'd say the crush front defines the C.M, and vice-versa. It seems to matter somewhat that the upper is free and the lower is constrained in the zero-g cases, but not too much.

How about 'firing' the top 2 floors at the lower 18?




Both upper and lower are completely destroyed by the 1/10th size impactor. No surprise! This was at 10x the previous velocity with the equal size blocks. What may not be obvious is that the connection strengths of the lower are set to 10x the value of those in the upper. VW destroys cargo truck parked next to wall, if it's going fast enough. Quite sure the wall is superfluous.

OneWhiteEye wrote:In fact, I do believe a challenge would be to create a system with sustained equal proportion of crush up and down.

Only possible in zero-G if material properties are the same in both components.

David B. Benson wrote:

OneWhiteEye wrote:In fact, I do believe a challenge would be to create a system with sustained equal proportion of crush up and down.

Only possible in zero-G if material properties are the same in both components.

See above!

Back to 'gravity-driven' collapse. This next trial is exactly the same as the first posting of 2 stories dropping on 18, except the static and dynamic friction parameters are set to zero whereas they were at the maximum in the earlier trial. The restitution (proportion of rebound in collision) in both cases is zero, lossy. Recall the first case resulted in breaking the single upper floor connection on the third impact. Here, the block rides down all the way to the bottom, where it finally experiences crush up:



Awesome.

OneWhiteEye wrote:Awesome.

You said it!

It seems models lately are just solid mechanics ones with solid slabs colliding like billiard balls flying away in various directions. Very well. I like it. It is a good attempt. But what happened to the sawdust-n-glue elements?
Please focus on the model, where upper part C crushes lower part A due to gravity only and where C and A have same structure and A is, say, 10 times bigger than C.
Crushing assumes elastic and plastic deformations and failures of the parts and their elements involved, and the objective is to find a structure that allows a smaller part C of this structure to destroy a bigger part A of the same structure assisted by gravity only.
In Benson's differential equation of crush down part C is assumed to be rigid (or just subject to 'negligible damages) at contact with part A. To copy that in a table top model would be too obvious! Part C is then not similar to part A at all.
The problem is, evidently, that reaction forces due to gravity forces at the collision will destroy part C quite quickly, at any scale.
Impossible challenge to show the opposite, I am happy to say.

OneWhiteEye --- A small improvement would be to color the upper part, say green, so that upper and lower are more easily distinguished.

Heiwa wrote:It seems models lately are just solid mechanics ones with solid slabs colliding like billiard balls flying away in various directions.

Yes, pretty much. Between billiard balls and dominoes, I favor dominoes.

Very well. I like it. It is a good attempt.

Thanks. It's a first attempt. With some minor reservations, I think it starts to approach a simulation of the Greening model. For that reason, I won't throw it out even though it will get superseded. It will be interesting, for me, to analyze this contrived system as if it were a real system. Unlike a real system, there are few unknowns and estimates, most of it is specified. The unknowns reside in the solver behavior under certain conditions, but simple tests can shed light on this. Therefore, one can avoid what I call the "Drake's equation syndrome" which is: nice relation, but you can plug in any values you want.

No need to guess at the masses or precise dimensions, they are specified. Some calibration of the connection breakage under dynamic conditions needs to be done to relate to the theoretical model, particularly to go from peak force and torque specification to impulse and therefore energy. Should this sort of simple simulation (under certain conditions) adhere to the principles in Greening's model, I think it would be a useful tidbit.

But what happened to the sawdust-n-glue elements?

Perhaps, by the time physical models are undertaken, it may be shards of broken glass and crazy glue. Or my favorite, flaming Tinkertoys.

Please focus on the model, where upper part C crushes lower part A due to gravity only and where C and A have same structure and A is, say, 10 times bigger than C.

Please focus on the simulation directly above your post. It's only 9 times bigger, I admit.

Crushing assumes elastic and plastic deformations and failures of the parts and their elements involved, and the objective is to find a structure that allows a smaller part C of this structure to destroy a bigger part A of the same structure assisted by gravity only.

Bolding mine. My definition of crushing includes breakage (fracture). Since it happens to be easiest to model, and isolation of factors is a desireable thing anyway, that's what I've started with, a very simple unit that provides structural integrity and consumes energy to fail. The discrete nature of the failure imposes limitations compared to a more realistic sim, but this corresponds to the discrete model simplification, anyway.

The problem is, evidently, that reaction forces due to gravity forces at the collision will destroy part C quite quickly, at any scale.

I do not believe this is the case for all systems, though may be true for some. Just my opinion. Would you mind clarifying or restating your position as to conditions of part A at the conclusion of part C destruction?

David B. Benson wrote:OneWhiteEye --- A small improvement would be to color the upper part, say green, so that upper and lower are more easily distinguished.

Good idea. I had a fairly nice app built last year, but failed to back up my code. Lost everything in a bad system crash, now I'm starting from scratch. No frills at this point, don't even have a floor grid or axes yet. I do back up my work these days.

Heiwa wrote:Crushing assumes elastic and plastic deformations and failures of the parts and their elements involved, and the objective is to find a structure that allows a smaller part C of this structure to destroy a bigger part A of the same structure assisted by gravity only.

I thought this sounded familiar.

Heiwa wrote:But the dominoes are neither deformed nor crushed.

I addressed this twice now, in two pages. The limitations have been acknowledged. The reasons why deformations are not included at this point have been given. In any work I do on this subject, it will likely be months before anything resembling true deformation in a material will be included, if ever. Just so that's clear and there isn't any ongoing impatience.

OneWhiteEye wrote:
1.

Crushing assumes elastic and plastic deformations and failures of the parts and their elements involved, and the objective is to find a structure that allows a smaller part C of this structure to destroy a bigger part A of the same structure assisted by gravity only.

Bolding mine. My definition of crushing includes breakage (fracture). Since it happens to be easiest to model, and isolation of factors is a desireable thing anyway, that's what I've started with, a very simple unit that provides structural integrity and consumes energy to fail. The discrete nature of the failure imposes limitations compared to a more realistic sim, but this corresponds to the discrete model simplification, anyway.

2.

The problem is, evidently, that reaction forces due to gravity forces at the collision will destroy part C quite quickly, at any scale.

I do not believe this is the case for all systems, though may be true for some. Just my opinion. Would you mind clarifying or restating your position as to conditions of part A at the conclusion of part C destruction?

Re. 1 you have to consider (a) elastic deformation, (b) plastic deformation, (c) fractures of columns and (d) where the fractured parts - column butt ends - displace to continue the destruction.
If only (a) takes place of columns, result is a bounce of part C. Same at (b) but not so pronounced. With (c) the interface changes - free column butt ends are formed - and now, newly broken elements - columns - are part of the action. What to they (d) do?
I assume they damage the weaker floors! The interface changes again.
Your dominoes do not show separate column and floor elements. As soon as a complete fracture of a column takes place, you must consider what the two dominoes previously connected by the joint column involved can do later! E.g.the dominoes' columns damage the dominoes' floors. Gravity will assist part C to damage A, but the reaction forces produced by gravity will also assist A to damage C.

2. Your problem is what happens in your system/model! If you can show that upper part C dominoes - columns and floors - destroy lower part A similar dominoes, while C dominoes are just 'neglibly damaged' ... very well. Then Benson will be happy.
In my humble opinion an equivalent number of dominoes of both parts A and C will be affected at collision and these dominoes will get entangled and friction between them takes over and arrests further actions. And as A contains more dominoes than C, A will always stop C. Benson doesn't like that, but I cannot make everybody happy. I would be happy if Benson changes his mind.

Nope. This is not a zero-G situation.

Heiwa wrote:Re. 1 you have to consider (a) elastic deformation, (b) plastic deformation, (c) fractures of columns and (d) where the fractured parts - column butt ends - displace to continue the destruction.

Oh yes, if modeling real structures is the objective. Not necessarily if the objective is merely demonstrating a principle (and perhaps the limits to its scope).

If only (a) takes place of columns, result is a bounce of part C.

I've gotten the top 18 stories to bounce on the lower 2 and then just stand there! I've obtained the gamut of results already. Only posted a fraction of it. Everything from total survival with bounce to rapid propagation of failure to the bottom well ahead of any dropping slabs. Crush up and stop. Crush up with simultaneous crush down at the bottom of the structure. Falloff of upper block. You name it.

Same at (b) but not so pronounced. With (c) the interface changes - free column butt ends are formed - and now, newly broken elements - columns - are part of the action. What to they (d) do?

Real collapse, 417m towers, very messy. My (apprentice) homunculus suggests you can stand by for the 30.1 years it will take to prepare an NIST/WTC7 style simulation - and then be crushed with disappointment to find it's only one solution, and wrong!

Your dominoes do not show separate column and floor elements.

I did have columns in my earlier sims, didn't work out too well. I am researching alternatives that provide some level of functional equivalence to debris and deformable materials which will work in this environment. For specific simulation, another environment is required.

If you can show that upper part C dominoes - columns and floors - destroy lower part A similar dominoes, while C dominoes are just 'neglibly damaged' ... very well. Then Benson will be happy.

I think he is, already.

In my humble opinion an equivalent number of dominoes of both parts A and C will be affected at collision and these dominoes will get entangled and friction between them takes over and arrests further actions. And as A contains more dominoes than C, A will always stop C.

For what it's worth, my opinion is there's a 63% chance of anything happening, if you look at it hard enough.

I would be happy if Benson changes his mind.

Give him a good reason, he might surprise you.