Is animal tissue better modeled as a solid or a fluid for terminal ballistics?

[Robert Williams]

There has been a running debate for some time on an archery forum with one rather simple question going unresolved.

Here are the opposing arguments. Can anyone shed light on which is most accurate?

Argument 1. Animal tissue must be modeled after a fluid for the purposes of terminal ballistics because it is, by content, mostly water and water is a fluid.

Argument 2. Animal tissue must be modeled after a solid for the purposes of terminal ballistics because, regardless of moisture/water content, it is not a fluid environment and moisture content is not one of the defining characteristics of fluid.

 

[Naty1]

Why not use something in between like jello...surely the military weapons manufacturers have some substance they use...it's not watermelons because those explode!

 

[Robert Williams]

Naty, thank you for the idea, but the quesion isn't whether ballistic gellatin would be a suitable alternative for testing terminal ballistics. We're more concerned with whether the properties of animal tissue are fluid or non-fluid.

 

[arildno]

Argument 1 is just silly, since cucumbers and jellyfish would qualify as "fluids"

As for argument 2, it seems silly too, since I have no idea what they mean by a "fluid environment".

Ask yourself instead:
Can animal tissues sustain shear stresses, and hence be able to store elastic energy through this mechanism?

If it can, then it has a property that normal fluids don't have.

 

[Robert Williams]

"a fluid is a material continuum that is unable to withstand a static shear stress".

I believe this is what is meant by a fluid environment; something like air or water.

 

[arildno]

"a fluid is a material continuum that is unable to withstand a static shear stress".

I believe this is what is meant by a fluid environment; something like air or water.

Well, and whatever has your second sentence (and hence the core of Arg 2!) anything to do with the first one?

 

[Robert Williams]

I think it's safe to say that the sponsors of argument number 1 actually would accept a cucumber or a jellyfish (particularly the jellyfish) to be modeled after a fluid. And silly or not as the concept might be, an acceptable proof would be helpful one way or another.

Ask yourself instead:
Can animal tissues sustain shear stresses, and hence be able to store elastic energy through this mechanism?

If it can, then it has a property that normal fluids don't have.

Of course, this would be a property that normal fluids don't have. Before adherents of the "animal flesh = fluid" hypothesis argue that storage of elastic energy is a property that "abnormal fluids" might possess, let's try to establish whether any sort of fluid might possesses such a property and not merely a "normal fluid". While this might sound silly, as well, since I am not aware of any "abnormal fluid" that would fit the description, it's still good to establish this sort of thing in the event that such a "silly" argument be put forward.

 

[Robert Williams]

Well, and whatever has your second sentence (and hence the core of Arg 2!) anything to do with the first one?

Am I to assume that there is something to which you object in the wording or is there something that you are not understanding or objecting to conceptually. The core of argument number 2 is that animal flesh is a solid and that because of this, animal tissue cannot be modeled as a fluid for the sake of terminal ballistics, regardless of the moisture content.

 

[nasu]

It seems that this is an argument about words and not facts.
You should study the properties of the object of interest and then compare them with these of fluids and solids.
You don't need to assume from start that your system is either/or (fluid or solid).
In general it is assumed that a fluid cannot sustain shear but this is a property that may depend on how do you apply the shear (how fast). See viscoelastic materials. Same material can be solid-like or liquid-like, depending on how fast you apply the external forces.

 

[tankFan86]

The book I have gives fluids the following definition:

\begin{quote}
A fluid is a continuous medium which has the property that when it is in equilibrium, the stress at every point is one of compression.
\end{quote}

Which is to say that when a fluid is a rest, the force on a particular material plane is entirely in the opposite direction as the material plane's normal vector.

It is still unclear to me whether or not animal tissue is a fluid under this definition.

P.S.
What the heck, I thought Latex commands worked around here...

 

[Robert Williams]

Actually, it IS required that there be a base assumption that the object is either fluid or non-fluid because the drag formula ONLY applies to an object moving through a fluid and actually the core argument is whether or not it is drag that is primarily responsible for stopping an arrow as it cuts it's way through animal tissue and/or bone. And supporters of that hypothesis, naturally must go on to propose that animal tissue is fluid since that is the only way to support the hypothesis.

While I do have to admit that I thought the one fellow vehemently arguing that animal tissue is a fluid was completely daft, I now have to wonder if the properties of fluids and solids are so complex that even fellows on a physics forum it's impossible to get any sort of consensus.

Fortunately, there are other ways to address the validity of the proposed solution that drag increases resistance 4 fold with a 2-fold increase in velocity as an arrow penetrates animal flesh. That is the model that the drag formula would provide. In reality, because there would be an accompanying four fold increase in kinetic energy to meet the fourfold increased requirement for energy, penetration would be to the same depth based on weight with velocity having no bearing whatsoever since every increase in velocity and ke is offset by the increase in drag, netting no additional penetration.

The formula for drag does not work. But I made the mistake of assuming that it would not be arguable that meat is not fluid.

I suppose it was rather silly of me to think that anything might not be arguable by those invested enough in their argument. So I am about to resolve myself that for the sake of this argument the world is flat because folk wisdom says it is.

 

[Andy Resnick]

There has been a running debate for some time on an archery forum with one rather simple question going unresolved.

Here are the opposing arguments. Can anyone shed light on which is most accurate?

Argument 1. Animal tissue must be modeled after a fluid for the purposes of terminal ballistics because it is, by content, mostly water and water is a fluid.

Argument 2. Animal tissue must be modeled after a solid for the purposes of terminal ballistics because, regardless of moisture/water content, it is not a fluid environment and moisture content is not one of the defining characteristics of fluid.

Hopefully, it should be clear by now that choosing an overly simplistic model is the root cause of the diagreement. Tissue is neither fluid nor rigid solid, and besides fluids and solids both have a range of physical properties. As does animal tissue- soft organs behave differently than bone. A better way to approach this question is simply "what idealized material best models animal tissue for the pupose of ballistics", There are tissue models for imaging and tissue models for mechanics, and they may be different.

 

[Robert Williams]

I don't think it's an overly simplistic proposition to identify animal tissue as either fluid or solid. Solids don't have to be hard or rigid in order to be a solid, by definition. I think what may be missing or going undisclosed is that the nature of penetration of fluid and solid are entirely different mechanisms. With solids, penetration is achieved by shearing. With fluids, penetration is achieved by displacement. Resistance to displacement increases geometrically with velocity but resistance to shear does not. With shearing being the mechanism, velocity actually increases efficiency and the more elastic the medium, the more benefit velocity provides, expending less energy stretching and moving the material to be sheared before shearing it.

Wet cardboard would be a close approximation to animal tissue - but not bone. Plaster of paris might be a good approximation for bone, but not muscle tissue. But no fluid is even close to an approximate representation of either one.

I state these things as a fact purely for the sake of hypothetical thinking, of course, if additional or contradictory facts can be brought to bear showing that the drag formula (applicable only for projctiles in fluids) is, indeed, the operative force that resists penetration of an arrow (or any other non-deforming projectile) through animal flesh, then I would be very interested in hearing or debating them to see what can be revealed.