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# Honeycomb Modeling

## Honeycomb Modeling

(OP)
Hi guys !
I'm working on Honeycomb materials and I'm going to use it in a sandwich beam. I derive equations and I'm sure about it ! in this equation, I have a shear modulus of core ( means Honeycomb ),G, which I don't know what it is !
I mean in this equation G is G13 or G23 ?!

I also found a book and it was written about honeycomb mechanical properties ! at that book, I formed the S matrix for honeycom, and surprisingly, that matrix isn't symmetric !! what's wrong with it ?!

### RE: Honeycomb Modeling

The shear modulus, in this context, refers to the transverse shear stiffness (G13 and G23). Some cores will have different values for G13 and G23, which can affect the result. Deflections, stability, etc. are affected by the transverse shear stiffness of the core.

### RE: Honeycomb Modeling

(OP)
Brian,

Thank you again & again ! It is so much useful.
and what about my second question ?! about the S Matrix ?! Could you help me about that?

Do you also know any useful site or book which could help me ?

Thank you so much !

### RE: Honeycomb Modeling

The shear stiffness matrix should be a symmetric 2x2 relating the shear forces/length Q13 and Q23 to the through-thickness shear strains gamma13 and gamma23:
[Qx] = [H11 H12][γ13]
[Qy] = [sym H22][γ23]

Any of the recommended refs on this page should do a good job and be a worthwhile investment, e.g. see:

There used to be some half decent stuff by Brandi Hampson at http://home.comcast.net/~brandihampson/cd/ and related material at http://www.mse.mtu.edu/~drjohn/my4150/ but it all seems to have been disappeared. (Demon3 first drew this to our attention in 2008.)

If you have access to online or hardcopy ESDU data items then 89013 might help.

Anyway, if your shear stiffness natrix isn't symmetric then something is wrong. How did you derive it?

### RE: Honeycomb Modeling

(OP)
Dear RPstress,

That was useful. but the links related to Brandi Hampson which you mentioned do not work ! Thank you again.

About derivation of my equations, I use this book to evaluate my honeycomb core mechanical properties:
" Cellular Solids: Structure & Properties_Second Edition by Lorna J.Gibson & Mikhael F.Ashby _ 1997 "

In this book,( Chapter 4_ from Page 93 up to 175 )discusses about Honeycomb Properties. I attached a part of that book which make me confused !! Please read it & give me your opinion about that.
I just mention about the [nu] bellow which are about Out-of plane propeties. In this book we have this equation:

[nu31]=[nu32]=[nu] : ( [nu]= refer to the pure material which our honeycomb is made )
[nu13]=[nu23]=0 ( approximately equal to zero )

I evaluate both in-plane & out-plane properties & and make S matrix.
Then, it shows that our S matrix will not be symmetric,doesn't it ?!
If I'm wrong, let me know please !!

### RE: Honeycomb Modeling

As I said, the Brandi Hampson and Dr John links have been 'disappeared,' Catch-22 style. If anyone knows of material covering similar ground (theory-based but reasonably explanatory, like a compact textbook with Mathcad files as well as text) on the web please let us know. It was quite a handy source.

I don't have that Gibson/Ashby reference. From the look of what you have excerpted, stretch the core in the 3-direction and it will contract in the 1- and 2-directions by the basic material Poisson's, stretch it in the 1- and 2-directions and it won't change its 3-direction dimension. I think that that is true for unsupported honeycomb core, though it might be a little bit questionable if the core is bonded to rigid face skins; it may depend if in-plane stress can be built up in the core by deforming it in-plane (the 1- and 2-directions), which cannot happen if the core is unsupported (it just deforms as a stress-free mechanism if the cell walls are free to bend).

The core shear matrix relates shear strains to the applied XZ and YZ shear forces (13- and 23-directions as long as X is in line with the core's ribbon direction) and makes no mention of in-plane deformations; shear the core in 13 (or 31) and it will deform in both 13 (and 31) and 23 (and 32) directions.

What does your S matrix look like?

PS: in your original post you said that you didn't know what G was. The manufacturer's data sheets are the usual starting point for this and document the G in the two primary directions for hexagonal (and rectangular) cells. If not you can approximate the properties from knowing the volume of material left in the cell walls and the basic core material, but it's only an approximation.

### RE: Honeycomb Modeling

(OP)
Thanks for your information !! They are so much useful.

My S Matrix looks like a orthogonal matrix, but it isn't symmetric !! because of that confusing equations for [nu] ( Poisson's ratio ) at that book, S Matrix is not symmetric !!

### RE: Honeycomb Modeling

If your S matrix is not symmetric, then it is wrong. You have messed something up with the sign conventions or properties. If you want more help, post in detail and with numeric values, every input value you are using and the stiffness matrix equations.

### RE: Honeycomb Modeling

(OP)
Dear SWComposite,

before posting in details, I have a question.I feel embarrassed to ask this question but I'm rookie at composite materials.

Is it important to know the direction of applied force in orthotropic materials ?
For example if we exert a force in x direction, other mechanical properties such as [nu]yz ( Poisson's ratio in y-z ) will be zero or it is independent ?

### RE: Honeycomb Modeling

Is it important to know the direction of applied force in orthotropic materials ? >yes

A material will have properties whether or not a force is actually applied; the properties don't magically appear only when there happens to be a force. You may be confusing stresses and strains with material elastic properties.

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