Averaging results across materials

[martin99]

Hi all,
I’m trying to convince myself that I can average von mises results across material boundaries for a this particular case:

Imagine a model with an orthopaedic implant (material 1) and bone (material 2) side by side (no contact elements, just different partitions) in a linear static analysis. Now bone has this amazing ability to remodel itself and as such can grow into the orthopaedic implant creating amazing fixation. Here is the bit I’m trying to justify. Now material 1 is fully ‘bonded’ to material 2 and as such isn’t a clear boundary anymore. Would averaging the results across the materials give a fair representation of the stress in the bone of a fully ‘bonded’ implant and conversely ‘unbonded’ if I don’t average across the material or partition.

Apologies for the non-technical description of the problem but it seemed like the clearest method. Any thoughts that could help would be gratefully received.
Ideas version 9

Martin

 

[Bhat165]

I am not sure why you want to average the result across the material boundary. Why cant you use individual material properties to calculate stresses in individual materials? Generally stresses are calculated at gauss points and extrapolated at nodes. So, if you use gauss point stresses you can use individual element properties to calculate stresses. On the other hand, if you use nodal stresses, you can average the nodal values "along" the material boundary to get result "along" material boundary. For the later case, you again use individual nodal values when you are outside material boundary.

I hope it can help you.

 

[Bhat165]

To further clarify:

Let element 1 of material 1 has a common boundary with element 2 of material 2 and let the boundary nodes are x and y. When you calculate stresses in gauss points of E1, you use M1 and extrapolate to nodes x,y. Similarly when you calculate stresses in gauss points in E2, you use M2 and extrapolate to nodes x,y. Now you have two values contributed to nodes x,y which you can average over. By this way you get average contribution of E1 and E2. Most softwares display nodal stresses by making average (ABAQUS for instance). So you just pick up nodal stresses along the boundary. Make sure your software does this.

To me this can be the only explanation (accoeding to my understanding of your problem).

 

[corus]

It sounds like you really have 3 materials, the middle material being the region of fusion. This is similar to the Heat Affected Zone (HAZ) in a weld of metals. Strictly speaking you should model this region too otherwise you are in effect making an assumption about the material at the fusion region that says it is some average of the other two. If you can justify this then it's a reasonable assumption to make otherwise I'd err on the cautious and obtain the stresses for each material as this will give you the higher value. Most codes will give you an option to not average stresses across material boundaries. I'd use that.

 

[martin99]

Many thanks for the replies,

I think Bhat165 clarification summed up the problem. I think I need to average across the material otherwise I do not get the contribution from the other material when viewing the results at the interface of the two materials. In an ideal world it would be nice to model the area of fusion as described by Corus but I don’t think the data is readily available to do this. Also in my problem averaging across the materials actually increases the stress in the area I am interested, not decreases as suggested.

Many thanks for your help; I have a clear argument in my head now.

Martin

 

[mantill]

Martin

you can't average von Mises stresses across material boundaries for two reasons.

1) At a fully bonded boundary it's the strains which are equal not the stresses.

2) You can't average von Mises stresses anyway, you have to average the individual stress components (x, y, z, xy, yz, xz) and then recalculate the von Mises stress.

Hope this helps

Marc

 

[Bhat165]

About the first point made by Marc: Its true that fully bonded material has same strain but different stress, so in reality averaging does not make sense. But for that you need to model the interface seperately as suggested by corus, which is not possible as Martin99 said, in that case average has to be done in some sense.
About the secdond point made by Marc: Its an important observation. You really cant average Von Misses stress directly. Its obvious.

Sudip

 

[brad]

You don't need to model the interface separately to get distinct stresses--you can change the averaging criteria such that the stresses are extrapolated to the nodes from each element, but are not averaged at the nodes.

This will manifest itself visually as a stress discontinuity at the nodes; however this will show a correct representation of the stresses in each material as they approach the nodes. (Note that this visualized stress discontinuity is in fact correct; a strain field for the problem posed will show continuity at the interface).

What code(s) are you using for processing and post-processing?
Brad

 

[martin99]

I'm using Ideas 9 for both processing and post-processing.

cheers

Martin

 

[SWComposites]

A primary rule of FE modeling is:

Never, ever average results across material boundaries! The result is pure rubbish. This is one of the many great dangers of automated contour plotting codes.

Steve

 

[Bhat165]

SWComposites:

Can you elaborate on your comment? Thanks.

 

[brad]

Take the example of a bimetallic strip of aluminum (E=70GPa) and steel (E=200GPa). (Note this example is a simplification to make a point).

For the same (simple uniaxial tensile) strain of 0.001, the aluminum will have a stress of 70 MPa and the steel will have a stress of 200 MPa. For similar element size, and decent material quality, these stresses when properly evaluated (with the stress discontinuity at the boundary) will be accurate for the respective materials. However, with averaging the resulting nodal stress would be (200+70)/2 = 135. This is understated for steel, and overstated for aluminum. It's a useless answer on both counts. Hence my earlier suggestion to have your averaging criteria set such that no nodal averaging occurs. I'm sorry that I don't know how to do this in IDEAS.
Brad