Linear or quadratic elements to calculate stress concentrations 1

[deyentl]

I have a model in which I have very high stress concentrations. The 3D model consists of fibres in a matrix. The entire top surface of the model is displaced by 0.1%. Z-symmetry is applied on the entire bottom surface, except for the middle fibre. This simulates the fact that that fibre is broken. Because of this, I have very high stress concentrations surrounding this broken fibre.

I have modelled the problem using 3D solid elements and tried both linear and quadratic elements. To my surprise the stress concentrations in the model with linear elements where higher, no matter how refined I made my mesh. I always believed that linear elements should result in the same stresses, if you just make your mesh fine enough. However, this was clearly not the case in this model.

Does anyone know the reason for this?

Best wishes,
de_yentl

 

[burningDiesel]

What kind of linear and quadratic elements? If you are talking about tetrahedral elements, this is totally plausible as it is well known that linear tets are overly stiff.
If you are using hex elements; Since you are modeling fibers in a matrix, I'm guessing one or both of these are polymers, so, (again guessing here) you might have a high poisson ratio, and you could be experiencing volumetric locking (which would explain why it doesn't get better with refining the mesh).

 

[deyentl]

Dear sdebock,

Thanks a lot for your prompt reply.

I’m easing hex-dominated elements in both cases. About 70-80% are hex elements, the other 20-30% are wedge elements.

The fibre properties are:
E1 E2 E3 v12 v13 v23 G12 G13 G23
15 15 230 0.25 0.0163 0.0163 6 13.7 13.7
And the matrix is indeed a polymer: E = 3 GPa and v = 0.4.

How can I check whether this volumetric locking is happening? And is there any way to improve/avoid this problem?

Your help is highly appreciated.

Best regards,
de_yentl

 

[deyentl]

Can anyone explain me how I can detect this volumetric locking in an automatic way?

 

[ESPcomposites]

Around the broken fiber, you may have a theoretically infinite stress concentration. This could explain why the linear and quadratic elements give different results (i.e. neither can accurately capture an theoretically infinite Kt).

Brian

http://www.espcomposites.com

 

[deyentl]

You are right ESPcomposites. But isn't it true that the quadratic elements should be more accurate, even in this case?