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Aneurysm in rubber FEM model in ABAQUS

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Posts: 9
Topic starter
(@yiwei)
Active Member
Joined: 15 years ago

Dear all,

During my research on rubber materials, I am trying to match results about aneurysm in rubber.

I am using an interesting paper:

Finite deformations of an initially stressed cylindrical shell under internal pressure International Journal of Mechanics Sciences vol.50 pp.92-103 (2008).

I am not a specialist in non-linear analysis, so something in the setting of my model (especially) for the Riks analysis could be wrong.

I cannot success in find out a localized aneurysm such as in the paper.

I am using ABAQUS as used in the paper.

However there are some aspects in the paper that not convince me so much.

So any advice/hints could be very useful.

Results presented are a comparison between ABAQUS and experimental results.

Material parameters used to describe the material and reported in the paper are:

Neo-Hookean C1 = 0.201906 MPa C2 = 0 MPa

MooneyRivlin C1 = 0.087167MPa C2 = 0.150843MPa

Ogden mu = 1.55886MPa alpha = 0.403913

First of all:

If I insert these parameters into ABAQUS and then I evaluate the material, seems that strain-stress curve for Ogden material and Mooney-Rivlin describe a totally different materials.

Anyone was involved in this kind of problems?

Any other paper present in literature about same problems?

If someone interested I can supply the .inp file of my analysis.

Thank you in advance for any answers/critics/suggestions.

Andrea

10 Replies
Posts: 3998
(@jorgen)
Member
Joined: 5 years ago

I am not familiar with the paper that you mentioned, but it is clear that the two material models (NH and MR) with the provided coefficients will not give the same stress-strain results.

- Jorgen

10 Replies
Posts: 9
Topic starter
(@yiwei)
Active Member
Joined: 15 years ago

Dear Jorgen,

Thank you very much for your reply.

So as I thought the material described (with these parameters) is different in every model.

Infact with this material I can obtain a generalized and not a localized aneurysm.

Changing material properties I can obtain a localized aneurysm as in the paper.

I tried to contact the author of paper, about problems to match their results but I didnt received any useful and meaningful answers.

If you have time to take a look at the paper I can send you via e-mail.

There are a lot of strange things in the paper.

First of all they used ABAQUS and selected a shell element with reduced integration to describe the hyper-elastic material (S4R) instead of using an element with hybrid (mixed displacement/pressure) formulation.

During the experiment they stretch (traction) a hollow cylinder of rubber and apply an increasing pressure until the aneurysm is formed.

FEM simulation is divided in two steps (I guess): a traction and a RIKS analysis.

At the end of the traction (as reported in the paper) they do not obtain a symmetric displacement, and this seems very strange to me (Fig. 14a)

Then instead of arc-length as output in the RIKS analysis they obtain the time (Fig. 14b), I dont know if I am missing something in the set up of RIKS analysis or in the post-process of the results.

Have you any comments about these doubts?

Do you know any other good reference about this topic?

Andrea

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Posts: 3998
(@jorgen)
Member
Joined: 5 years ago

If you cannot match the published results then it may very well be that the original authors made one or more mistakes.

Do you have to match their results, or can you simply solve the problem in your own way?

-Jorgen

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Posts: 9
Topic starter
(@yiwei)
Active Member
Joined: 15 years ago

I can solve the problem in my own way.

This paper could be very useful to understand the right procedure in order to simulate the aneurysm and to learn more about FEA for rubber materials.

For example could S4R (shell with reduced integration) element be consider an effective and efficient element to simulate rubber material?

Or from a theoretical point of view it is non recommended, instead from an engineering (practical) point of view can be used and good (reliable and consistent) results can be obtained?

Andrea

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Posts: 3998
(@jorgen)
Member
Joined: 5 years ago

1) Yes, S4R elements are suitable for rubbers (assuming that you are interested in thin shell-like structures)

2) I dont understand your question :confused:

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Posts: 9
Topic starter
(@yiwei)
Active Member
Joined: 15 years ago

I will try to explain in more details my doubts.

My questions are related to volumetric locking and the selection of a good element to avoid this problem.

In theory seems to me that mixed (hybrid) formulation should be used in order to avoid volumetric locking problem.

One of the most advanced shell formulation is the MITC shell by K.J. Bathe and was formulated to avoid shear and membrane locking in shell and plate.

But also this shell element should be affected by volumetric locking if involved in analysis with incompressible material (rubber), if I am understanding the problem.

I think ABAQUS uses a similar formulation for shell element

So my question is: is S4R element not affected by volumetric locking ?

If yes is it due to a reduced integration?

Or the S4R is affected by volumetric locking (so it is not recommended in theory) but not so much and therefore it is used very often in simulations?

However seems to me that in scientific literature a solid 3D element with hybrid formulation (e.g. C3D8H) is generally preferred to shell element in analysis involving incompressible material.

Is this correct? Am I missing something?

I know that 3D solid element and shell element are based on different assumptions, but sometimes you could use both elements to solve efficiently your problem.

Thank you to clarify me this doubts about the volumetric locking and the right selection of the element for an incompressible material.

Andrea

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