## Ambiguity in 2D plane stress linear elasticity.

Numerical methods and mathematical models of Elmer
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
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### Ambiguity in 2D plane stress linear elasticity.

I use elmer for simulating 2D geometries. With a 2D domain upon calling the 'Linear Elasticity' solver, by default the z-displacements are given as 0.
This happens even when "Plane stress = True" flag is used, whence the results are in a conflict (z-displacement = 0 and z-stresses are also = 0).
Please suggest me ways to verify the obtained solutions, and to resolve this problem.

Further, the non-linear solver does not compute stresses post solving process. Please advice on the same.

mika
Posts: 207
Joined: 15 Sep 2009, 07:44

### Re: Ambiguity in 2D plane stress linear elasticity.

Hi,

The nonlinear elasticity solver should be less handicapped with respect to this. If the plane stress option is active (Plane Stress = True in the equation section), you should obtain the normal strain in the z-direction via post-processing. The stress computation should also work by having in the solver section

Solver ...
Procedure = "ElasticSolve" "ElasticSolver"
Calculate Strains = True
Calculate Stresses = True
...

The idea of the plane stress option is to reduce the problem into 2-D so that the z-component UZ of the displacement does not appear in the equations that are solved in the first place. Producing UZ could be a post-processing task but Elmer doesn't offer any routine for this currently. So, the best strategy (although this doesn't yet produce the consistent UZ by post-processing) might be to apply the nonlinear solver. If the case is genuinely linear, the nonlinear iteration should terminate quickly and shouldn't pay too much, or one could also suppress the nonlinear iteration completely by setting Nonlinear System Max Iterations = 1. The nonlinear solver produces approximations of the nonlinear strain measure, which should anyhow be close to the linearized strains when a linearized model could also be used.

Best regards,
Mika
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
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### Re: Ambiguity in 2D plane stress linear elasticity.

@mika : Thanks for the response.

With plane strain, the z-component strains are agreeably zero. But with 'plane stress = true', where I expected the z-strains to be non-zero, they remain zero. PFA 'linear.sif' and 'linear.ep' demonstrating this.

Had the non-linear solver computed strains or stresses, I could have checked with them. But the non-linear solver doesn't compute stresses or strains. PFA 'nonlinear.sif' and 'nonlinear.ep' in support of this.

Concern 1 is computing stresses with non-linear solver.
Concern 2 is correctness of the plane stresses result, which may have non-zero z-strain components.
Attachments
linear.ep
linear.sif
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
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### Re: Ambiguity in 2D plane stress linear elasticity.

Non-linear attachments mentioned in the above reply.
Attachments
nonlinear.ep
nonlinear.sif
mika
Posts: 207
Joined: 15 Sep 2009, 07:44

### Re: Ambiguity in 2D plane stress linear elasticity.

Hi,

What Elmer version do you have?

The nonlinear elasticity solver do have the ability to compute stresses and strains. To exemplify this, I modified the test case .../fem/tests/elasticity/ as

https://github.com/ElmerCSC/elmerfem/co ... 867555c2a1

so that the strains and stresses are now computed. I even attach a visual verification of this feature when the case is solved by setting Plane Stress = True.
Screenshot from 2018-06-12 09-27-14.png
-- Mika
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
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### Re: Ambiguity in 2D plane stress linear elasticity.

Thanks mika

I tried using the sif file u provided and ran into the following error msg :
"Model Input: Unlisted keyword: [surface traction 2] in section: [boundary condition 2]"

The log file attached for ur ref.
Attachments
log.txt
Log of sim upon using the sample sif file referred above (in GIT)
mika
Posts: 207
Joined: 15 Sep 2009, 07:44

### Re: Ambiguity in 2D plane stress linear elasticity.

Hi,

This message shouldn't appear if Elmer has been compiled from recent source files. Your Elmer version is too old, so my advice is to get a newer version of Elmer and to run the case again.

-- Mika
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
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### Re: Ambiguity in 2D plane stress linear elasticity.

Hi Mika

Thanks for your last response. Since we get back to our FE analyses after quite sometime, we are in need of your suggestion.

The Elmer version we had was not compiled by ourselves, we just followed the instructions in https://www.csc.fi/web/elmer/binaries from our ubuntu 16.04 system. We still are in need for help to get : Stresses in non-linear elasticity, Normal-tangential boundary conditions, etc.
The pre-compiled version on the web page might be old..?
Your suggestions would be of great help to us.

Thanks.
mzenker
Posts: 1999
Joined: 07 Dec 2009, 11:49
Location: Germany

### Re: Ambiguity in 2D plane stress linear elasticity.

Hi,

if you install elmer using launchpad as described here viewtopic.php?f=2&t=4413, you will always get a recent version since the launchpad packages are updated rather often.

HTH,
Matthias
skoushik
Posts: 20
Joined: 22 Jan 2018, 01:55
Antispam: Yes

### Re: Ambiguity in 2D plane stress linear elasticity.

@mzenker : Thanks for the above advice - works like magic.