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Issue with large strain analisys (poisson x strains)

Issue with large strain analisys (poisson x strains)

Issue with large strain analisys (poisson x strains)

Dear all,

I am performing a large strain analysis and had some difficult in understanding some results. The issue was with an hyperelastic Marlow-material model, but I tried to develop a simpler one to show what is happening. Hope you can help me to make it clear.

-The simplified model is 3D analisys of a rectangular bar.
-Dimensions are 4.00 x 2.25 and 60.00 mm length (length in U3 direction).
-Material is linear elastic isotropic, with Young Modulus 5000 MPa and Poisson 0.44.
-***Non-linear geometrics is enabled***.
-The boundary conditions are: one 4.00x2.25 face fixed for U3 displacements, and the opposite face displaced by 100 mm also in U3 direction. I know values may be a bit strange, but focus on the results obtained.
- Mesh is all of C3D8R bricks, reduced integration, reasonably fine size.

For LE results (standard abaqus output), I obtained:
LE33= 0,9808; LE11 and LE22= -0,420.
Deformed geometry: 2.6281 x 1.4783 x 160 mm

Ok, first I can use the Logarithm Strains (LE) to obtain the Engineering Strains (E), using E = exp(LE)-1 (derived from the classic LE=ln(E+1))
Hence, E33= 1,667; E11 and E22= -0,5220

However, I can also calculate these Engineering Strains using the final dimensions, where:
E33= (160-60)/60= 1,667; E22= (4.00-2.6281)/4.00= 0,3430; E33= (2.25-1.4783)/2.25= 0,3430

Here it is possible to verify that the engineering strains are OK for the 33 direction, but are not as expected for 22 and 11 directions.
Also, I was in doubt about how abaqus uses the poisson information. In principle, I believed that the 0.44 coefficient could be checked using the Engineering Strains, once in tests it is obtained with extensometers. What I found was:
poisson (LE values)= 0,420/0,9808= 0,428
poisson (E values, calculated from LE)= 0,5220/1,667= 0,313
poisson (E values, calculated from dimensions)= 0,3430/1,667= 0,206

So, it seems that Abaqus used poisson to calculate the transverse LE values, which was not what I expected. Even though, in a model simple like that I couldn´t find out why it was not exactly 0.44.

For information, I ran this same model using NLGeom=off. For this case, abaqus output was the Engineering Strain. Results are below:
E11= 1.667; E22 and E33= -0.7333;
Deformed geometry= 1.0667 x 0.60 x 160 mm which leaded to the same E11, E22 and E33 shown in the line above.
The calculated LE would be: LE11= 0.9808; LE22 and LE33= -0.55;

From this, poisson values would be:
poisson (LE values, calculated from E)= 0,55/0,9808= 0,56
poisson (E values)= 0,7333/1,667= 0,44

Here, Abaqus used the poisson to calculte the transverse Engineering Strains, and all values are "as expected".

Concluding, what I would like to understand:

- Why transverse LE strains for the first model are different when calculated from final dimensions and from abaqus output? The same formula worked for the 11 direction...
- For large strain abaqus uses the poisson for calculating Logarith Strains? Does it make sense? I have not seen any information regarding "converting" poisson anywhere, and it doesn´t seems logical to me.

RE: Issue with large strain analisys (poisson x strains)

Linear elasticity is only valid for small strains.

RE: Issue with large strain analisys (poisson x strains)

As far as I know using large strains change the way calculation is done in Abaqus, considering actual dimensions instead of initial dimentions.
Probably there is more than that with the large strain analysis, but can´t see how it would affect the poisson x strain relation, once that by definition poisson should be (transverse eng. strain / longitudinal eng. strain), and by definition eng. strain should be (l-lo)/l.
Both are different from expected...

RE: Issue with large strain analisys (poisson x strains)

Linear elasticity is still invalid for large strains, even when you activate NLGeom.

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