## Issue with large strain analisys (poisson x strains)

## Issue with large strain analisys (poisson x strains)

(OP)

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.

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)

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

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)