# Linear elasticity extension to finite strains - ABAQUS

Hello!

I am coding my own non-linear FE model in FORTRAN (non-linear material and geometry) and I am following some papers regarding finite strain extensions of small strain plasticity algorithms (Bathe, Simo, Owen, Peric... around the beginning of the nineties) which mainly base the extension on the relationship between the Kirchhoff stress and the logarithmic strain. I am using Henckys hyperelastic material (linear relationship between the two aforementioned stress and strain tensors) to model the elastic bit of my model and I am now checking different simple cases, comparing these with ABAQUS.

For some cases, mostly when the deformation gradients are diagonal or very very close to diagonal, our results are very similar, but when I have considerable off-diagonal terms, the results diverge quite a bit (up to 20% in some cases). I wondered at some point if there were any bugs in my code, so I checked and it seems to be correct, and I obtain a very good convergence (with a similar convergence criteria than the one ABAQUS uses, it converges in the same number of iterations, so I guess that my tangent operators are also correct).

At this point I am wondering... is ABAQUS using the same model as me? Which is the model ABAQUS uses when you use linear elasticity in a finite strain regime? Is it using Henckys hyperelasticity? I have read in the ABAQUS manual that you shouldnt use linear elasticity even in a finite strain regime with strains superior to 5%, that you should use hyperelasticity instead, so I guess that the answer is no, but I would still like to know what model ABAQUS uses to simulate this.

Thank you very much!

Francesc Levrero.

No, I believe that Abaqus still uses a linear elastic model at large strains (if you ask it to).

I went through that exercise myself a few years ago and I believe I got good agreement between my own code and Abaqus also at finite strains. I dont think I did anything special. Just make sure you got the volumetric part right...

-Jorgen

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