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Hencky hyperelasticity and other linear stress-strain relationships

Hencky hyperelasticity and other linear stress-strain relationships

Hencky hyperelasticity and other linear stress-strain relationships

(OP)
Hello!

I am trying to write my own non-linear (geometry and material) FE code to solve large biomechanical problems. I am mostly interested in irreversible effects so I use the multiplicative decomposition of the deformation gradient. I model the elastic bit of my systems with Hencky hyperelasticity (linear relationship between the Kirchhoff stress and the logarithmic strain). The code is finished and now I am trying to benchmark it with some comparisons with ABAQUS.

I noticed that for simple deformation cases (like for instance diagonal deformation gradients), the results are the same (this is expected as you can find in the literature that a lot of these finite linear stress-strain relationships produce very similar results in simple deformation cases), but when I do a bit more complicated case (such a bending), my results differ a bit (around 20-30%) in some of the stress/strain components (at the integration points) in the elements I evaluate.

I am using fully integrated linear hexahedra (with the modified deformation gradient F bar, since ABAQUS uses it by default with fully integrated quads and hex). The material I use in ABAQUS is the linear elastic material with the non-linear geometry flag activated, with the same Young's Modulus and Poisson's ratio as the ones I use in my code. My question is.... what model does ABAQUS use when you use finite strain with the linear elastic option activated? Is it Hencky's hyperelasticity (since I cannot find it in the 'hyperelasticity' section). I also checked for possible bugs in my code, but I use convergence criteria as strict as the one ABAQUS uses, and we converge in the same number of iterations (so I assume that my tangent operators are exactly defined). Any ideas?

Thanks for your help! Regards,

Francesc.

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