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tangent stiffness in ansys - usermat


pacificstandardtime
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(@pacificstandardtime)
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hi all.

im trying to implement a finite strain (hyperelastic) law in ansys using usermat. i have a problem in defining the tangent stiffness operator. i thought that ansys uses the (usual) stiffness:

the piola transform (push forward) of dS_kl/dC_mn

S = second piola kirchhof stress

C = right cauchy green deformation tensor

from reading very interestin threads on this homepage i have understood that this might not be the case. i have noticed that a some one uses a numerical perturbation of the jaumann rate of the kirchhoff stress and obtain good convergence. i can also read that the correct stifness should be the derivative of the cauchy stress with respect to the logarithmic strain.

so, to my question, do enyone know how to transform dS_kl/dC_mn or the push forward of dS_kl/dC_mn to the desired stiffness (analytically). this would be very helpful to me.

many thanks

per

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Jorgen
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Hi Per,

First remind me, is there a hyperelastic user-material option in Ansys? That option exists in Abaqus, and significantly simplifies the addition of custom hyperelastic material models.

It might be possible to transform the stiffness you mentioned to a more a suitable representation. However, I dont recall a seeing a reference for that.

What I would do is to directly derive the tangent stiffness in the form you want from the strain energy density.

-Jorgen

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pacificstandardtime
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hi, tahnks for this reply.

yes, there is a hyper option in ansys, but my idea is to use the usermat and implement this simple neo-hookean type of material first, to make things run, and then continue with a more advanced model.

i agree with you that your suggestion is the best way! i have implemented this material law in a similar manner in abaqus. if i remember right abaqus uses a variation of the kirchhoff stress wrt a strain energy. the problem is that i cannot find proper documentation of which stiffness operator (variation) to use in ansys. do you know which is the correct relation for ansys, the same as for abaqus!?

kind regards

per

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Jorgen
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Sounds like a good idea to start with a hyperelastic material.

I am not sure, and I dont have a reference handy, for what stiffness operator is needed by Ansys. My guess is that it is the same as what is used by Abaqus...

-Jorgen

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pacificstandardtime
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many thanks Jorgen

i will investigate this further

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