tangent stiffness in ansys - usermat

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

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