I am currently quite confused on how to correctly account for the voigt/nye notation. When using an energy potential, the tangent can be computed with the second derivative wrt. the strain.
In general, i find it easier to just use the “regular” tensor notation, the tangent is 3x3x3x3. It is simply more convinient, as I have my equations on paper the same way. However, if I transform the strain tensor to the 6-vector, I have to account for a factor 2 in the shear components. This leads to a factor 1/2 or 1/4 in the tangent, for simple shear or where we have two shear strains in the derivative.
But I am a little confused on when this actually has to be considered. Giving some trouble I have with a finite difference implementation, I think I messed that up somewhere. Is there maybe someone that can shed some light for me here?
Leave out the factor 2 and set up your tensors as normal. Then sort them into the correct positions of the vectors for the stress and the tangent.
! stiff(21): consistent tangent stiffness matrix in the material
! frame of reference at the end of the increment. In
! other words: the derivative of the PK2 stress with
! respect to the Lagrangian strain tensor. The matrix
! is supposed to be symmetric, only the upper half is
! to be given in the same order as for a fully
! anisotropic elastic material (*ELASTIC,TYPE=ANISO).
! Notice that the matrix is an integral part of the
! fourth order material tensor**, i.e. the Voigt notation
! is not used.**
I am sometimes cautious when, for example in umat_ciarlet_el.f, further subroutines are referred to as “Voigt”. My understanding is that Calculix merely stores the components in vectors to save space by exploiting symmetry properties.
The factor 2 would be needed if otherwise calculations in Voigt notation yielded different results than in full notation, because the shear strains would only be taken into account once instead of twice.