Prof. Bangerth,
I agree that one will have to first define "symmetry" for higher-order
tensors. Perhaps one solution, at least for the 4th-order tensors, could be
to have a function 'symmetrize()' (or some other name) with additional
arguments specifying the type of symmetry, i.e. the so-called - minor
symmetry (A_{ijkl} = A_{ijlk} = A_{jikl} = A_{jilk}) or the major symmetry
(A_{ijkl} = A_{klij}) or both. I'll try to write a patch.
JP,
Thanks! I decided to change my parameterization for now.
Regards
Vinayak
On Thursday, July 25, 2024 at 2:56:31 AM UTC+5:30 Jean-Paul Pelteret wrote:
> Hi Vinayak,
>
> I wrote a reply a few days ago, but apparently I managed to address it to
> Wolfgang rather than the mailing list. Oops... I know that you've made some
> progress since then but since maybe these details could be of some further
> interest I've copied it verbatim. I think that the last sentence aligns
> with what you've already done.
>
> -----------------
>
> To answer your earlier question [from 18 July] directly, I think that the
> feature that you're looking for is called make_symbolic_function()
> <https://dealii.org/current/doxygen/deal.II/namespaceDifferentiation_1_1SD.html#aca52d0daf28725a318c088ad5af47c8f>
>
> for scalars, or make_[vector
> <https://dealii.org/current/doxygen/deal.II/namespaceDifferentiation_1_1SD.html#aab0b7e232cfce4ec2ce1103c9b2355b6>,
>
> tensor
> <https://dealii.org/current/doxygen/deal.II/namespaceDifferentiation_1_1SD.html#ae7b8f65f088b8a48270a8f0bd6827bdb>,
>
> symmetric_tensor
> <https://dealii.org/current/doxygen/deal.II/namespaceDifferentiation_1_1SD.html#ab1ce6976f2bbd7f477f2f7e5312c2428>]_of_symbolic_functions()
>
> for higher dimension entities. These allow you to generically express
> symbolic functions with other functions as arguments, and differentiate
> correctly.
>
> That said, I don't think that this is what you want to do. There is an
> example in the tests for step-44, namely
> tests/symengine/step-44-sd-quadrature_level_0[1,2,3].cc
> <https://github.com/master/dealii/blob/3473bfcca7d6524a187588d2644998ddc807f082/tests/symengine/step-44-sd-quadrature_level_01.cc>
>
> that exploits the relationship between det(b) and det(F) = sqrt(det(b)) =
> sqrt(det(C)) to compute the kinetic variables and their derivatives. I
> think that you'd be able to solve your problem most easily if you follow
> suite. Otherwise you'd really have to differentiate with respect to F,
> which you state as being the true parameterisation of the energy, and then
> push forward the Piola-Kirchoff stress tensor and its linearisation (e.g.
> using the functions in the namespace Physics::Transformations
> <https://dealii.org/current/doxygen/deal.II/namespacePhysics_1_1Transformations.html>
>
> if any of them seem like good candidates).
>
> -----------------
>
> Best,
> Jean-Paul
>
>
> On Thursday, July 18, 2024 at 8:01:51 PM UTC+2 Wolfgang Bangerth wrote:
>
> On 7/18/24 00:22, Vinayak Vijay wrote:
> >
> > But here, it looks like the information about the composition of the
> functions
> > is not being stored somehow, maybe because it reduces the expressions to
> the
> > independent variables ("x" in this case). What change should I make to
> obtain
> > dg_dy? The independent variable remains "x" of course.
>
> I do not actually know enough about SD to help with this. The way I read
> the
> code is that you declare x to be an independent variable, whereas y is
> not.
> Intuitively, I would have expected the underlying library to raise an
> exception when you try to compute the derivative with regard to anything
> other
> than an independent variable.
>
> I think you'll have to find out what underlying SD library your example is
> using, and then read through the documentation of that library to see how
> to
> approach the issue. Alternatively, you can of course define a function
> g_of_x
> and another g_of_y, and depending on whether you want to compute the
> derivative with regard to x or y, you choose one or the other.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
>
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