Dear Jean-Paul,
Thank you very much for your answer.
I still have to figure out some of the calculations you suggested me to do,
but I got the concepts and the reason why the gradients are defined on the
deformed configuration rather than on the initial one.
Best,
Claire
Le lundi 7 novembre 2016 19:35:18 UTC+1, Jean-Paul Pelteret a écrit :
>
> Dear Claire,
>
> You are right that this is a total Lagrangian formulation but that doesn't
> mean that one is restricted to defining the problem in terms of fully
> referential quantities.
>
> One can arrive at the same conclusion from a number of starting points,
> but ultimately its because we'd chosen to integrate spatial quantities on
> the reference configuration. Along with that, following from the weak form
> we need shape functions defined in the spatial configuration in order to
> perform the integration correctly. These can be computed using the chain
> rule: d/dx_{j} [N^{I}] = d/dX_{K} [N^{i}] . dX_{K}/dX_{j} = d/dx_{j}
> [N^{I}] . F^{-1}_{jK}.
>
> Does that help at all? Its a good exercise to derive the variational
> problem with a fully referential or two-point description, and then with
> some relatively simple (although tedious) manipulations you would end up
> with the formulation adopted in the tutorial.
>
> Best,
> Jean-Paul
>
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