My view here is that the problem is quasi-static and hence time serves to order events. Hence a displacement increment can be viewed as equivalent to the velocity.
For example, let’s fix the number of time-steps to 10. If the total time is 1s or 10s we should get the same results (assuming the timing of the application of loading is scaled based on the assumption that time simply order events). Best, Andrew > On 27 Jun 2021, at 02:19, Michael Li <lianxi...@gmail.com> wrote: > > Hi Jean-Paul, > Thank you for the nice explanation and information! It cleared out my concern > and helped me understand the related concepts of vorticity and rotation. > Vorticity (1/2 curl of velocity) stands for the rotation rate (angular > velocity) but the infinitesimal rotation tensor gives the rotation angle > (curl of displacement). Do correct me if I’m wrong. > > Now I’m excited to learn how to make my first patch. > > - Michael > > From: Jean-Paul Pelteret <mailto:jppelte...@gmail.com> > Sent: Saturday, June 26, 2021 2:57 PM > To: dealii@googlegroups.com <mailto:dealii@googlegroups.com> > Subject: Re: [deal.II] Questions on Step-18 > > Hi Michael, > > What’s written in the implementation suggests that computing the curl of the > displacement (increments) is the right thing to do in this instance: > > Nevertheless, if the material was prestressed in a certain direction, then > this direction will be rotated along with the material. To this end, we have > to define a rotation matrix R(Δun) that describes, in each point the rotation > due to the displacement increments. It is not hard to see that the actual > dependence of R on Δun can only be through the curl of the displacement, > rather than the displacement itself or its full gradient (as mentioned above, > the constant components of the increment describe translations, its > divergence the dilational modes, and the curl the rotational modes). > > I think that this is because the displacement field for solids is analogous > to the velocity field for fluids, for which that equation in the Wiki link > was expressly written (Compare incompressible linear elasticity to Stokes > flow — the equations have the same form). Furthermore, having dug through my > continuum mechanics notes, I now see that this specific rotation matrix is > called the “infinitesimal rotation tensor > <https://antoniobilotta-structuralengineer.github.io/MyWebSite/SMbook_en/infinitesimal_sec_strain_chap_en.html>” > and is defined as the antisymmetric part of \grad u. Since step-18 is > dealing with incremental updates, the incremental form of the rotation tensor > is computed. > > Sorry for the confusion. So, to my understanding it’s just the factor of 1/2 > that needs to be added. > > Best, > Jean-Paul > > > On 26. Jun 2021, at 16:14, Michael Lee <lianxi...@gmail.com > <mailto:lianxi...@gmail.com>> wrote: > > I would be happy to do the comparison and make the fix. But before doing > that, I want to make sure I understand the formula correctly. > > When we calculate the rotation matrix, it seems that the du (incremental > displacement) is used. > // Then initialize the <code>FEValues</code> object on the present > // cell, and extract the gradients of the displacement at the > // quadrature points for later computation of the strains > fe_values.reinit(cell); > fe_values.get_function_gradients(incremental_displacement, > displacement_increment_grads); > > Should we use the velocity (), since ? > > Can you check this as well? > > > Best, > Michael > > > > > > > On Sat, Jun 26, 2021 at 1:48 AM Jean-Paul Pelteret <jppelte...@gmail.com > <mailto:jppelte...@gmail.com>> wrote: > Following Andrew’s explanation, I suppose that this is relation for which > we’re lacking the factor of 1/2, right? > > https://en.wikipedia.org/wiki/Angular_velocity#Angular_velocity_as_a_vector_field > > <https://en.wikipedia.org/wiki/Angular_velocity#Angular_velocity_as_a_vector_field> > > If so, then maybe we should link to this equation in the tutorial > documentation too. > > If this is wrong in the deal.II code, would you be interested in writing a > patch to correct this? It should be an easy fix, and a good first patch to > contribute to the library! > > I concur — it would be great if you’d be willing to write a patch that fixes > this! It would be interesting to see the effect on the results of the > tutorial. > > Best, > Jean-Paul > > > > On 26. Jun 2021, at 05:58, Wolfgang Bangerth <bange...@colostate.edu > <mailto:bange...@colostate.edu>> wrote: > > On 6/24/21 6:32 PM, Michael Li wrote: > > Andrew, thanks for confirming that. The missing 1/2 does not affect the > demonstration of functionalities of deal.II but it may change the results. > > If this is wrong in the deal.II code, would you be interested in writing a > patch to correct this? It should be an easy fix, and a good first patch to > contribute to the library! > > If you're curious about ho to write a patch, take a look at > https://github.com/dealii/dealii/wiki/Contributing > <https://github.com/dealii/dealii/wiki/Contributing> > > Best > W. > > > > On Sat, Jun 26, 2021 at 1:48 AM Jean-Paul Pelteret <jppelte...@gmail.com > <mailto:jppelte...@gmail.com>> wrote: > Following Andrew’s explanation, I suppose that this is relation for which > we’re lacking the factor of 1/2, right? > > https://en.wikipedia.org/wiki/Angular_velocity#Angular_velocity_as_a_vector_field > > <https://en.wikipedia.org/wiki/Angular_velocity#Angular_velocity_as_a_vector_field> > > If so, then maybe we should link to this equation in the tutorial > documentation too. > > If this is wrong in the deal.II code, would you be interested in writing a > patch to correct this? It should be an easy fix, and a good first patch to > contribute to the library! > > I concur — it would be great if you’d be willing to write a patch that fixes > this! It would be interesting to see the effect on the results of the > tutorial. > > Best, > Jean-Paul > > > > On 26. Jun 2021, at 05:58, Wolfgang Bangerth <bange...@colostate.edu > <mailto:bange...@colostate.edu>> wrote: > > On 6/24/21 6:32 PM, Michael Li wrote: > > Andrew, thanks for confirming that. The missing 1/2 does not affect the > demonstration of functionalities of deal.II but it may change the results. > > If this is wrong in the deal.II code, would you be interested in writing a > patch to correct this? It should be an easy fix, and a good first patch to > contribute to the library! > > If you're curious about ho to write a patch, take a look at > https://github.com/dealii/dealii/wiki/Contributing > <https://github.com/dealii/dealii/wiki/Contributing> > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bange...@colostate.edu > <mailto:bange...@colostate.edu> > www: http://www.math.colostate.edu/~bangerth/ > <http://www.math.colostate.edu/~bangerth/> > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <https://groups.google.com/d/forum/dealii?hl=en> > --- You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/32840123-c6f5-abd9-18bb-03f06b5f918e%40colostate.edu > > <https://groups.google.com/d/msgid/dealii/32840123-c6f5-abd9-18bb-03f06b5f918e%40colostate.edu>. > > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <https://groups.google.com/d/forum/dealii?hl=en> > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/1D258AD6-FC4C-43B7-9056-A4B21114D694%40gmail.com > > <https://groups.google.com/d/msgid/dealii/1D258AD6-FC4C-43B7-9056-A4B21114D694%40gmail.com?utm_medium=email&utm_source=footer>. > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <https://groups.google.com/d/forum/dealii?hl=en> > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/CAEyr2zhNeyCO_tyXpw%2Bzgh4DAwzCmAGHG5W9y8RnLMswq_O10A%40mail.gmail.com > > <https://groups.google.com/d/msgid/dealii/CAEyr2zhNeyCO_tyXpw%2Bzgh4DAwzCmAGHG5W9y8RnLMswq_O10A%40mail.gmail.com?utm_medium=email&utm_source=footer>. > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <https://groups.google.com/d/forum/dealii?hl=en> > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/1ADF3B07-54FB-4DDA-A848-1D7F9168D4A6%40gmail.com > > <https://groups.google.com/d/msgid/dealii/1ADF3B07-54FB-4DDA-A848-1D7F9168D4A6%40gmail.com?utm_medium=email&utm_source=footer>. > > > -- > The deal.II project is located at http://www.dealii.org/ > <http://www.dealii.org/> > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > <https://groups.google.com/d/forum/dealii?hl=en> > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/99FD763E-ABDF-46F5-A62C-D4427C562103%40hxcore.ol > > <https://groups.google.com/d/msgid/dealii/99FD763E-ABDF-46F5-A62C-D4427C562103%40hxcore.ol?utm_medium=email&utm_source=footer>. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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