The Strain Tensor and its Weird Formula

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  • Опубліковано 29 січ 2025

КОМЕНТАРІ • 60

  • @DrSimulate
    @DrSimulate  10 місяців тому +23

    Hi, in this video I use the gradient of the displacement without much elaboration. Would you be interested in a video on gradient, divergence and rotation of fields?

    • @Cookstein2
      @Cookstein2 10 місяців тому +3

      Oh go on then

    • @erayyildiz9562
      @erayyildiz9562 10 місяців тому +1

      Absolutely.

    • @sagsolyukariasagi
      @sagsolyukariasagi 10 місяців тому +1

      Keep going on! Perfect explanations with great visualizations. I stuck at large deformations (differential geometry, tangent spaces), I hope you touch them in future, too.

    •  9 місяців тому +1

      of course!

    • @stitaswain7349
      @stitaswain7349 5 місяців тому +1

      Yes very much. Plz keep explaining topics in such beautiful manner.

  • @meer911
    @meer911 10 місяців тому +3

    High quality stuff you putting out here. Nailing the animations and the concept flow. Would love to see more from you.

    • @DrSimulate
      @DrSimulate  10 місяців тому

      Thanks a lot! Appreciate it 🚀✨

  • @jimpal5119
    @jimpal5119 10 місяців тому +3

    Excellent explanation and visuals! Would love a video covering any nonlinear topic!

    • @DrSimulate
      @DrSimulate  9 місяців тому +2

      Thanks a lot! :) More videos on nonlinear continuum mechanics are planned. I find nonlinear CM very interesting but it was hard to understand when I saw it the first time ...

  • @vasiliisivovol7943
    @vasiliisivovol7943 2 місяці тому +1

    Thank you for your work! This invaluable information was explained clearly.

  • @josuecorleto569
    @josuecorleto569 6 місяців тому +1

    Great explanation! I like the use of animations to illustrate these concepts.

  • @Cookstein2
    @Cookstein2 10 місяців тому +3

    Great! looking like the start of a valuable series of videos

  • @Alfurwan
    @Alfurwan 9 місяців тому +2

    i love how your videos always leave me smarter than before!

  • @prateekskaushik
    @prateekskaushik 6 місяців тому +2

    Really well explained, thank you for providing such qualitative content!

  • @vegetablebake
    @vegetablebake 4 місяці тому +2

    Another great intuition explained visually.

  • @yunusemresurmeli9980
    @yunusemresurmeli9980 10 місяців тому +2

    Great video, I liked the detailed philosophy of this topic. I'm waiting for other videos.

  • @thescientist1839
    @thescientist1839 8 місяців тому +1

    Keep making videos man. Slowly your channel will get 1 M subscriber within a year.

    • @DrSimulate
      @DrSimulate  8 місяців тому

      Thank you so much! ❤️

  • @amarug
    @amarug 5 місяців тому +2

    Well done, love it!

  • @interhaker
    @interhaker 9 місяців тому +1

    A beauty to behold.
    Keep us posted the algorithim will definitely make you blow up

  • @PK24_Singh
    @PK24_Singh 2 місяці тому +1

    Well thanks for the mathematical interlude that helps the understanding! How was that arrived at..must be some story behind it?

  • @apoorvvyas52
    @apoorvvyas52 9 місяців тому +2

    Good explanation. Good topic. Good animations. Overall an excellent video. Please also cover computational fluid dynamics topics also in some of your videos.

  • @joaopedrorocha5693
    @joaopedrorocha5693 Місяць тому

    This was amazing! Thanks!

  • @CAEProfHan
    @CAEProfHan 2 місяці тому +1

    great video! Thank you.

  • @rezaafshar3832
    @rezaafshar3832 8 місяців тому +1

    Superb videos! thanks a lot. Keep it up!

  • @elshons1576
    @elshons1576 10 місяців тому +2

    Can you do a video about finite strain and why is defined as the difference of squares of two infinitesimal line segments?

    • @DrSimulate
      @DrSimulate  9 місяців тому +1

      I want to do a video about finite strain and the different strain measures. Stay tuned :)

  • @Bledy49
    @Bledy49 9 місяців тому +2

    Great video, what's your background?

    • @DrSimulate
      @DrSimulate  9 місяців тому

      Thanks! I studied computational engineering and did my PhD in computational mechanics :)

  • @shivamrajput6368
    @shivamrajput6368 9 місяців тому +2

    Thankyou for visualising this concept using animation…. I am currently working on large deformation, can you please suggest me some related resources.

    • @DrSimulate
      @DrSimulate  9 місяців тому

      I worked a lot with "Nonlinear Solid Mechanics" by Gerhard Holzapfel, but I find it a bit too detailed for a beginner. Let me know if you come across a more didactic explanation. I would be very interested! :)

  • @Prashanth-yn9zd
    @Prashanth-yn9zd 5 місяців тому +1

    The gradient of displacement tensor is zero for the translation of a body coz, translation is defined as u(x) = u_0, where u_0 is constant

    • @DrSimulate
      @DrSimulate  5 місяців тому +1

      That's right. Do I say something contradicting in the video? If yes, can you tell me were? :)

    • @Prashanth-yn9zd
      @Prashanth-yn9zd 5 місяців тому +1

      @@DrSimulate sorry, you did not say anything contradicting. I added this info so that if someone wants to know why the displacement tensor is zero for the translation, they can find it in the comment section.

    • @DrSimulate
      @DrSimulate  5 місяців тому +1

      @@Prashanth-yn9zd Ahh, I see. Thanks, appreciate it! :D

  • @edhead76
    @edhead76 9 місяців тому +2

    I'm learning about tensors in AI, and tensors have been making my mind mush for a few days. Visual aids really help, even when the physics is a bit over my head. Nice video!

  • @imaginarynumber416
    @imaginarynumber416 8 місяців тому +1

    Hi could you make a video about the material and spatial coordinates with intuitive explanation?

    • @DrSimulate
      @DrSimulate  8 місяців тому

      Hey, it's definitely planned, but unfortunately not in the immediate future, because I want to finish other videos first. Stay tuned and thanks for your patience :)

  • @lorenzoferrara8652
    @lorenzoferrara8652 7 місяців тому

    Very good explanation!
    A question: how can we link the skew-simmetric part of the displacement gradient to the rotation?
    Thanks

  • @RahulSuresh-r2y
    @RahulSuresh-r2y Місяць тому

    I have a doubt. When the rotation is done, I find that the cube side dimension will increase..i.e. the point at origin is same, but the point on the X3 axis shifts right, so length increased. Then there is strain no?
    I took x = X + U for transformation.
    Can you please explain?

    • @DrSimulate
      @DrSimulate  Місяць тому

      @@RahulSuresh-r2y You are right. This is all under the small strain assumption. For large strains, this displacement field would describe a rotation and deformation of the infinitesimal element.

  • @plutothetutor1660
    @plutothetutor1660 8 місяців тому +2

    It's notable that (A + A^T)/2 is always diagonalisible.

    • @DrSimulate
      @DrSimulate  8 місяців тому

      May be addressed in a future video :)

  • @TheChoosenBoi
    @TheChoosenBoi 10 місяців тому +2

    Very Nice channel

  • @hamzazaheer3783
    @hamzazaheer3783 10 місяців тому +2

    Thanks for your Videos. I am fresh graduate in mechanical engineer (BS). I want to get into computational simulation especially multiscale modelling of composite. Right now i am learning continuum mechanics and FEA (Basic Concept). Do you have any advice for me ?

    • @DrSimulate
      @DrSimulate  10 місяців тому

      Sounds great! 💪If you want to learn multiscale modeling, check out these unsurpassable lecture notes by Dennis Kochmann: ethz.ch/content/dam/ethz/special-interest/mavt/mechanical-systems/mm-dam/documents/Notes/CompMultMod_Notes.pdf

    • @hamzazaheer3783
      @hamzazaheer3783 10 місяців тому +1

      @@DrSimulate Thanks for your help . Can't wait to see your upcoming videos.

  • @aj-uo3uh
    @aj-uo3uh 5 місяців тому

    "The gradient of the displacement field" Displacement is a function from R^3 to R^3 while the gradient (looking at wikipedia) works on functions from R^3 to R. So for me its not clear what this means.

    • @aj-uo3uh
      @aj-uo3uh 5 місяців тому +1

      Ah I see a little further in the video you mean with gradient what I would call the total derivative. Never mind :)

  • @VahidNegahdari
    @VahidNegahdari Місяць тому

    thanks

  • @VahidNegahdari
    @VahidNegahdari Місяць тому

    The examples provided were not rotations at all.
    Note that a rotation matrix cannot have a row of zeros.

    • @DrSimulate
      @DrSimulate  Місяць тому

      @@VahidNegahdari Here you are mixing two different concepts. You are talking about rotation matrices that if multiplied by a vector rotate that vector. I'm not talking about those in this video. :)