The strain tensor and its weird formula

This video is part of a series of videos on continuum mechanics (see playlist: • Continuum Mechanics .
The strain tensor is a mathematical construct to quantify the deformation of matter in continuum mechanics. But the formula for the strain tensor looks unintuitive at a first glance. In this video, the (small or infinitesimal) strain tensor is introduced, and its formula is explained.
Keywords: continuum mechanics, solid mechanics, fluid mechanics, partial differential equations, boundary value problems, linear elasticity, small strain elasticity, infinitesimal strain elasticity, kinematics
Music:
Prelude 2 - VGM Mark H / prelude-2
Abandond Station - VGM Mark H / abandoned-station

[@ComputationalModelingExpert]

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]

Oh go on then

[@erayyildiz9562]

Absolutely.

[@sagsolyukariasagi]

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.

of course!

[@thescientist1839]

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

[@ComputationalModelingExpert]

Thank you so much! ❤️

[@apoorvvyas52]

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

[@ComputationalModelingExpert]

Thank you!!!

[@meer911]

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

[@ComputationalModelingExpert]

Thanks a lot! Appreciate it 🚀✨

[@jimpal5119]

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

[@ComputationalModelingExpert]

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 ...

[@rezaafshar3832]

Superb videos! thanks a lot. Keep it up!

[@yunusemresurmeli9980]

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

[@ComputationalModelingExpert]

Thank you !! ♥

[@Alfurwan]

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

[@ComputationalModelingExpert]

[@Cookstein2]

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

[@ComputationalModelingExpert]

Thanks :D

[@interhaker]

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

[@edhead76]

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!

[@ComputationalModelingExpert]

Thanks!

[@plutothetutor1660]

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

[@ComputationalModelingExpert]

May be addressed in a future video :)

[@Bledy49]

Great video, what's your background?

[@ComputationalModelingExpert]

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

[@elshons1576]

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

[@ComputationalModelingExpert]

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

[@lorenzoferrara8652]

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

[@shivamrajput6368]

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

[@ComputationalModelingExpert]

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! :)

[@TheChoosenBoi]

Very Nice channel

[@ComputationalModelingExpert]

Thanks! :)

[@imaginarynumber416]

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

[@ComputationalModelingExpert]

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 :)

[@hamzazaheer3783]

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 ?

[@ComputationalModelingExpert]

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]

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