Why we need the Volumetric-Deviatoric Split

This video is part of a series of videos on continuum mechanics (see playlist: • Continuum Mechanics .
The volumetric-deviatoric split (or dilatational-distortional split) is an important concept in continuum mechanics. The strain tensor is split into a shape-preserving and a volume-preserving part, which is useful for example in the context of material modeling.
Keywords: continuum mechanics, solid mechanics, material model, constitutive law, linear elasticity, Poisson effect, small strain elasticity, infinitesimal strain elasticity, Cauchy stress tensor, volumetric, dilatational, hydrostatic, spherical, deviatoric, distortional, isochoric
Music:
Prelude 2 - VGM Mark H / prelude-2
Abandond Station - VGM Mark H / abandoned-station

[@arods]

I have a Ph. D. in mechanics and years of experience as a researcher. Your video is amazingly well explained and quite pedagogical. Congratulations!

[@DrSimulate]

Thank you so much!!

[@CarryModeActive]

Ich schreibe in ein paar Tagen Festkörpermechanik und die Herleitung vom Split ist immer gefordert. Durch die Visualisierung ist mir gerade nochmal einiges klarer geworden :D Merci!

[@5eurosenelsuelo]

I had to rewatch it a few times because it's not a simple topic but the explanation is absolutely fantastic. Thank you very much for sharing.

[@DrSimulate]

@@5eurosenelsuelo Thank you 😁

[@vineethravi3493]

Your channel has recieved a good amount of subscribers, I believe. Keep up with the good content.

[@DrSimulate]

Thanks :)

[@AhmedAli-ew2eh]

Thank you for these videos. This is one of my favourite channels. I hope you do some videos on isogeometric analysis.

[@DrSimulate]

@@AhmedAli-ew2eh Oh, that's an interesting suggestion. I will consider it! :)

[@mirmashrafiahasan6459]

It would be great if you provide some resources of rigorous mathematical explanation of the formula you have provided. And obviously great visuals. Thanks for putting in so much time and energy for us.

[@DrSimulate]

Thanks :) are you referring to a specific equation or a rigorous mathematical treatment of the problem in general?

[@JérémieKouotang]

Wonderful simulation

[@benvanzon3234]

Looking forward to see your video about linear isotropic elasticity! I am currently doing my thesis partially on anisotropic linear continuum mechanics, where I study phonon tunneling and it's quite a challenging subject

[@DrSimulate]

@@benvanzon3234 It sounds challenging indeed! All the best for your thesis! Unfortunately, I may not cover anisotropy in the next video, but for sure at some point in the future :)

[@benvanzon3234]

@@DrSimulate Thank you very much! It's great to hear that you're also making quite a bunch of videos about linear elasticity, for some reason there arent many on youtube. If you're looking for a great resource on acoustic fields and waves + their interaction with piezoelectrics, I recommend "Acoustic Fields and Waves in Solids, 2nd Edition," by B.A. Auld.

[@DrSimulate]

@@benvanzon3234 Thanks, i didn't know the book. Regarding elasticity videos, you may check out the channel by Clayton Pettit

[@ishfaqtakkar210]

You're genius!! Hats off!

[@DrSimulate]

@@ishfaqtakkar210 Thanks :)

[@changename5954]

Das ist wirklich gut, besten Dank!

[@DrSimulate]

Gern :)

[@kamalahmadov4418]

I am eager for the next part. Could you please share any documentation or resources where I can explore this topic further?

[@DrSimulate]

If you are looking for full lectures, check out this channel: www.youtube.com/@ClaytonPettit

[@Prashanth-yn9zd]

Amazing explanation!! Thank you, It would be great if you could make videos on Non-linear continuum mechanics in the future!!

[@DrSimulate]

Yes, I hope I can make it soon ... :)

[@vinitfirke2201]

Your videos are amazing. Weiter so!

[@DrSimulate]

@@vinitfirke2201 Danke :)

[@user-oo2si4oy1g]

Thanks for this excellent explanation of volumetric and deviatoric strain-it really helped clarify the concepts! One quick question: I often see the terms ‘dilation,’ ‘dilatation,’ ‘hydrostatic strain,’ ‘mean normal strain,’ and ‘volumetric strain’ used in various texts. Are these essentially referring to the same concept (the isotropic part of strain that changes volume), or are there subtle distinctions between them? I’d love to hear your insight on how (or if) they differ.

[@DrSimulate]

I would say that the terms "dilatiational strain", "hydrostatic strain", "volumetric strain" can all be used interchangeably. The mean normal strain is something else. The dilatiational/hydrostatic/volumetric strain is a tensor, but the mean normal strain should be a scalar value.

[@bhavaniprasad5396]

the explanation was speechless

[@TheAncientColossus]

When will you provide the 81 parameter constitutive model? Or symmetry of the compliance tensor? Isotropic, transversely isotropic, orthotropic, anisotropic, plane stress, plane strain, elastic, inelastic concepts? Maybe after this, yielding?

[@DrSimulate]

All of this is planned at some point, but producing the videos takes a lot of time :/ thanks for your patience :)

[@TheAncientColossus]

8:22 How is this purely deviatoric tensor different from the second invariant, which represents the deviatoric? This makes no sense. Why are there two definitions for a single parameter?

[@DrSimulate]

@@TheAncientColossus Do you mean the invariant 1/2 dev(eps) : dev(eps)?

[@TheAncientColossus]

@DrSimulate No the second invariant of any 2nd order tensor is: 1/2 tr(A)^2 - tr(A^2)