Why we need the Volumetric-Deviatoric Split

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

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[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!

[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!

[eurosenelsuelo]

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.

[BCarli]

Thank you. This is very helpful, well done.

[vineethravi]

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

[AhmedAli-eweh]

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

[benvanzon]

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

[mirmashrafiahasan]

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.

[Prashanth-ynzd]

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

[oosioyg]

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.

[kamalahmadov]

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

[arash]

Hi,
It was fantastic! Thanks.
I am thinking if the deviation at 7:28, is the only solution to fulfil the condition?

[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?

[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?