Talk:Continuum mechanics

Taxonomy

I disagree with the definition of continuum mechanics (at least, in concert with the continuum postulate page). As it stands, the continuum postulate definition requires both a fluid and a solid, but elasticity (physics) does not study fluids at all. So, this cannot be correct.

The common definition of continuum mechanics is that it approximates solids and fluids as continuous material (ignoring the existence of atoms). Therefore, differential equations are an appropriate mathematical method.

Support for this view on the Web is at [1][2].

I'll attempt a fix in a day or so, pending comments from others. -- hike395 15:22, 5 Nov 2003 (UTC)

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I've never heard the term "solid mechanics" used, and I've done work in continuum mechanics (years ago). Rheology is also a sub-field, not a super-field of continuum mechanics. -- hike395 01:38, 8 Feb 2004 (UTC)

My understanding of rheology is that it embraces the deformation of materials in general, without making any assumptions about being a continuum so it could treat materials with granular structure, powders, mixtures or suspensions. I hold no brief for rheology but want to sort out the mess that is rheology, continuum mechanics, fluid mechanics (v. poor at the moment), strength of materials, elasticity and plasticity. In what ways does continuum mechanics differ from rheology if the latter is a sub-field? Cutler 01:46, 8 Feb 2004 (UTC)

I agree that the taxonomy for these fields in Wikipedia is poor at the moment. My memory is that papers on rheology mostly covered non-Newtonian fluids like polymers, which would make it a branch of fluid mechanics. For example, see the abstracts at [3]. The number of people who say they study rheology seems to be smaller than the number who study fluid mechanics (who seem to call themselves "Applied Mathematicians" or "Aeronautical Engineers", anyway).

I've also heard "elasticity" used for both the theory of solids (what you call "solid mechanics") and, of course, for the linear stress/strain property that is well known. Maybe we should make one of the pair (Elasticity theory,Solid mechanics) be an overview of the physics of solid continua, and the other be a redirect? Then, Elasticity and Plasticity can just refer to properties of solid matter.

The other thing to note is that the theory of elasticity covers liquid-like materials in two ways:

1. Plastic materials that yield above a certain stress level.
2. Viscoelastic materials that have velocity-dependent internal forces.

So, it isn't a clean distinction, anyway.

Given that the taxonomy is in a mess, is there any standards body that we can appeal to that has figured this out? -- hike395 07:03, 8 Feb 2004 (UTC)

I agree that the rheology stuff you see in general is about non-Newtonian fluids but I think that is because all the other ground has been taken by conventional disciplines and that's all that's left to the newer discipline. However, I suspect that the ambition of the rheologists is wider and all-embracing. The definition in the article is the same as on the Society of Rheology website so I think that the words are right, it's really a discussion about usage we're having here. Prehaps we should try modifying the rheology article and see what response we get.

Using the term elasticity to cover elasticity and plasticity seems to me to pose some problems. What do we then call the elastic regime and how differentiate it? We could use the shear stress concept but that might be a barrier to those requiring a simple account.

What would work for me would be

Big subject rheology?	Other stuff: aggregates, suspensions, powders
	Continuum mechanics	Solid mechanics or strength of materials	Elasticity
			plasticity (physics)	some overlap - rheology?
		Fluid mechanics	non-Newtonian
			Newtonian

Cutler 12:56, 8 Feb 2004 (UTC)

I think I have an idea. What is the study of all materials, regardless of state (i.e., continuous, crystalline) ? Why, materials science, of course. So, the hierarchy (on the physics/science side) could be

• Materials science (physics of any material)
  • Crystallography
  • Solid-state physics
  • Physics of powders (etc.)
  • Continuum mechanics
    • Solid mechanics/Theory of elasticity (one is article, other is redirect)
      • Elasticity (physics)
      • Plasticity (physics)
    • Fluid mechanics/Fluid dynamics (some debate about this: one is article, other is redirect)
      • Aerodynamics (study of things that fly)
      • Computational fluid dynamics
      • Newtonian fluid mechanics
      • Rheology/Non-newtonian fluid mechanics
• Mechanical Engineering (engineering related to materials)
  • Materials Engineering (rolling, sintering, etc.)
  • Strength of materials (engineering aspects of solid mechanics)
  • Aeronautics
  • Pneumatics
  • Hydraulics
  • Metallurgy

I think that making rheology the top-level wouldn't be consistent with common usage. In order to make the articles NPOV, however, we should mention in the text of both Materials science and rheology that rheology claims to cover any material that flows or deforms, although practically rheologist study non-Newtonian fluid mechanics.

Comments? --- hike395 05:00, 9 Feb 2004 (UTC)

No comments, so I went ahead and did edits for the material science & solid mechanics branch of the tree. -- hike395 06:50, 13 Feb 2004 (UTC)

What must be avoided is a situation where if a user looks at continuum mechanics they get one account of the world but if they look at rheology they get another and at strength of materials yet another and I've been struggling with how to make that possible. How do you feel about the table:

Continuum mechanics	Solid mechanics or strength of materials	Elasticity
		Plasticity	There is an overlap here as plastic solids have some properties characteristic of fluids. This broader subject is sometimes knows as rheology.
	Fluid mechanics	non-Newtonian fluids
		Newtonian fluids

We then need to make this OK for the rheologists. The thing is, the same table needs to appear in rheology or it will look weird to the uninitiated. BTW, I have recently redone viscosity if you are interested.Cutler 11:09, 13 Feb 2004 (UTC)

It's OK with me. --- hike395

Done it - rheology. Let's see how long it lasts. Any comments? What is still missing in continuum mechanics is some indication of how far the assumption of continuity can be stretched. Does the subject embrace colloids? What are the practical limits? I don't know the answer so it would help me. Cutler 11:37, 13 Feb 2004 (UTC)

I don't know the answer to your questions --- I learned solid mechanics as mathematical physics. -- hike395 18:43, 14 Feb 2004 (UTC)

A 1980 author writes "constitutive equations are also required in other branches of continuum physics, such as continuum thermodynamics and continuum electrodynamics" so "continuum whatever" is a big group, anything that models matter as continuous stuff. IDave2 (talk) 15:43, 23 September 2009 (UTC)

Not a regular wiki-person, but I saw a few glaring errors in

the elasticity / continuum mechanics and related articles

1) Strength of materials is definitely NOT the same as the theory of elasticity. It is an engineering approach to solve solid mechanics problems with large contributions from people like Timoshenko in the early 20th century. The 'strength of materials' approach (almost) entirely avoids the elastic field equations and their solutions.

2) The definition of elastic material provided here is incorrect. Briefly, an elastic material is one in which the work done by external forces acting on the body is stored as (and is equal to) the Elastic Potential Energy, which is completely recoverable on unloading. Thus it is perfectly possible to have non-linear elastic materials.

3) You don't 'apply stress', you apply loads. Stress is a DEFINED quantity, as opposed to loads (forces). For example, it is convenient to define the stress as a symmetric second-rank tensor but it is possible to define an alternative, asymmetric stress (Lagrangian stress)

Thanks for your views. Be bold and make an edit. This whole area would benefit from a few extra informed editors. However, please note that this is an encyclodaedia so we should give a general description that it intelligible to the bright 12-year-old and then proceed to an exact definition that would be meaningful to an expert. Cutler 09:42, 18 February 2006 (UTC)

link to or section describing lagrangian vs eulerian descriptions?

I've looked around for a while, and couldn't find any article describing the Eulerian and Lagrangian descriptions of a deforming material. This leads me to suggest that either someone create such an article, or, if it exists, make its presence more obvious, or, if it is plenty obvious, please tell me where to find it. My homework grade thanks you. 128.83.69.57 02:35, 10 March 2007 (UTC)

Editions April 13 2008

I started including introductory topics of continuum mechanics. So far, sections on the concept of continuum, configuration of a continuum, and kinematics of a continuum have been included. There is still a lot more to write. Sections on conservation of mass, conservation of momentum, conservation of angular momentum, thermodynamic laws... are needed. This article should be the portal to solid mechanics and fluid mechanics. There should be a logical flow from this article to these other articles. Please review in detail what I have written, specially the equations. I think the writing also needs some improvement.--Sanpaz (talk) 04:10, 14 April 2008 (UTC)

Merger of convective derivative into continuum mechanics

Why do you (Sanpaz) want convective derivative to be merged into continuum mechanics? Crowsnest (talk) 21:23, 19 April 2008 (UTC)

The topic of Convective derivative does not seem to need its own article. This topic can be placed within the Continuum mechanics article and still retain all its content. Additionally, it brings the content of the article into context. However, If the Convective derivative topic needs to be expanded later then the page should be re-open. Sanpaz (talk) 23:16, 19 April 2008 (UTC)

As far as I am concerned: go ahead. However, it is important that people can find "convective derivative", if they search for it. So I would suggest that in the case of a merger, convective derivative becomes a redirect to the appropriate article or section. Crowsnest (talk) 07:18, 21 April 2008 (UTC)

Please note there are many redirects to here, e.g. advective derivative, substantive derivative, substantial derivative, material derivative, Lagrangian derivative, Stokes derivative and particle derivative. Crowsnest (talk) 11:40, 22 April 2008 (UTC)

I'm against this. I think the topic deserves it's own article; it's a big enough concept. — Ben pcc (talk) 22:41, 10 May 2008 (UTC)

Ok, I will take the merging label off Sanpaz (talk) 23:09, 10 May 2008 (UTC)

The name of the article

To me the name Continuum mechanics doesn't make any sense and wander why not something like Mechanics of continuous media or even something better. --Gulmammad (talk) 16:04, 20 May 2008 (UTC)

Continuum mechanics is a well established term. For instance Google Books gives over 800 results when searching on "continuum mechanics" in the book title, and Google Scholar over 2000 articles with the exact phrase in the title. Further, in my view, the name makes sense: just like particle mechanics describes the mechanics of particles, continuum mechanics describes the mechanics of a continuum. Crowsnest (talk) 21:17, 20 May 2008 (UTC)

Actually in above I meant Continuous instead of Continuum. And what I was wandering at was those results of Google, almost no-one uses "my version" of the name, while one of the Landau edition books, vol. 8, has similar name, Electrodynamics of Continuous Media. --Gulmammad (talk) 21:36, 22 May 2008 (UTC)

Continuous media already redirects here. Perhaps Mechanics of continuous media is another good redirect to add, and include this phrase in the head of the article. I would leave the name of the article as it is now. – Crowsnest (talk) 21:56, 22 May 2008 (UTC)

Empty Space

While most believe that matter is a bundle of energy separated by empty space, this is not true. There is no empty space in the universe. All space where matter doesn't exist is permeated by fields: electromagnetic and gravitational to say the least. It is the fundamental essence of space that permits matter to exist. Thought experiment time: close a box and draw a perfect vacuum. Remove all matter and then all energy and fields from it. What are the physical properties of the inside of this box? It has no mass, no fields, no energy. This is the definition of nothing, yet when you open the box the universe fills it right back up. Nothing has the ability to support matter and energy. This is in itself a physical property and therefore the space is not empty. It is potential. —Preceding unsigned comment added by 75.70.62.142 (talk) 16:09, 30 December 2008 (UTC)

Question of 'b'

Hi all, I'm wondering if we can remove the coordinate system vector 'b' from this introductory page. It is only used once, which usually leaves me wondering "where did this come from?", and is promptly dispensed with after being mentioned. I am browsing four CM books and only one (Chung) explicitly mentions a warped coordinate system traveling with the particle. I see that such an approach introduces (in addition to 'b') three more axis vectors and lets one write some expressions with a vector-type notation rather than summation or matrix notation, but it is not required to obtain the important CM operators like Jacobian, stress and rate of change of strain tensors, and so on, and I think the article would be less cluttered and better as an intro if we (quietly) don't mention 'b' and its (optional) coordinate system. Thoughts? IDave2 (talk) 20:40, 26 September 2009 (UTC)

Question of balance

I would guess that solid mechanicians don't expect new steel to "flow into" their steel bars but, if it did, then wouldn't this invalidate the Jacobian assumption? For example, if some new oil just flowed into my deformed body (gross!) then there is no (inverse) mapping relating it to the reference body (because it does not exist in the reference body) so we can no longer use J or F like before? IDave2 (talk) 21:35, 26 September 2009 (UTC)

Physicists have very little to do with Continuum Mechanics

I believe it is not reasonable to consider Continuum Mechanics a branch of physics. Only a tiny proportion of research into continuum mechanics over the last 60 years or so has been performed by physicists - (a notable exception being magnetohydrodynamics, because of its importance for the study of plasmas in stars & planets). Most "famous" physics departments (at least in the US) have almost no one working in continuum mechanics. The theoretical work is done by applied mathematicians and practical work by engineers. Very few physicists sit on the editorial boards of mechanics journals. I think it is reasonable to say that physicists have no more than an elementary understanding of the behavior of deformable continua - an average physicist's idea of "mechanics" (at the mesoscale) begins and ends with rigid bodies and "potential" fluid flows.

The reasons for this are interesting and multi-fold - the explosive, "headline grabbing" developments in atomic and modern physics in the 20th century being one of them. At any rate, I don't think it should be classified as a branch of physics any more. Commutator (talk) 07:30, 18 October 2009 (UTC)

You just stated an opinion, with no reference. Continuum Mechanics is a branch of physics that uses a mathematical theory (continuum theory). Whether physicists, engineers, or mathematicians use it more or not at all is another issue, which does not take away the fact that it is a theory to interpret the physical world. Please read Continuum Mechanics by Irgens page 2, and also Continuum Mechanics by Ellis Harold Dill pages 1 and 2. sanpaz (talk) 02:16, 19 October 2009 (UTC)

Hi Sanpaz, would you object to a sentence in the article stating that most of the research in continuum mechanics is not performed by physicists? In the sense you describe it, it is physics, but it is certainly an area of physics neglected by physicists. Truesdell says something to this effect in pages 8 & 9 of his book (Nonlinear-field theories of mechanics), I'll try to dig up more modern references about it.Commutator (talk) 13:25, 19 October 2009 (UTC)

I think it would be something good to state in the article with Truesdell as the reference. However, it would be good to have a more recent reference (if you could find one) that states that currently research into continuum mechanics is rarely done by physicists. sanpaz (talk) 14:55, 19 October 2009 (UTC)

An effort to improve the continuum mechanics area

Hi, I've just edited the lead in a way in which I hope is helpful, aiming to make it slightly more accessible in the first instance, but keep some of the detail that was there. I'm keen to help out in improving the whole of this branch of Wikipedia, so I'd be interested to see if there is anyone out there watching these articles who I can ask for guidance/advice? Thudso (talk) 23:12, 10 December 2009 (UTC)

Hi Thudso, I am also interest in this topic and have worked on this and other pages related to Continuum Mechanics (stress (mechanics), Deformation (mechanics), Infinitesimal strain theory and Finite strain theory. I saw your changes and I think they were good. I'll be around if you want to discuss about these topics. If you feel something needs to change do it and explain why and usually if people agree it will stand. If people disagree then a discussion about the change happens. At least that is my approach. Sometimes is better to say what you want to change and then ask for input (if the change is too big). Apart from that enjoy editing. All these pages on continuum mechanics sure need more working hands like yours. sanpaz (talk) 00:40, 11 December 2009 (UTC)

I have edited the first paragraph after the ToC. I looked up the "Hill-Mandel condition" described, and found that Ostaja-Starzewski cites only books from the 1960s which use this term, but sources up to the present day referring to the "Hill condition". I therefore changed "Hill-Mandel" to "Hill", see P.245 in Ostoja-Starzewski for details. I was wondering if Hill condition need a separate article? Probably a little overkill at the moment, since what we already have needs improving first, but at some point in the future, I hope! Having read through the next paragraph, I think the two need to be merged, I might get some time to spend on this a little bit later. Thudso (talk) 16:50, 11 December 2009 (UTC)

Just been working on the second paragraph. I noticed that most of the original work there is yours, Sanpaz. I was wondering what the difference between $\ \kappa _{t}$ and $\ \chi$ that is introduced further down the page is? Thudso (talk) 22:30, 11 December 2009 (UTC)