Talk:Continuum mechanics

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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)

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

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)

[edit] 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)
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