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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)
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)
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 |
A 1980 author writes "constitutive equations are also required in other branches of continuum physics, such as continuum thermodynamics and continuum electrodynamics" [1] so "continuum whatever" is a big group, anything that models matter as continuous stuff. IDave2 ( talk) 15:43, 23 September 2009 (UTC)
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)
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)
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)
Why do you ( Sanpaz) want convective derivative to be merged into continuum mechanics? Crowsnest ( talk) 21:23, 19 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)
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)
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)
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)
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)
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)
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)
The balance of momentum expressed in the article in the reference configuration, using the transpose of the first-Piola Kirchhoff stress tensor looks WRONG. It seems to me that the equation should be the same, but using the first-Piola Kirchhoff stress tensor itself and not its transpose.
Reference : Marsden, J., & Hughes, T. (1994). Mathematical foundations of elasticity.
Could anyone confirm or infirm ?
Does granular mechanics fall under the general heading of continuum mechanics? It's part of the continuum mechanics group here at DAMTP, but I don't know whether that's anomalous or not (Cambridge can be anomalous sometimes). -- jftsang 09:01, 15 June 2015 (UTC)
If we use the definitions
then we get
which does not fit with the energy conservation law in the Lagrangian frame given by this page, which has the transposed of . The same problem could be shown for the momentum equation.
I think that the equations, which are currently,
should be replaced by
Can someone confirm this?
I think different heat flux vectors should also be used for Lagrangian and Eulerian formulations! — Preceding unsigned comment added by DeNayGo ( talk • contribs) 11:26, 12 January 2017 (UTC)
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In the section Concept of a continuum, the following three paragraphs deal with criteria for application of the continuum assumption. These paragraphs are not essential to the article since they do not discuss or explain the continuum concept itself but rather raise possible questions about its validity and its application. For an article which tries to explain a fundamental idea whose basic concept is not excessively difficult to grasp, these paragraphs are too detailed, and I suggest they should be removed. Alternatively – if other editors feel these paragraphs are truly important – they might be moved to the end of the article as a new section.
Here are the three paragraphs:
The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical homogeneity and ergodicity of the microstructure exists. More specifically, the continuum hypothesis/assumption hinges on the concepts of a representative elementary volume and separation of scales based on the Hill–Mandel condition. This condition provides a link between an experimentalist's and a theoretician's viewpoint on constitutive equations (linear and nonlinear elastic/inelastic or coupled fields) as well as a way of spatial and statistical averaging of the microstructure.[1]
When the separation of scales does not hold, or when one wants to establish a continuum of a finer resolution than that of the representative volume element (RVE) size, one employs a statistical volume element (SVE), which, in turn, leads to random continuum fields. The latter then provide a micromechanics basis for stochastic finite elements (SFE). The levels of SVE and RVE link continuum mechanics to statistical mechanics. The RVE may be assessed only in a limited way via experimental testing: when the constitutive response becomes spatially homogeneous.
Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.
I prefer not to remove these paragraphs myself as I am not qualified in this field. I hope someone with more knowledge will consider doing so. Dratman ( talk) 18:04, 17 March 2019 (UTC)
Hello, for those interested I have just edited the explanation section. Minor rephrasing and more links, see the diff here https://en.wikipedia.org/?title=Continuum_mechanics&diff=1130035568&oldid=1126094519 Adigitoleo ( talk) 08:54, 28 December 2022 (UTC)
I would suggest removing/replacing the car traffic example. I made some small edits for conciseness, but have left it in at the moment. However, I don't think the example is a great fit for the following reasons:
For now I think I will move the example down further, if there are no objections I will remove it in the next month. Adigitoleo ( talk) 11:45, 28 December 2022 (UTC)
This
level-4 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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)
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 |
A 1980 author writes "constitutive equations are also required in other branches of continuum physics, such as continuum thermodynamics and continuum electrodynamics" [1] so "continuum whatever" is a big group, anything that models matter as continuous stuff. IDave2 ( talk) 15:43, 23 September 2009 (UTC)
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)
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)
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)
Why do you ( Sanpaz) want convective derivative to be merged into continuum mechanics? Crowsnest ( talk) 21:23, 19 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)
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)
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)
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)
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)
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)
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)
The balance of momentum expressed in the article in the reference configuration, using the transpose of the first-Piola Kirchhoff stress tensor looks WRONG. It seems to me that the equation should be the same, but using the first-Piola Kirchhoff stress tensor itself and not its transpose.
Reference : Marsden, J., & Hughes, T. (1994). Mathematical foundations of elasticity.
Could anyone confirm or infirm ?
Does granular mechanics fall under the general heading of continuum mechanics? It's part of the continuum mechanics group here at DAMTP, but I don't know whether that's anomalous or not (Cambridge can be anomalous sometimes). -- jftsang 09:01, 15 June 2015 (UTC)
If we use the definitions
then we get
which does not fit with the energy conservation law in the Lagrangian frame given by this page, which has the transposed of . The same problem could be shown for the momentum equation.
I think that the equations, which are currently,
should be replaced by
Can someone confirm this?
I think different heat flux vectors should also be used for Lagrangian and Eulerian formulations! — Preceding unsigned comment added by DeNayGo ( talk • contribs) 11:26, 12 January 2017 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Continuum mechanics. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 16:31, 12 August 2017 (UTC)
In the section Concept of a continuum, the following three paragraphs deal with criteria for application of the continuum assumption. These paragraphs are not essential to the article since they do not discuss or explain the continuum concept itself but rather raise possible questions about its validity and its application. For an article which tries to explain a fundamental idea whose basic concept is not excessively difficult to grasp, these paragraphs are too detailed, and I suggest they should be removed. Alternatively – if other editors feel these paragraphs are truly important – they might be moved to the end of the article as a new section.
Here are the three paragraphs:
The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical homogeneity and ergodicity of the microstructure exists. More specifically, the continuum hypothesis/assumption hinges on the concepts of a representative elementary volume and separation of scales based on the Hill–Mandel condition. This condition provides a link between an experimentalist's and a theoretician's viewpoint on constitutive equations (linear and nonlinear elastic/inelastic or coupled fields) as well as a way of spatial and statistical averaging of the microstructure.[1]
When the separation of scales does not hold, or when one wants to establish a continuum of a finer resolution than that of the representative volume element (RVE) size, one employs a statistical volume element (SVE), which, in turn, leads to random continuum fields. The latter then provide a micromechanics basis for stochastic finite elements (SFE). The levels of SVE and RVE link continuum mechanics to statistical mechanics. The RVE may be assessed only in a limited way via experimental testing: when the constitutive response becomes spatially homogeneous.
Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.
I prefer not to remove these paragraphs myself as I am not qualified in this field. I hope someone with more knowledge will consider doing so. Dratman ( talk) 18:04, 17 March 2019 (UTC)
Hello, for those interested I have just edited the explanation section. Minor rephrasing and more links, see the diff here https://en.wikipedia.org/?title=Continuum_mechanics&diff=1130035568&oldid=1126094519 Adigitoleo ( talk) 08:54, 28 December 2022 (UTC)
I would suggest removing/replacing the car traffic example. I made some small edits for conciseness, but have left it in at the moment. However, I don't think the example is a great fit for the following reasons:
For now I think I will move the example down further, if there are no objections I will remove it in the next month. Adigitoleo ( talk) 11:45, 28 December 2022 (UTC)