Could anyone explain/link me to an explanation of the specific derivation of Silling's peridynamic equation of motion? I read his 2000 paper where he proposed this model, as well as quite a few other papers regarding the topic, but I'm not sure I understand how the equation was derived from the EOM in classical continuum mechanics. I understand how it applies to his model, but not how he arrived at that equation from CCM. Could be totally going right over my head. First-year engineering grad student, go easy on me lol.
Would also love to hear if anyone has experience using this model for any interesting applications! Thanks!
Here is his 2000 paper for reference: https://scholar.google.com/citations?view_op=view_citation&hl=en&user=XAjk6swAAAAJ&citation_for_view=XAjk6swAAAAJ:u5HHmVD_uO8C
So it's been two weeks and while I like the concept of continuum mechanics I don't much care for how the prof teaches class. Is there a textbook (that wasn't originally written in 1969) that can explain this class better? My prof also doesn't seem to believe in examples to explain things like inidical notation so I've basically been reteaching myself.
Hello, I am a Mechanical engineering masters student and I had my first lecture on Continuum Mechanics this week, because of my automotive background I don't have the best understanding of mathematics. So, I would like to ask what area, chapter of mathematics I need to focus more in order to understand continuum mechanics equations. Thank you
Fluid/continuum mechanics seems to have been abandoned as both a teaching and a research topic by every physics department I’ve considered. I have a book from the 1960s bemoaning this trend. It’s possible to get a BS then PhD in physics without ever seeing the Navier-Stokes equations either in coursework or as part of your research, even though it is used in the structure of self-gravitating bodies, models of the nucleus and cosmology, and studying fluid/continuum mechanics can serve as a relatable gateway to field theory concepts like the stress-energy tensor in GR and QFT. The NS equations are one of the Millennium Prize problems. But physics departments not only removed it as a core topic, most of them don’t even seem to teach it.
Why?
EDIT:
I meant a course dedicated to it, not as a component of the intro classes.
Hello everyone, I have a quite simple problem of continuum mechanics which due to my rusty knowledge I haven't been able to solve and I was hoping some of you could help me.
Imagine you have a thin cilindrical piece of rubber of thickness [;d;] and radius [;R>>d;] squeezed between two cilindrical plates which apply a normal stress [;\sigma_n;] to the two flat surfaces of the rubber. Suppose also that the rubber is glued to the two plates, so that the displacement of the rubber parallel to the plates is zero at the interfaces.
Is there a simple analytical solution to the problem given the boundary conditions? Is it correct to assume that the principal strains parallel to the surfaces ([;\epsilon_{tt};]) go to zero for any "altitude" [;z;] ([;0<z<d;]) in the limit [;d\to0;] (at least close to the center of the cilinder)? I'm interested in calculating the hydrostatic pressure [;p=\frac{1}{3}\sigma_{ii};], which if the parallel strains indeed tend to zero equals simply [;\sigma_n;] in the same limit, assuming linear elasticity and a Poisson's ratio [;\nu;] of 0.5 (which is the value commonly used for rubbers).
In a previous (now deleted) post in r/Physics I was told by u/BigManWithABigBeard that indeed the hydrostatic pressure [;p;] should indeed equal [;\sigma_n;] in this limit, as suggested by this paper. Now, I'm actually working on modelling the solubility of gases in such rubbery films, and the important question is the following.
Suppose you are dissolving one molecule of a gas in that film. What is the displacement work [;\delta W;] needed to achieve this? Usually in thermodynamics you would calculate it as [;\delta W = p\delta V = \sigma_n\delta V;], where [;p;] is the hydrostatic pressure and [;\delta V;] the partial molar volume (divided by Avogadro's number) of the particle. Intuitively, however, one would expect that the material swells somewhat isotropically which implies that the work done by the external load is only [;\delta W = \sigma_nA\delta d \approx \frac{1}{3}\sigma_n\delta V;] (i.e., the swelling occurs laterally as well in the direction normal to the plates). Here [;A;] is the area of the flat surfaces, and I've used the fact that for isotropic swelling we have [;\delta d = \frac{d}{3V}\delta V = \frac{1}{3A}\delta V;].
Any suggestion? This apparent inconsistency has been really tro
... keep reading on reddit ➡Say I have a block of cheese, measuring 1m in the x-axis, 2m in the y-axis, and 3m in the z-axis.
Say I put some strain on this block of cheese, so that the strain tensor (which I will denote with a u) has diagonal elements u_xx = -0.05, u_yy = -0.06, and u_zz = -0.07. All other elements of the strain tensor I assume are equal to 0.
My question is, what is the new volume of the cheese, given this strain tensor?
Method 1:
u_xx (the first element of the strain tensor along the diagonal) as I understand it, represents relative contraction/extension in the x-direction. So, since u_xx is -0.05, I would expect the block of cheese to decrease by 5% in the x-direction, i.e. the length goes from 1m to 0.95m. Similar arguments for u_yy and u_zz give the new volume of 0.95m*1.88m*2.79m = 4.92m^3.
Method 2:
The relative change in volume is given as the divergence of the displacement field d, equivalent to the trace of the strain tensor u.
The trace of the strain tensor is -0.05 - 0.06 - 0.07 = -0.18, so a relative decrease in volume of 18%. This yields 4.98m^3.
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Why is it that I get to different results, what am I doing wrong here?
I am using the textbook: "Physics of Continuous Matter" by Lautrup, if that helps.
Hello all, quick description of my situation to clear up what i'm looking for, I am mechanical engineering student who took last year off studies and now i have an interview coming up for an internship but but i find myself lost since i haven't done anything related to engineering for a whole year and to top it off I lost all of my study materials, so what i'm looking for is online courses that cover continuum mechanics / solid mechanics / thermo-mechanics especially anything related to constitutive models for linear/non-linear elastic/plastic/viscoelastic.... materials and the derivation of those models, anything that emphasizes on energy approaches is a plus and if you have anything on FEA please do share :)
Ps: I do realize that this is a broad request but if you have anything related please help, thank you.
Yes, I know gravity and magnetisme. Thoes are the only examples I have ever read/heard. A lot of texts even write "volumetric loads, e.g. gravity or magnetisme etc."
What is etc.? I would love more examples! :)
Thanks!
Why do we consider bodies as continuum in solid mechanics, why aren't we accounting for the interatomic spaces? And what are the limitations to analysis of solids using Continuum mechanics
So, I finished this awfully hard class. The thing is, I still don't know what's its application in structural engineering, to be specific, in the designing process. Could someone sharing its application ? It would be great if it's designing applications, if not, that's also appreciated.
Thank you.
Warning: long post about sound.
Background: I'm a chemical engineer working on a certain process that involves high-speed ejection of gases/gases moving at supersonic speeds and running into stuff and so on. The speed of sound is coming up in a lot of the equations I am working on and it seems like I need to understand the significance of it.
From a quick search, I see that sound is a pressure wave. So there are certain regions in place which have high pressures and certain regions in space with low pressure. I understand that the further away you are from the source, the lesser the intensity of the sound (lesser pressure due to energy losses). But since it is a pressure wave, does that mean there are spots in space where there are not a lot of particles vibrating and propagating the "sound"? So if I am talking to somebody, does it mean that there are spots between the person and me where I won't receive their sound as intensely?
As a side question, what happens in these low pressure spaces? Is it just... empty - has very low energy particles?
Next up, what happens when you cross the speed of sound? When you make sound (talk), you are generating energy that propagates like a wave - what happens when a particle/body moves at that speed? Does it create temporary low pressure zones which results in a sharp pressure gradients that causes a pressure wave to form?
More generally, why does classic continuous body mechanics fail to capture what happens at the speed of sound? Why is it such an important threshold?
I apologize if this is a stupid question worthy of an RTFM... But I would be glad if somebody could direct me to the manual.
It sounds like a really interesting topic. I'm a mechanical engineer in the final year of my UG. I might do my PG in biomedical engineering, or stick to mechanical/automotive and go the FEA route.
What is the field really about? Applications? Scope?
Hi, I’m a third year Applied Maths student and I’m interested in reading more into continuum mechanics for one of my modules...does anyone know any good textbooks(preferably well known or with a free pdf version) talking about Equilibrium, Dynamics, Deformable bodies, Introduction to linear elasticity and fluid mechanics.
I have no physics background outside of highschool and the course is aimed at mathematicians more than physicists if that makes sense.
Edit: mixed up physicists with physicians
I'm about to register to take a grad course in Mechanical Engineering as a non-degree student to prepare to apply to MechE M.S. programs. Due to logistics, my only option is most likely Continuum Mechanics.
I'm wondering what will this be useful for? Since I'm not well versed with its applications, it seems to me like it's a more generalized Mechanics of Solid Bodies course, so that would end up strengthening my mechanics fundamentals.
What kind of tools should I expect by taking this course and where would it lead me in studies?
Can you help a MechE out? I'm trying to figure out the differences in the ways matter is studied between engineering and physics, and what are the reasons for the discrepancies?
In engineering (particularly mechanical and civil engineering), the scope of the study of matter is relegated to continuum mechanics, which attempts to explain the reactions of continua of solids and fluids subjected to forces. In this field of study, the relations of motion and forces are established using continuity equations, such as the Navier-Stokes equation. A large portion of this field of study is concerned with solving these PDEs using finite element methods.
I should mention that a significant body of work within continuum mechanics is experimental in nature. This gives rise to the use of Buckingham Pi Theorem, curve-fitting, statistics, and algebraic atrocities like the Colebrook equation for internal pipe flow.
My question is, how does condensed matter physics differ from continuum mechanics? What are the goals of condensed matter physics? Are there any ways natural phenomena are explained differently in condensed matter physics, such as turbulence? Thanks!
Has anyone chosen to take this as a graduate level course? If so can you provide some feedback on the experience? Also, can you refer a good textbook to become familiar with the material? Thank you!
Has anyone taken MAE671 Continuum Mechanics with Mayeur? If so, how was it?
