Continuum mechanics in physics education

[vco]

I came across this article about the near absence of continuum mechanics in university-level physics education:
http://www.troian.caltech.edu/papers/Gollub_PhysToday_Dec03.pdf

I have wondered this issue myself: why is continuum mechanics mainly studied by engineers rather than physicists, even though it is a fundamental field of physics?

The strange outcome is that classical mechanics appears to be the only branch of physics where the engineering approach is more complex than that of the physicists. Of course, continuum mechanics is merely an approximation, but it is certainly a more advanced approximation than point masses, rigid bodies and springs which the physicists are more familiar with when dealing with classical mechanics.

Any thoughts on this?

 

[Dr. Courtney]

I came across this article about the near absence of continuum mechanics in university-level physics education:
http://www.troian.caltech.edu/papers/Gollub_PhysToday_Dec03.pdf

I have wondered this issue myself: why is continuum mechanics mainly studied by engineers rather than physicists, even though it is a fundamental field of physics?

The strange outcome is that classical mechanics appears to be the only branch of physics where the engineering approach is more complex than the physicists' approach. Of course, continuum mechanics is merely an approximation, but it is certainly a more advanced approximation than point masses, rigid bodies and springs which the physicists mainly associate with classical mechanics.

Any thoughts on this?

The article is pretty good and basically right. The general trend in undergrad physics has been to require fewer hours of physics and math for graduation, not more hours. So the question becomes, if you add continuum mechanics, what do you take out? Convincing physicists that it is "important" is not enough, it needs to be more important than what it replaces. If you teach at a level that requires a thorough knowledge of PDEs and tensor analysis, you need room for mastery of the extra math also.

One would also need to account for the fact that you may be giving up material that IS important background on the PGRE, PhD qualifying exams, and required graduate courses for material that is much less important. This is not a question of _fundamental_ importance, but rather that continuum mechanics is not as important downstream as other topics, because there is a higher expectation that undergrads arrive well prepared in other topics.

The time available for math and physics in an undergrad physics major is close to a zero sum game: it is either steady or slowly decreasing. I don't think you'll be able to convince the non-physicists at most unis that it is sufficiently important to INCREASE the number of hours in math and physics required for graduation. So within the existing credit hours in math and physics, you need to decide what topics are less important.

 

[hilbert2]

Continuum mechanics, especially the large deformation theory, is based on very empirical and ad hoc constitutive equations (stress strain relations) that are chosen so that they work in practice for a particular engineering problem. A physicist may be more interested in classical mechanics problems like "What kind of central force fields lead to orbit trajectories that are elliptic and exactly trace themselves?" or "Under what assumptions can we set an upper limit for the sensitivity of a three body point mass system to initial conditions?". The physicist's questions are related to fundamental natural laws while the engineering approach is based on finding something that just works for a problem.

 

[vco]

Thank you for your thoughts. It seems that the main reasons why continuum mechanics is generally excluded from physics education are:

1. Other topics in physics are more relevant career-wise.
2. There is no room in the curriculum.
3. It requires high-level mathematics.
4. There are some "loose ends" in the theory.

By the way, hilbert2, it is good to see a fellow Finn here.

 

[hilbert2]

By the way, hilbert2, it is good to see a fellow Finn here.

Good to see you too. :) Are you an engineering or physics student?

-Teemu

 

[vanhees71]

I also find it a pity that hydro is no more a standard topic in the physics curriculum. The reason were nicely given in the Physics Today article cited above. The strongest argument concerning pedagogics for me is that indeed you get a better understanding of what's behind the various manipulations of 3D vector calculus, which is the most challenging subject in the undergrad (theoretical) physics curriculum (at least from my own experience when I first learned about it). On top it's also a fascinating subject from a physics point of view. The reason for this are given in the Physics Today article.

The only argument in this article, I don't buy, is the lack of hydro books. There are tons of good hydro books around. My favorites are

A. Sommerfeld, Lectures on Theoretical Physics, vol. II
Landau&Lifshitz, Course on Theoretical Physics, vol. VI

The former has a particularly useful introduction to vector calculus making the differential and integral operations very intuitive. As usual L&L is the most straight-forward text on the subject. There's nothing superfluous in it with a lot of applications and, for me as a theoretical heavy-ion physicist most important, also an introduction to relativistic hydro.

 

[Demystifier]

The strange outcome is that classical mechanics appears to be the only branch of physics where the engineering approach is more complex than that of the physicists.

The engineering approach is always more complex (but less abstract) than that of physicists. Physics is a fundamental science which studies basic principles, while the idea of engineering is to apply those basic principles to something useful - and therefore complex. Here are some examples:
- The physical principles of statics are very simple (physicists spend perhaps two hours to learn about them), but to project a 200-meters-long bridge takes very complex statics.
- The physical principles of electronics are not so hard, but an advanced electronic device can be very complex.

 

[vco]

Good to see you too. :) Are you an engineering or physics student?

I am a mechanical engineer. I graduated a couple of years ago (M.Sc.) and I am currently working as a structural analyst.

The engineering approach is always more complex (but less abstract) than that of physicists. Physics is a fundamental science which studies basic principles, while the idea of engineering is to apply those basic principles to something useful - and therefore complex.

Yes, this is absolutely true. Maybe I should not have used the word "complex". What I meant was that in classical mechanics engineers "dig deeper" into the theory than physicists. In other fields of physics it is the other way around.

 

[Demystifier]

What I meant was that in classical mechanics engineers "dig deeper" into the theory than physicists. In other fields of physics it is the other way around.

Well, it depends on what do you mean by "deeper". Physicists certainly dig deeper in topics such as geometrical interpretation of Hamiltonian mechanics. On the other hand, engineers may dig deeper in numerical simulations of turbulence in fluid mechanics. The former is more fundamental, the latter is more related to practical applications.

 

[Chestermiller]

Continuum mechanics, especially the large deformation theory, is based on very empirical and ad hoc constitutive equations (stress strain relations) that are chosen so that they work in practice for a particular engineering problem. A physicist may be more interested in classical mechanics problems like "What kind of central force fields lead to orbit trajectories that are elliptic and exactly trace themselves?" or "Under what assumptions can we set an upper limit for the sensitivity of a three body point mass system to initial conditions?". The physicist's questions are related to fundamental natural laws while the engineering approach is based on finding something that just works for a problem.

In my practical industry experience, constitutive equations must satisfy certain specific constraints (such as the principle of material objectivity) and, although, in many cases (such as axial flow of a viscoelastic fluid in a tube), the kinematics of the deformation may allow some simplifications, for more complex deformations, the formulation and determination of the constitutive equation must still adhere to these constraints.

My industry experience also indicates that constitutive equation development and application are not the only values of Continuum Mechanics. Continuum mechanics provides a general framework for formulating and solving fluid and solid mechanics problems, even in cases where the constitutive behavior is relatively simple, such as for Newtonian fluids and Hookean solids. My advice is that, if a physicist wants for succeed in industries that require some chemical engineering, civil engineering, or mechanical engineering knowledge, a background in Continuum Mechanics is highly desirable. At least, that is what I have seen working with physicists in industry.

 

[Paul Colby]

I have to laugh a little having found this unrealized gap in my training. I'm sure there are many more. I'm currently looking at both piezoelectric and linear elasticity theory. The learning curve is much steeper than I would have thought. It's also quite interesting in its own right.

 

[vco]

I also think that continuum mechanics doesn't get enough credit for its level of difficulty.

Many physicists/engineers commonly think that Maxwell's equations or the Schrödinger equation are among the hardest equations in physics. However, these are merely linear PDEs, whereas for example the Navier-Stokes equations (fluids) are nonlinear PDEs and thus very tricky to solve. For solids, large-deformation or plasticity equations are also nonlinear.

The math in continuum mechanics is at a comparable level as in general relativity, but many people do not know this because in continuum mechanics the phenomena themselves are very familiar.

If someone tells a layperson they are working on say quantum mechanics, the layperson might respond "Wow, that must be really hard and math-intensive!" But they don't show similar admiration for a person who is developing a numerical simulation code for a ventilation fan, for example.