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The Renaissance of Continuum Mechanics

Dear friends of IMechanica:

 

Primary data mining through Web of Science
reveals that the number of papers containing “continuum mechanics ” increases
rapidly these years. This is a very exciting fact to our mechanicians. Thus, I
wrote a short paper titled “The Renaissance of Continuum Mechanics”, which was just
published online via:

 

http://www.zju.edu.cn/jzus/iparticle.php?doi=10.1631/jzus.A1400079 (The full paper can be downloaded.)

 

This paper may also serve an introductory
purpose in courses on the subject of continuum mechanics. You are all welcome
to make comments or further suggestions. The abstract of the paper is given
below:

 

Continuum mechanics, just as the name
implies, deals with the mechanics problems of all continua, whose physical (or
mechanical) properties are assumed to vary continuously in the spaces they
occupy. Continuum mechanics may be seen as the symbol of modern mechanics,
which differs greatly from current physics, the two often being mixed up by
people and even scientists. In this short paper, I will first try to give an
illustration on the differences between (modern) mechanics and physics, in my
personal view, and then focus on some important current research activities in
continuum mechanics, attempting to identify its path to the near future. We can
see that continuum mechanics, while having a dominating impact on engineering
design in the 20th century, also plays a pivotal role in modern science, and is
much closer to physics, chemistry, biology etc. than ever before.

Comments

Dibakar Datta's picture

 Dear Dr. Chen,

 This is a very nice article. It reminds me what Leonardo da Vinci once said :

 Mechanics is the paradise of the mathematical sciences,because by means of it one comes to the fruits of mathematics. 

I also find these notes very interesting : 

http://www3.nd.edu/~rroeder/ame20241/history.pdf

http://www.math.vt.edu/people/gao/amma/amma07/amma3-08.pdf

http://www.eolss.net/sample-chapters/c05/e6-161-02-00.pdf

 

Regards,
Dibakar Datta 
PhD Candidate ; Major : Solid Mechanics
Shenoy Research Group
BROWN UNIVERSITY
Providence 02912 , USA

Thanks Dibakar for the useful information.  

Weiqiu

Zhigang Suo's picture

Dear Weiqiu:  Thank you so much for posting your wonderful review of the advances of continuum mechanics in the last decade.  It is always interesting and useful to know the historical development of a subject, and form a long perspective.  

A main function of a graduate course, I believe, is to talk about the development of the subject, make the subject alive, humanize the giants, and give students the confidence that they too can contribute to the subject.  After all, the subject lives through our students and through theirs.

It is also helpful to learn the development of a subject from multiple authors.  I recently enjoyed reading a book by Gerard Maugin published in 2013, entitled Continuum Mechanics through the Twenties Century.  

In looking this book up on Amazon, I also found that the author has just published a book entitled Continuum Mechanics through the Eighteenth and Nineteenth Centuries.  I Look forward to reading it.    

Dear Zhigang,

 

I do agree with your opinion about the necessity to talk about the development of a subject in the related course. I have found that the students' interests will increase if there are attracting stories.

I have read through Maugin's book, which has also been cited in my short paper. But I don't know his new book. Thanks very much for this information! I like very much of his writing, and look forward to reading the new one. 

Weiqiu

Arash_Yavari's picture

Dear Weiqiu:

Thanks for posting your interesting review paper. A couple of quick remarks:

1) I think it’s perfectly fine to be excited when seeing more papers published in recent years that contain “continuum mechanics”. But does this really mean more advances in continuum mechanics? I very much doubt it. When there are more and more journals people publish more and more papers and you would see more on "continuum mechanics”, in particular.

2) Newton was certainly one of the greatest scientists of all time but I’m not sure if he was “the greatest”. Also please note that there are no “three fundamental laws of motion”; there is only one law. The so-called first and third laws of motion are consequences of the “second” law.

Regards,
Arash

Zhigang Suo's picture

Dear Arash:  Excellent questions on the advances in continuum mechanics.  Several examples of the last century set a standard:

  1. Nonlinear rheology.  This advance originated from fundamental considerations, and from the need to understand metals and polymers.  The atomic nature of metals and molecular nature of polymers were established early in the past century.  Although continuum mechanics is not formulated in terms of atomic and molecular structures of matter, they clearly inspire the development of nonlinear rheology.
  2. Fracture mechanics.  This advance would be difficult without microscopic pictures of bond breaking and energy dissipation.
  3. Finite element method.  This advance goes hand in hand with the advent of computers.  

The Big Three have all showed that advances in continuum mechanics have strongly correlated with activities elsewhere in science and technology.  Of course, all these advances address very real problems of our life.

The Big Three are all still well and alive.  All have new and interesting applications.  All have unresolved issues.  Furthermore, a quick look at the past Themes of the Journal Club will reminds us of what have kept mechanicians busy and excited.

It will be fun that people comment on individual topics where they see emerging advances in continuum mechanics. 

Jing_Yang's picture

Dear Prof. Chen,

I benefit a lot from your class "Continuum Mechanics", where you introudced us to  the branches, history, classical books,interesting stories in mechanics. Thank you.

As mentioned in your paper, the era of renaissance of continuum mechanics has come. Recently, I read quite a few papers about continua coupled with electromagnetic effects. Here are papers I read:

[1]L.P. Liu. An energy formulation of continuum magneto-electro-elastics with applications, J. Mech. Phys. Solids 62:209-227, 2014.

[2]L. P. Liu. On energy formulations of electrostatics for continuum media. J. Mech. Phys. Solids 61, 968-990, 2013.

[3]Ericksen,J.L.,2007.Theory of elastic dielectrics revisited.Arch.Ration.Mech.Anal.183(2),299-313.

[4]Steigmann,DavidJ.,2009. On the formulation of balance laws for electromagnetic continua.Math.Mech.Solids14(4),390-402.

[5] Ericksen, J. L. On formulating and assessing continuum theories of electromagnetic fields in elastic materials. Journal
of Elasticity, (2007)

In principle, electromagnetic continua are governed by force, momentum equations as well as Maxswell equations. However, the couple of short-range, local mechanical forces and long-range, nonlocal electromagnetic forces pose  challenges on the formulation of them to some extent.

We may add this topic into the syllabus of the course "Continuum Mechanics" and use related papers as supplementary readings.

Sincerley,

Jing

 

 

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