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Learning Continuum Mechanics

I would like to make a career in Finite Element MEthod with concentration on topics like XFEM,Mesh-free methods--

However, I am yet to mmake a start.To give you my background I ahve a good knowledge of subject of Strength of Materials,Linear Finite Element Analyis-including coding structrial analysis involving beam elements,plate elements,plane stress and plane strain elements-all linear FE.

I have good programming skills-C,VB,MathCAD and know basis of C++ well

I havee just undergone a course on Linear Algebra through the MIT opencourseware.

I have not yet studies the subject of continuum mechanics.

Though, I did undergo a course on Theory of Elasticity in my MAstyers degree, not very confident of the same.

My questions are:

1.What should be my next action-in view of studying a detailed course (Self study of course) before I proceed to pursue my higher research studies?

2.What are the books you refer for my question in 1. above?

3.I want to pursue my research in area of XFEM (i understand what it isand find interesting-but not familaiar with the Math involving it and in depth study-just have an introductory knowledge of XFEM)

4. Based on 3. above and my very brief view of my knowledge status, can you suggest some books I should be reading to get a confidence on my subjects?

 Please help! 

Zhigang Suo's picture

An excellent textbook on continuum mechanics is Nonlinear Solid Mechanics by G.A. Holzapfel.  You can also find many online books and notes.

Thanks Zhaing.

Some basic questions:

  1. How is continuum mechanics different from conventional solid mechanics?
  2. Would it be better t first read a text on Non Linear Finite Element Analysis by Crisfield than a text on Continuum mechanics based on my research ideas as I've listed below?



Temesgen Markos's picture

Continuum mechanics deals with any material that you can model as a continous media. It can be solids,fluids, electromagnetic fields etc. Motion, deformation, conservation of mass and momentum, tensor analysis etc which are ideas useful irrepective of the specific material you are dealing with are the topics you would read in a continuum mechanics text.

 Now if you are only interested in solid mechanics applications, you can pretty much start with theory of elasticity or advanced solid mechanics texts. The first few chapters will usually will give you the material needed from continuum mechanics. If you are really interested in applied and computational mechanics though, I would say still go ahead and read a continuum mechanics text.I personally think working through a continuum mechanics text disciplines the reader.

I would find it difficult to read a nonlinear FEA text without having a good background in large deformation theory. Here too I would say read a book like the one Prof. Suo recommended. But most nonlinear FEA books have preliminary chapter on the continuum/solid mechanics principles. You can do that too.

Talking of XFEM or mesh free methods (which I have never worked with), I don't think you need to read nonlinear FEA to understand them. Wait for Drs. Dolbow, Sukumar or Bordas to reply on this. 


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