Continuum mechanics Definition and 89 Threads

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

I was wondering if anyone knows of a good book on the mathematical theory of continuum mechanics. I have looked online, and the only ones I can seem to find are like your average physics or applied mathematics book. I want something with rigorous theoretical formulation of the subject. It...

Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point...

Hi all, I'm currently trying to teach myself continuum mechanics (as I am enrolled in a course for which continuum mechanics is a pre requisite and have never taken such course) I have been reading a book by mase and mase "introduction to continuum mechanics for engineers" 2nd edition. I...

What's the difference between analytical and continuum mechanics?

For a day and a half now we have been trying to calculate a self-assigned problem. However, this has not turned out to be easy and build-up frustration has lead us to this forum. Our challenge was to calculate what under pressure a food packing company needs in it's jars to make sure the lid...

Homework Statement A large cylindrical tank of radius R is full of water to a height h(t). This drains under gravity out of the bottom of the tank through a small hole of radius r. The acceleration due to gravity is g. The pressure of the air can be assumed to be the same at the top and at...

I have never had an advanced classical mechanics class, only elementary level treatments using mostly Newtonian approaches, on very simple mechanical systems. I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology, which studies...

Homework Statement http://img683.imageshack.us/img683/7060/selection001l.png Homework Equations \epsilon^{pl} = \epsilon - \epsilon^{el} \epsilon^{pl} = \epsilon - \frac{\bar{\sigma}}{E} r = \frac{\epsilon_w}{\epsilon_t}The Attempt at a Solution I'm stuck trying to calculate \bar{\sigma}...

Continuum Mechanics Books - help please Hi all.. Im almost done with this course in the current semester .. just academically .. I really haven't ' felt ' this subject .. haven't truly understood it ..so I'm re reading it these vacations . I need a v good book .. please suggest the best...

Homework Statement The components of stress in the x_i reference Cartesian system at a point of interested have been determined to be: \left[\begin{array}{ccc} 500 & 0 & 300 \\ 0 & 700 & 0 \\ 300 & 0 & -100 \end{array}\right] \mathrm{MPa} Determine the principal values and directions of...

I've looked at a few Physics programs and none seem to cover any time of fluids or continuum mechanics in general. It seems to be a very relevant subject to cover but it's only slightly addressed in one of the lower level classes. In these classes they usually only going over Bernoulli's...

Homework Statement http://imageshack.us/photo/my-images/513/selection027.png" http://imageshack.us/photo/my-images/513/selection027.png Homework Equations E_{ij}=\frac{1}{2} \left( \frac{\partial{u_i}}{\partial{X_j}} \frac{\partial{u_j}}{\partial{X_i}} - \delta_{ij}\right)...

Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.

Hello, I'm not sure if this is the right place to ask about Continuum Mechanics or if the right place would be the engineering forums, but since Continuum Mechanics is a branch of Classical Mechanics, I thought it might be the place. My question is about Stress. Why does the stresses on...

Homework Statement see attachment. Homework Equations Navier Stokes continuity equation: The Attempt at a Solution So what I tried to do was to use the above equation to see if it equals zero. del(rho)/del(t)=del(xyz-t)/del(t) =-1 then to make the deriving easier...

how easy does it become to learn general relativity after a good course in continuum mechanics?

Hello! I read somewhere about intro to continuum mechanics. There was a vector \vec{\mu} and displacement vector \delta\vec{\mu}. As vector \vec{\mu} move, it will get new position \vec{\mu}'=\vec{\mu}+\delta\vec{\mu} \vec{\mu}'=\vec{\mu}+\frac{\partial\vec{\mu}}{\partial x_i}\delta...

Hi I'm looking for a good, in depth book on continuum mechanics and classic gauge theory. Can you suggest something? What I know about the subject is the chapter in Goldstein's classical mechanics.

I can do Calculus reasonably well in the context of multi-variables and simple undergraduate problems, but its all algebraic, I don't have a geometric understanding of how it is that the solving happens. Fortunately, with the Lagrangian method, I can appresciate at least qualitatively how one...

Homework Statement Mechanics of Deformable Media (Bhatia and Singh), 5.2: Consider a long rod of elastically isotropic material of L standing vertically in a vacuum in equilibrium under the gravitational field of the earth, then: (i) What are the boundary conditions for \sigma_{ij} on the...

Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.

i am currently reading a book about continuum mechanics. they define derivatives of tensor valued functions of tensors in such way: http://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics ) it seems to be related covariant derivative, but i can not figure out its meaning in physics...

the book "Introduction to tensor calculus and continuum mechanics" hi please help me ! i've try to find appendix d of this or solution that excersise anyone can help me ? any link or full version of this book thart have "appendix d" my english languge not good sorry thanks a lot bye

Homework Statement A body which in the reference configuration is a unit cube with its edges parallel to the coordinate axes undergoes the following deformation: x1=a1(X1+sX2), x2=a2X2, and x3=a3X3 (where a1,a2,a3,s are constants). determine the lengths of its edges after the...

Hey, all. What would be some good books on continuum mechanics for undergraduates majoring in Physics? I'm familiar with Timoshenko's book that's used in Engineering, but I'm looking for something a Physics student may use. Thanks in advance.

Homework Statement A catilever beam with rectangular cross-section occupies the region -a \leqx1 \leqa , -h \leq x2 \leq h , 0 \leq x3 \leq L The end x3=L is built-in and the beam is beant by a force P applied at the free end x3=0 and acting in the x2 direction. The stress tensor has...

example 3.30: Let the stress tensor components σij be derivable from the symmetric tensor field φij by the equation σij = εiqkεjpmφkm,qp. Show that, in the absence of body forces, the equilibrium equations are satisfied. I don't have any idea have to solve this problem. Can someone help...

Hey, I've picked up a book on continuum mechanics to do a bit of studying by my self. As this topic is somewhat odd (difficult) I wonder if anyone knows of a place where students of continuum mechanics meet for discussion? I'm not sure if there is a subforum here at physicsforums which deals...

Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it. Everyone: If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection)...

I need to learn optics, SR and continuum mechanics for my physics qual exam in June. Can anyone suggest some books that would be appropriate for self study?

I have the oppurtunity to take a class called continuum mechanics. Has anyone here taken the subject?, did you find it interesting and most importantly useful in your work? It sounds pretty fun, but I don't know if it is that useful for later. So could you be so kind as to tell me how it has...

I have a question about FEM applied to stress/strain type of problem, is this the right section to post it? -Thank you

I started reading a great textbook and thought I would share some of its finer points. It is a great introduction to mechanics of solids and liquids, although the title explicitly states Earth and Environmental Sciences. http://www.science.mcmaster.ca/~geo/faculty/emeriti/middleton/index.html...

what are the open and still not yet answered problems in continuum mechanics as of today? i reackon navier-stokes equations solutions is something that is related to the issue, right?

Here is a free and downloadable textbook on Tensor Calculus. http://www.math.odu.edu/~jhh/counter2.html Scroll to bottom of page to find pdf files.

...I'm currently studying R. Aris, "Vectors, Tensors, and the Basic Eqns. of Fluid Mechanics." What are some of the other classic references for the mechanics of continuous media?

What is continuum mechanics. What does the word "continuum mean"? What is discrete?

Does anyone know good books on tensor analysis, especially need to learn it to understand continuum mechanics. Thank you.