iMechanica - elasticity - Comments

Paper

ChrisL — Wed, 19 Nov 2008 08:43:48 -0500

Erwan,

I would be very thankful if you could email me this paper chris.ladubec@nrc.ca

Thank you.

Let me share my view on

Milli — Fri, 31 Oct 2008 07:51:11 -0400

Let me share my view on your question.

Bulk modulus,K, is often assumed time-indepenent. The reason behind this lies on the assumption that the material in subject is highly incompressible and has a high bulk modulus value.If the material is incompressible, then it implies that the possions ration is nearly 0.5 always and thus can be taken time-indepenent. The main point here is, the material has to be highly incompressible for the assumption to remain valid.

Voids

Arash_Yavari — Tue, 12 Aug 2008 16:12:10 -0400

Dear Rezwan:

Thank you for your interest.

Of course you can think of "damage" or any measure that describes "damage" as a microstructure field. However, the question should be how useful the formulation is. My motivation in this paper was to see why there are so many different possibilities for "balance laws" and if there is any way to understand this starting from first principles. In many works balance laws are simply postulated and it's not clear if what one sees is the personal choice of the author(s) or there is more into the given formulation.

For damage you may look at the following paper:

Fu, M.F., Saczuk, J., Stumpf, H. 1998 'On fiber bundle approach to damage analysis' Int J Engng Science 36, 1741-1762.

The presentation is geometric but somewhere in the middle they assume Euclidean ambient spaces. Again, the question you should always ask yourself is whether you can gain anything using geometry. For your damage evolution problem, you should first see why the formulation based on Euclidean ambient spaces is not satisfactory (is this really the case?) and then try to formulate the theory geometrically. I had a look at the paper you sent me (don't want to mention the author) but didn't see anything but some "nice" interpretations of what is already known.

I hope this helps.

Regards,

Arash

RE: Balance Laws in Continua with Microstructure

Rezwanur Rahman — Sun, 10 Aug 2008 15:23:22 -0400

Hi Dr. Arash

This paper is very interesting indeed. This paper can be helpful regarding considering the issue of damages/voids/defects in the continuum (with respect to the microstructure field). I would like to mention that the Article 5.1 named: A Geometric Theory of Elastic Solids with Distributed Voids is expressive about cosidering damages/voids. According to our previous discussion, this material void velocity can be considered as "Local Martingale". And some random nucleation of new void(s) can cause this velocity to be a stochastic process containing sudden jumps. Besides that we can deal with a density function of void velocity instead of a single void. Please let me know about your opinion regarding this.

Thanks

Rezwan

Thank you zhangzhuo

hitzhangzhuo — Mon, 30 Jun 2008 07:59:13 -0400

Thank you

zhangzhuo hitzhangzhuo@gamil.com

Thanks for sharing. Yi

Yi Han — Thu, 12 Jun 2008 13:00:10 -0400

Thanks for sharing.

Yi Han hyxjtu@gmail.com

Sorry about the mistake

Rezwanur Rahman — Wed, 11 Jun 2008 14:42:04 -0400

I had little mistake. The name of the book is:

Topology : James Munkers

I am sorry for this.

Thanks

Rezwan

Concept of Manifold (Books)

Rezwanur Rahman — Wed, 11 Jun 2008 14:39:45 -0400

Hi Dr. Yavari

I would like to add some more books on topology and theory of manifolds. These books are the very nice in discussing about these bastract mathematical topics, as far as I have seen:

Topogy : James Munkers.

Riemannian Manifolds, An introduction to Curvature: John M. Lee

Introduction to Topological Manifolds: John M. Lee

These books are very lively in explaining the physical concept of basic general topology, Homotopy theory,differntial geometry and theory manifolds.

Thanks

Rezwan

John M. Lee

Arash_Yavari — Wed, 11 Jun 2008 14:25:16 -0400

Dear Rezwan:

John M. Lee is an excellent writer indeed.

Regards,
Arash

Concept of Manifold

Rezwanur Rahman — Wed, 11 Jun 2008 14:13:19 -0400

I am trying to give some basic introduction on the works related to Topologial/Differentiable Manifolds. It is very common that a illustrative explanation makes any topic more lively. Unfortunately sometimes the abstract mathematical concepts are very difficult to be illustrated. However, the concept of manifold can be visualized as a geometric entity; more clearly surfaces. Simply any plane, surface of sphere and ellipsoid etc are manifolds in a sense. But the basic concept extentends to more complexity. In eucliden space we can use Pythagorian theorem but in a curvilinear space its not true in glabal sense. If we take the limiting condition it is then possible to think as euclidean space (Suppose a point on the sphere, a very small region surrounding that point may be dealt as euclidean space but if we keep going far from the point on the sphere we can't conserve this idea). So in order to deal these kind of problems the concept of manifold came. So if we draw a line on a sphere that is no longer a line. Hence we need to use Differential Geometry. Using the theories of differential geometry we can find the length, tangent sets on the line (Actually path). If we have more than one lines we can fine the shortest line or path which are called Geodesics. The Riemannian manifold comes when we deal with these kind of concepts. As mentioned earlier, a path on the sphere is not necessarily a straight line, so the pythagorian theorem must be modified little bit. Hence Riemannain metric comes into the scenario. We can say sphere as smooth surface. So it is Riemannian manifold. Because we can have a continous tangent space on the sphere. The concept of Riemannian manifold made the analysis easier.If we use topological operation such as a sphere is deformed to be an elliosoid, we can say a smooth manifold becomes another smooth maniflod. So it is a homeomorphism which preserves the differentiability condition on every point. Now if a question comes in mind that when a sphere became an ellipsoid, will they become totally independently seperate entities? In order to find this question we have to look for invariance property. The invariance features will say that both of the manifolds are the same at some extent. I tried to give this above explanation in order to give a physical idea of manifolds. In theoretical physics maniy fields such as relativity (Obvious;y general one), magnetohydrodynamics, plasmadynamics, quantum machanics, string theory etc they use these beautiful mathematical tools in order to explain plysical phenomena. Now a days in many theories such as fracture mechanics, damage mechanics, particale dynamics (Dr. Yavari's paper) etc are being tried to be explained by the concept of classical differential geometry. Please kindly have alook on the following link if some one is more interested on the theory of manifold.

"http://www.math.washington.edu/~lee/Books/Manifolds/c1.pdf" Instead of going through the text books this above document is very helpful to have a basic idea at a glance.

Thanks

Rezwan

You should try to have this as a Liquid paper

Mike Ciavarella — Wed, 11 Jun 2008 05:33:40 -0400

Dear Arash

your paper will be read by few, and you say you are not willing nor able to make it simpler and more accesible. But in the future, this will change. This is because your paper is "solid", and there are too many papers around.

See my recent posts

LiquidPub Project: Scientific Publications meet the Web, a project from University of Trento

My letter of resignation from the board of Int J Solids and Structures / ELSEVIER
“Leading Opinion: Peer review as professional responsibility: A quality control system only as good as the participants.

even if you have just 5 minutes, it is good to read Leonardo

Mike Ciavarella — Tue, 10 Jun 2008 16:56:03 -0400

michele ciavarella
www.micheleciavarella.it

good point

Arash_Yavari — Tue, 10 Jun 2008 15:33:50 -0400

Dear Mike:

You have a very good point here. I agree that it is important to write clearly and in a way that people can follow the ideas, derivations, etc. I personally do not like unnecessary abstraction and complicating things that are intrinsically simple. I think good ideas are simple and should be explainable in simple words. Having said all that, one should just hope that people follow what s/he writes. In the case of this paper, I've done the best I could.

Again in simple words, there are different approaches in deriving the governing equations of a given theory. It is, in principle, useful and important to understand the connection between these different formulations. For example, you can start from F=ma or from Principle of Virtual Work. These are "equivalent". But it seems some formulation(s) is preferable in a specific application. A good example is the weak formulation of finite element method.

Regards,
Arash

SSPh Basis functions for meshless methods

rbatra — Tue, 10 Jun 2008 14:54:38 -0400

Romesh C. Batra

It seems that the SSPH basis functions described
in Computational Mechanics, 41, 527-548, 2008 are easy to use in
meshless methods.

Arash thanks for your reply and your effort: I remain confused!

Mike Ciavarella — Tue, 10 Jun 2008 04:38:48 -0400

I am not implying you should change style from mathematical one, but then you should NOT expect engineers to read you! This is life

michele ciavarella
www.micheleciavarella.it