iMechanica - computational mechanics - Comments

Smoothness of crack tip fields in X-FEM and error estimation

Stephane Bordas — Wed, 29 Oct 2008 06:44:15 -0400

Dear Pooyan,

What you are describing is not a problem with your code (at least not necessarily).

There are many papers on this topic, for instance, I recommend the following:

http://doi.wiley.com/10.1002/nme.1601 by Karihaloo Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically …

Direct evaluation of accurate coefficients of the linear elastic crack tip asymptotic field by Karihaloo again

XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials still by Karihaloo

Derivative recovery and a posteriori error estimate for extended finite elements by Marc Duflot and Stephane Bordas

http://www3.interscience.wiley.com/journal/119054430/abstract by Marc Duflot and Stephane Bordas

A recovery-type error estimator for the extended finite element method based on singular+smooth … by Rodenas, etc.

A Global Explicit Residual Based Error Estimator for the eXtended Finite Element Method in … by Geniaut and Delmas

A simple error estimator for extended finite elements (Marc Duflot and Stephane Bordas and Phong Le)

Numerical Aspects of the extended Finite Element Method by Peters and Hackl

Do let me know if you would like preprints of those articles, which I could provide.Our XFEM matlab code could be of interest to check your code as well. I wonder if you could describe what you mean by extrapolation technique specifically?

Many thanks,

Dr Stephane Bordas

http://people.civil.gla.ac.uk/~bordas

X-FEM tip enrichments

pooyan broumand — Tue, 28 Oct 2008 10:33:26 -0400

Hi ;

I am modeling quasi-static crack propagation with x-fem .

for calculation of SIFs I used the extrapolation method , but I found that the displacements at the tips are not very smooth and are turbulated. and as the result the SIF calculated are not correct .

Why the displacements are not smooth, and there exist a high gradient in the tip element. is it in X-Fem nature or it is my code problem?!

another thing is that where should the points to be used in SIF calculation be located ?

In FEM they are located at the edges of the crack but in X-FEM there are turbulances near the crack edge and this will affect the results.

thanks

The link does not work....

Mike Ciavarella — Fri, 18 Jul 2008 16:30:32 -0400

Can you post again, or else can you attach please the conditions directly on imechanica?

Porto is a nice place .... particularly in July, so if the conference is not unreasonably expensive.... ;)

Thank you Biswajit!

HariKrishna — Mon, 16 Jun 2008 09:39:32 -0400

Thank you Biswajit!

re: Strain rate

Biswajit Banerjee — Fri, 13 Jun 2008 01:23:26 -0400

Consider a test where you put a specimen in a loading machine and apply a displacement. The displacement starts at u=0 at t=0 and reaches a value of u=d_1 at t=t_1. If the plot of u vs. t is linear, i.e. u = (d_1/t_1) t, then the rate at which the displacement is applied (du/dt) is constant and equal to d_1/t_1. This is the displacement rate.

Associated with the displacement is a strain e=du/dx (say). For a linear elastic material, at t=0 the strain is e=0 and at t=t_1 the strain is e=d_1/L The strain rate is the quantity de/dt = d_1/(t_1 L).

For plastic deformations we use a similar idea of incremental linearity and can therefore calculate a strain rate associated with small increments of time. Read Hill's book on the theory of plasticity for more details.

-- Biswajit

Re:Time dependent vs Independent

HariKrishna — Thu, 12 Jun 2008 13:02:47 -0400

Can Someone please point me to some source where I can read about this?

Thank you

polyhedral deformations in carbon nanotubes

Marino Arroyo — Wed, 04 Jun 2008 07:35:43 -0400

Dear Ashkan,

Very interesting paper! Related to some of your comments in the paper, we actually have found and described polyhedral deformations in carbon nanotubes, and have characterized the effective nonlinear structural response in this regime. These are described in

Arias and Arroyo, PRL 100:085503 (2008)

Arroyo and Arias, JMPS, 56(4) (2008)

Arroyo and Belytschko, PRL 91:215505 (2003)

Best regards

Marino

-- Marino Arroyohttp://www-lacan.upc.es/arroyo/Universitat Politecnica de CatalunyaCampus Nord, C2-204Jordi Girona 1-3Barcelona, 08034Tel: +34 93 4011805Fax: +34 93 4011825

Re: Dear Sukumar i am using

abshaw — Wed, 28 May 2008 18:27:44 -0400

Dear Vivek,

Theoretically we need np=(n+p)!/n!/p! (n ane p are respectively the physical dimension and consistency) no of points within the support of the kernel function in order to make the moment matrix non-singular. However from numerical perspective we generally take ‘slightly’ bigger support. But ‘arbitrarily’ large support may lead to an exaggerated smoothness in the approximation. Consequently system matrix may lose diagonal dominancy and becomes ill-conditioned.

Now the question is how big the support should be? That depends on many things such as particle density, the function you are approximating (solution of PDE), how the particles are distributed within the support etc. Best way (in the context of EFGM) of choosing an ‘optimum’ support size is numerical experiments.

It is relevance to mention that there exist some mesh-free techniques which does not rely on any user defined support size. For instance NEM (you can find a brief introduction and references on sukumar’s webpage), NURBS-based mesh-free methods (doi:10.1016/j.cma.2007.11.024).

Hope it helps.

Cheers!!

Hi

CanhLe — Fri, 18 Apr 2008 18:34:32 -0400

Hi Vivek,

Theoretically, the more nodes is used, the better result will be obtained. But it's not correct in your situation! It may relate to A matrix in MLS, when large number of nodes is used, A rapidly becomes ill-condition. This results in inaccuracy solution if invert form of A is used. As a solution to this problem, LU decomposition can be employed in determing shape function and its derivatives.

No maximum of D_max is ruled, but D_max should be chosen so that do not lose local character of shape function.

Hope this helps.

Cheers,

Canh Le

Canh V. Le, PhD Student
Department of Civil and Structural Engineering
The University of Sheffield
Mappin Street,
Sheffield, S1 3JD, UK.
Phone: GB +44 1142225724
http://www.cladu.shef.ac.uk/new

Dear Sukumar i am using

vivek varshney — Sat, 26 Jan 2008 06:48:23 -0500

Dear Sukumar

i am using EFG in my thesis. i got confuse in one stage. please clear my
doubt.in this method D_m= D_max*C_i is there. where D_m is the radious of
influence.It has been written in many papers D_max is generally taken as
2-4 forstatic analysis. but i have a doubt in that. for convergence study
when i am increasing the no of nodes (more than 1000),i am not getting
good
convergent result when i have taken D_max=3. now when i am increasing the
value of D_max say 5,6,7,8 then i am getting better convergent
value(Energy norm is reducing on increasing the no of nodes). Am i right
or not ? So how should i take the value of D_max. what is the maximum
value of D_max can i take ? please help me.
So what is the appropriate value of D_max which i should take?

thanks

Library for design patterns/idioms

N. Sukumar — Sat, 19 Jan 2008 00:41:09 -0500

Good luck, Biswajit. A C++ library that contains implementations of design patterns and idioms is Loki.

Dear Biswajit, Wish you

Teng Li — Fri, 18 Jan 2008 10:25:43 -0500

Dear Biswajit,

Wish you the best in your new post, and we look forward to your coming back to iMechanica.

-Teng

C++ Idioms and Design Patterns...

Ajit R. Jadhav — Thu, 17 Jan 2008 22:59:28 -0500

Dear Biswajit,

Good that you broached this topic up... I was wondering if discussions related to programming would be appropriate here at iMechanica---especially, discussions at a somewhat more abstract level (i.e. not concerned with the syntax of languages etc.)... Also, the more serious amongst tutorial codes in C++... I was already wondering if I should be posting some of my code my general blog site... So, I was really delighted to see your above post here...

About C++ idioms. A very closely related topic is Design Patterns. For example, see here and here.

With that said, I have a word of caution, though. IMO it is best *NOT* to try to use design patterns right in the first iteration of a major version of your software--v 1.0 or v 2.0 or whatever....

I know I am sounding like an unenthusiastic fool who has no respect whatsoever for the abstract or high-level design here... But the way I loook at it, there has been sometimes too much of a good thing w.r.t. the high-level abstract design too... Just for example, notice that issues and factors such as data locality (cache and virtual memory), ease of IPC and of parallelization, etc. ought to enter software design... Yet, as a matter of fact, a lot of issues of this nature cannot become as clear as they should be, until the first cut is already over. (We don't have to wait until the profiling stage, but at least a major chunk of the code ought to first exist before people can really get such parts right.) Hence, it is sometimes better to go ahead with a simple scheme involving a minimal number of very loosely coupled classes, and then put them all together into a better framework... A real bottom-up design exercise, in a sense....

Of course, my above comment does not apply to your above post of C++ idioms (or your example of the Factory idiom)... I just wanted to qualify my recommendation of design patterns, that's all...

-----

Biswajit, on a personal note: If you want to quit USA, that's good (ask me why (!)) but you don't want to therefore return to India, do you?

One way or the other, I enjoyed your answers over a range of issues here... Let me wish you the very best in your new environment, and, as Zhigang said, do let us know once you are ready to chat here at iMechanica again... I look forward to interacting with you soon again...

--Ajit

Best wishes for Biswajit

Zhigang Suo — Thu, 17 Jan 2008 21:07:33 -0500

Dear Biswajit: Thank you so much for your contributions to iMechanica. I have learned much from you. Please let us know when you are settled in your new environment. Good Luck and best wishes, Zhigang

Re: MIT Faculty Position in Computational Mechanics

Managers — Mon, 26 Nov 2007 15:08:51 -0500

As Webmaster for the Department of Mechanical Engineering at MIT, I am
assisting with the faculty search process on the technical side. I read
the question about the Computational Mechanics position, specifically
the process for submitting documents including CV, research statement,
teaching statement, etc.

Interested applicants need to set up a user account at
http://search-meche.mit.edu/ by selecting the "Login" link. During the
process of setting up an account, the applicant is prompted to upload
PDF documents including CV, research statement, and teaching statement.

Please let me know if you have any further questions.

Thanks,
j e f f

--
Jeff Matson
Webmaster, MIT MechE
jmatson@mit.edu
617-452-3076