iMechanica - discontinuities in mesh free methods - Comments

problems in representation of the study domain

Chainette. Leila — Fri, 16 Dec 2011 03:41:24 -0500

Hello,
I'm working on modelling of induction heating in electromagnetics with meshfree methods (EFG method).
I want to have explanations on the techniques used in the modelling of
different regions in presence (air, ferromagnetic material,...) in the
global domain of study.
thank you

problems in representation of the study domain

Chainette. Leila — Sat, 10 Dec 2011 01:38:32 -0500

Hello,
I'm working on modelling of induction heating in electromagnetics with meshfree methods (EFG method).
I want to have explanations on the techniques used in the modelling of different regions in presence (air, ferromagnetic material,...) in the global domain of study.
thank you

I am not sure about

DukeKim — Sat, 17 Sep 2011 09:49:49 -0400

I am not sure about it, overoll

Auto Adaptive interface treatment

maxrobert — Wed, 23 Feb 2011 13:32:44 -0500

Hi, i'm new in the meshfree method. I'm doing my master dissertation in an Auto Adaptive Interface Treatment for the EFGM in eletromagnectic problems. I believe that it can be used for cracks too, just adjust the method. I'm brazilian, and presented in poster format in MOMAG 2010. Each interface has a precision, and for each interface contact it has test points that the mean relative errors between the test points compared to the interfaces precision decide wich interface has to be discreted again. Well, sorry for my english, i didn't practice for a long time haha. I believe that i'll finish my work between July and October. If it could help you, tell me. Thanks.

crack in meshless methods

Jafar — Sun, 03 Oct 2010 02:01:32 -0400

Sukumar,

I'm working in extending discrete least squares meshless (DLSM) method on modelling crack propagation.

http://imechanica.org/node/9020

Regards this I have a question:

What is the general form of partial differential equation governing a elasticity problem when existing a crack in the domain?

Best Regards

Jafar

Interest method, thank you.

mixmagtmb — Thu, 18 Dec 2008 15:25:18 -0500

Interest method, thank you.

a related thread on meshless methods

Zhigang Suo — Sat, 21 Jun 2008 17:25:13 -0400

Please also see a related thread: The future of meshless methods.

TAHOE

Roozbeh Sanaei — Mon, 12 Mar 2007 04:02:48 -0400

Sandia's Tahoe may be useful package in this regard. For Atomistic-Continum Bridging. quasicontinuum is multiscale package in this field too.

local extrinsic PUM enriched EFG for crack propagation modelling

vinh phu nguyen — Sat, 10 Mar 2007 12:17:06 -0500

Hi,

You should look at papers of Timon Rabczuk using the following link
http://www.lnm.mw.tum.de/Members/rabczuk

I can summarize the basis ideas of the method. I assume that you already know the EFG. Using the local partition of unity concept, we incorporate discontinuous function (Heaviside function H(x)) into the EFG approximation to model the discontinuity due to the crack. So, nodes with domain of influence cut by the crack are enriched by the H(x). It means:

u(x) = phi_I(x)u_I + phi_J H(x) a_J, phi : MLS shape functions as usual

It is the second part of the approximation who handles the crack.

For linear elastic fracture mechanics, since you know the singular field at the crack tip, you can also add them into the approximation. So, nodes whose support contain the crack tip are enriched by the asymptotic functions describing the singular field around the tip.

For numerical integration, the background integration cells are used. To get better accuracy, cells cut by crack are divided into triangles (2D) as done in XFEM.

They called the method, XEFG (eXtended EFG). The method can be applied to nonlinear materials, large deformation and cohesive cracks. The problem of crack iniation based on loss of hyperbolicity can be handles with ease.

Hope that it was clear.

Phu

RE: PIMs are discontinue

abshaw — Tue, 13 Feb 2007 13:26:53 -0500

Generally PIM is not conforming and produces discontinuity in the approximation as domain moves. However there is a way to restor conformability. You may see this reference Liu et al., 2005, "A linearly conforming point interpolation method (LC-PIM) for 2D mechanics problems", International Journal of Computational Methods, 2, No. 4,

PIMs are discontinue

83684024 — Mon, 12 Feb 2007 13:59:57 -0500

As you know, the PIM shape functions produce a discontinue approximation and it is suitable for methods with local discretization such as MLPG. But I am not sure about it.

Re:PIM with EFG ?

abshaw — Wed, 07 Feb 2007 14:22:48 -0500

Usual form of EFG is based on MLS approximation of the target function. However, to my knowledge any approximation scheme can be used.

PIM with EFG ?

83684024 — Mon, 05 Feb 2007 17:11:04 -0500

Is it possible using PIM shape function with EFG method?

discontinuities in mesh free methods

robilant — Tue, 30 Jan 2007 11:48:54 -0500

Thank you for all your insightful replies.

The Cracking particles don't really solve my problem because I would need something that is:

- as much independent as possible from sampling density (of the particles)

- unified tratment for non convex object and artifical discontinuities (it seems to me that only the visibility criterion fullfills this need)

- very efficient to compute, to be applied in a 3D interactive context.

I'm currently trying to find a way to extend the visibility criterion to something less prone to unwanted discontinuities.

Thank you again,

Rob

A paper using phase field to simulate dynamic fracture

Jinxiong Zhou — Fri, 26 Jan 2007 15:49:45 -0500

Gracie,

There are several papers about use of phase field to simulate dynamic crack propagation, particularly in brittle materials. Alain Karma have done very excellent research work on this topic. One of their paper is entitled "phase-field model of Mode 3 dynamic fracture". You can find the paper via arXiv: cond-mat/0105034, 2001.

discontinuities in mesh free methods

robilant — Tue, 23 Jan 2007 05:40:17 -0500

Hello,

I wish to ask where to find literature about introducing discontinuities in the shape functions to simulate cracks in mesh free methods.

I found the visibility criterion, the diffraction method and the transparency method referred in the (I think vey good) survey by Fries and Matthies "classification and overview of meshdree methods" but nothing else.

thank you,

Rob