iMechanica - X-FEM - Comments

A good book

wilkins aquino — Thu, 25 Dec 2008 11:16:26 -0500

Tuhin:

The following book is great as an introduction to functional analysis and its application to variational methods.

D. Reddy, Introductory Functional Analysis: With Applications to Boundary Value Problems and Finite Elements

Which problems

Scott Johnson — Tue, 16 Dec 2008 00:09:38 -0500

I know the question was what material to read in order to understand the X-FEM method; however, it may also help to know what aspects of powder mechanics you are researching to determine whether X-FEM is the most appropriate method to use. Powder mechanics can be especially sensitive to the appropriate RVE for continuum methods, and many dense, dynamic powder systems are difficult to characterize using such approaches.

Depending on the application, a host of other numerical methods may help to study your problem of interest. Some popular approaches include:

multi-phase Eulerian hydrocodes (e.g., the open source MFIX at NETL)
meshless Lagrangian continuum methods (e.g., Element-Free Galerkin (EFG) or Smoothed Particle Hydrodynamics (SPH))
discontinuum methods (e.g., hard sphere particle dynamics or Discrete Element Methods (DEM))

Thanks a lot

Tuhin Sinha — Sat, 13 Dec 2008 00:01:28 -0500

Thanks a lot Dr.Sukumar..I'll try that book and see how it goes..

Re: Math background

N. Sukumar — Fri, 12 Dec 2008 21:56:22 -0500

Tuhin,

The very basics of functional analysis (vector spaces, norms, etc.) would suffice to develop an understanding of the math required in basis-set approaches such as FEM/X-FEM. The best book for FEM and also for X-FEM/PUFEM in this regard is: Strang and Fix ("An Analysis of the Finite Element Method", Prentice-Hall, 1973). It provides the essentials on the math for one (without a math degree) to readily understand and appreciate FEM, and still remains a classic in the field. Most FEM textbooks quickly get into the implementation of the method (shape functions, B matrix); S&F provide the mathematical basis of the FEM, as the title indicates, which would aid in understanding partition-of-unity FE methods. Hope this helps?

Mathematical background for X-FEM

Keng-Wit Lim — Fri, 12 Dec 2008 21:22:03 -0500

Take a course in real analysis followed by functional analysis in your math department.

At the same time, you can read any book related to analysis to develop the background.

Post Doc Application

Egemen Teomete — Tue, 20 May 2008 18:37:55 -0400

Howe Hall Room 1200Iowa State University Ames Iowa 50011 May 20, 2008 Dear Dr. Moes, I am writing to you for application of the post doc positions on X-FEM for the simulation of fracture in composites. I have been working on micro damage modeling due to wire saw cutting process of brittle materials in my PhD. I am sure that I will be very productive while working with you. I worked on finite element modeling of composites using homogenization techniques and mechanical testing of rock, concrete and steel during my M.Sc. I have been working on wire saw induced damage on brittle materials in my PhD. Silicon wafers in semi conductor and photo voltaic industries are sliced using wire saw process. Wire saw process is also used to cut piezo ceramics for actuator and sensor applications. I have been making experimental work on wire saw cutting of Alumina ceramics and working on analytical damage models that will relate the wire saw process parameters with roughness and waviness damage on the cut surface. The indentation damage models and contact mechanics are a starting point for me for the development of a wire saw damage model. I have taken courses on Molecular Dynamics, Continuum Mechanics, Elasticity, Plasticity, Fracture Mechanics and Fatigue, Mechanical Properties of Materials, Finite Elements and Process Engineering. Thus I have a good understanding of mechanics of materials in multi scales. I can send my resume to you if you can provide me your email. I would be pleased if you can contact me via my email: egemen_teomete@yahoo.com. Yours sincerely, Egemen TeometeEmail: egemen_teomete@yahoo.com

Post-Doctoral position available on X-FEM

Ratnesh Khandelwal — Fri, 18 Apr 2008 06:49:07 -0400

Dear Nicolas Moes,

I have recently submitted my PhD thesis titled "Studies on the Evaluation of Thermal Stress Intensity Factors for Bi-material Interface Cracks" under the guidence of Prof J. M. Chandra Kishen at Indian Institute of Science, India.

During the course of my PhD program, I worked on the analytical and computational appraoch for structural and thermal related bi-material interface fracture problems and worked on my self developed "Finite element & bimaterial interface fracture analysis" code. During my doctoral studies, i have developed interest in the following fileds.

Solid Mechanics
Finite Element Method
Fracture and Fatigue Analysis
Bi-material interface crack Problem

I would be quite interested in working on the above mentioned problem under you as post doctoral candidate. Please, let me know the further details through my E-mail ID.

regards,

Ratnesh khandelwal

PhD. Student, IISc, Bangalore

ratneshk@gmail.com

FMM and quasi-static/dynamic crack growth

N. Sukumar — Sat, 01 Sep 2007 17:07:54 -0400

Dear Roy et al.,
Thanks for your comments. Sorry for the time-delay. Probably some further clarifications are needed in the text so as to not mislead the reader. Use of `front velocity' is standard in the FMM/level-set literature, and hence we have used the same (even though dynamic fracture is not considered). As Biswajit pointed out, the expressions for the stresses are for a static/quasi-static (classical) Westergaard's crack solution. No inertial contribution is assumed in the paper. As John alluded to, the FMM is independent from the crack mechanics/physics. Given a crack front and the `velocity' prescribed on it, the FMM allows one to just update the position of the new crack location. For dynamic fracture, there might be stability issues when too large a `time step for FMM' is taken, but in principle, the algorithm can be applied.

Equation (31) of Sukumar's paper

Biswajit Banerjee — Sat, 01 Sep 2007 16:30:31 -0400

John,

I believe the sine-cosine expansions in the stress field near the crack tip are based on the work of Westergaard (JAM, 6, p. A49, 1939) and Sneddon (PRSL-A, 187, p. 229, 1946) and can also be derived from the work of Williams (later) and Michell (earlier). I don't think any of these derivations considered the effect of body forces or inertia. The sine-cosine expansions might only work for certain forms of the acceleration function (and for negligible accerlerations) - which is probably what Roy is referring to. You can try plugging in the expressions for displacement in the full Navier equations (including the inertia term) and you will see that it is hard to get the forces to sum up to zero except for special cases.

Biswajit

re: dynamic crack simulation with fast marching

John E. Dolbow — Fri, 31 Aug 2007 18:06:39 -0400

Roy,

The FMM can be applied to quasi-static as well as dynamic processes. I don't see any reason why what Suku has done could not be extended to dynamic fracture, but will allow him to comment further.

Dynamic crack simulation?

Luoyu Roy Xu — Fri, 31 Aug 2007 15:48:47 -0400

Dear Suku,

This is a very challenging topic, and I believe you’ve made significant contributions. Since you’re using the fast marching method, my impression is that you’re dealing with a dynamic crack. However, equation (31) is applicable for a static 3-D crack, not a dynamic crack. Can you use the same approaches to simulate a dynamic crack (for example, the crack tip speed is at least 10% of the shear wave speed)? Thank you for presenting nice work.

Roy