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Need a hand to pull me into the world of XFEM !!
Dear all,
I am new to X-FEM, started reading papers a couple of weeks before. I understood, functions[heaviside,sign..] are used to enrich the nodes to simulate virtually the discontinuity and asymptotic functions are used to charecterize the crack tip,other than this regular FEM nodes are there. I have few questions.
1.what is the role of the asymptotic functions and its unknown co-efficient 'b' in charecterizing the crack tip. What are the parameters do these functions exactly charecterize means wat are the details can we extract from these fns n co-effs?
2.I think the simulation will start with the initial crack. after inverting the k matrix we get u(classical fem disp) , a (crack opening length b/w the new surfaces ??? ) , b (not sure wat this is , my guess is crack tip's new displacement ??? ), How the new segment of crack growth(n its direction) is calculated ?? as till now SIF's never came into picture??
3.which parameter will be incremented for the second step and how the result from the first step is used in the second step? say in quasi-static.
I know some questions are really dumb for those who are familiar with XFEM, Kindly help me in understanding the above questions. Thanks in advance.
mike
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xfem for beginners
Hi Mike,
In below, I am trying to answer your questions.
1. The asymptotic functions are only used for cases where exact solutions are known such as in linear elastic fracture mechanics (all we know the Westeergaard solution.). In other cases, only enriched by Heaviside function is enough as done in cohesive cracks modelling.
2. You were talking about crack propagation simulation with xfem. So, starting with an existing crack, the nodal unknowns are computed, including the displacement dofs (u) and enrichment dofs (b). Then, you then use some criteria to compute the crack propagation angle, and provided a crack advance length, you update the crack geometry, then the process is repeated again.
There are many criteria for this depending on LEFM or cohesive cracks. Noting that xfem can be used for crack initiation too.
There is a simple xfem Matlab code, available for free for which you can get by writing to Dr. Stephane Bordas at stephane.bordas@gmail.com.
You can also write to me at nvinhphu@gmail.com for discussion concerning xfem, if you like.
Good luck.
P
I am a PhD student in
I am a PhD student in Department of Mechanical Engineering of University of Aveiro, Portugal.
I studied papers on XFEM methods and I am trying to implement XFEM
in my finite element code to enrich the asymptotic near tip crack
field, but I am having a difficulty.
I constructed the strain-displacement matrix in the FEM method, then
we have Kuu, Kua and Kaa stiffness matrices. My problem is that I want
to invert Kaa to perform static condensation of the enriched degrees of
freedom and I cannot invert Kaa because a lot of eigenvalues of this
matrix are zero. I cannot find any bug in my implementation. Did you
experienced similar problems with your implementation or did you
perform enrichment in a different way?
If you could help me, I would appreciate it very much!Sofia. hd movies cheap
Stiffness matrices in X-FEM
You can not do static condensation, as is done in many FE
formulations where there are basis functions that are non-vanishing
only in the interior of the element. In X-FEM, the "a" coefficients
also have to be solved for globally. So,
when you solve the linear system (after imposing the essential boundary
condition), you should have "u" and "a" coefficients as unknowns and
both are obtained simultaneously. An easier means to come to this
inference is to take a basis-centric viewpoint. The X-FEM or GFEM
(also FEM) consists of trial functions that are formed via a linear
combination of basis functions. With X-FEM, the number of basis
functions increases vis-a-vis FEM, and ergo, the number of unknown
coefficients that one must solve for also goes up.
Trying to do solve problems in one-dimension on paper or via coding
would be helpful to develop a good understanding of the method. I
have assigned a homework in couple of my previous course
offerings on this topic, and will post the same sometime next
week for it might be of some use to get started.
P.S: A PUFE homework exercise has been posted here.
A simple X-FEM example in one-dimension (worked out on paper...)
Hi Sofia and Mike:
A simple X-FEM example in one-dimension (worked out on paper...) can be found on my web-page. Search for "An interface element based on the partition of unity"; the example is worked-out in Section 5 and Appendix A.
Thx for concern
Thx Dr.Sukumar n Dr.Simone for the concern.