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