On Fri, Nov 21, 2014 at 1:57 PM, Xujun Zhao <xzha...@gmail.com> wrote:
> Thank you very much for those information. If this involves MOOSE, I think
> I should bring Dmitry in :-)
>
Definitely. Are you working with him? We work with him quite a bit, and
we've had some discussions on this topic in the past.
> It seems both LibMesh and MOOSE are working to implement xfem on fracture
> problems. Is this for dynamic cracks or just static ones? How about the
> weak discontinuity problems, for example, material interfaces.
>
My work in MOOSE is focused on crack propagation. It's a dynamically
changing crack topology, but it's not a dynamic problem in the sense of
including the inertial terms in the solid mechanics PDEs. We don't really
have good support for dynamic solid mechanics problems in MOOSE yet,
although it's in the works. That won't really change much relative to
XFEM, though.
We haven't done anything for material interface problems, although we have
some other problems of that nature that we'd like to use XFEM on.
Ben Kirk can speak better to what he's doing in libmesh, but I think he's
planning on using XFEM for moving shock fronts, and I think the main thing
he's done at this point is implement a method for triangulation of the
elements cut by those interfaces.
> To Ben Spence:
>
> What does 'partial element' mean? is it the element cut by the
> discontinuites or the sub-triangles after division for integration purpose?
> Typically, numerical quadrature in those elements requires a nonlinear
> mapping of quad points between two reference coordinates. One of the
> possible ways to avoid nonlinear mapping is to use rational basis (shape
> function).
>
We're using the phantom node approach of Hansbo and Hansbo, where the cut
elements are replaced by two overlapping elements, each with a physical and
a non-physical component. Those are what I refer to as partial elements.
Ideally, we can just use the same integration points in the partial
elements that we used before they were cut so we don't have to map anything.
A. Hansbo and P. Hansbo. A finite element method for the simulation of
strong and weak discontinuities in solid mechanics. CMAME,
193(33-35):3523–3540, 2004.
>
> On the other hand, how do you handle the hanging nodes for AMR in xfem?
> Any problem?
>
I'm sure we will run into challenges using AMR with XFEM. It would be
really cool to get the two working together, but we need to get the basics
working first.
-Ben
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