Thank you for your answer and sharing those information.
Yes, I am working with Dmitry at Argonne:-). We have considered using the
xfem/pum to model particulate flow problems which may involve either
singular type enrichment or interface type enrichment. I have also worked
on xfem/lsm modeling of microstructural evolution during my PhD at
Northwestern and am interested in extending it to 3D parallel case.
Hansbo's approach is a smart way to do it. I am not sure if it is
straightforward to incorporate crack tip asymptotic enrichment. In his
original paper, only weak and strong discontinuities were studied.
I remember I have read a thesis on dealing hanging nodes with xfem, but not
at hands now. I will check my home computer after work. It might be useful.
Xujun
On Fri, Nov 21, 2014 at 4:00 PM, Benjamin Spencer <benjamin.spen...@inl.gov>
wrote:
> 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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