Mathematical perspective on XFEM implementation for models involving contribution on interfaces
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Mathematical perspective on XFEM implementation for models involving contribution on interfacesData
2024Cita bibliográfica
Cao-Rial, M.T, Moreno, C. & Quintela. P. (2024). Mathematical perspective on XFEM implementation for models involving contribution on interfaces. Mathematics and Computers in Simulation, 218, 266-291. https://doi.org/10.1016/J.MATCOM.2023.11.012
Resumo
[Abstract] Models involving interfaces with discontinuities or even singularities of some fields across them
are very frequent in real life problems modelling. In the last decades, the use of the eXtended
Finite Element Method (XFEM) instead of the traditional FEM has become more and more
popular, mainly because of two advantages: the mesh of the domain can be independent of the
interface position, therefore avoiding remeshing, and it allows to enrich an area with specific
shape functions fitted to the particular properties (singularities, discontinuities) of the expected
solution, obtaining more accurate results with less computational efforts. Nevertheless, a critical
point of XFEM is its implementation since it varies from one problem to another, due to the
different kind (and number) of degrees of freedom on each node. A diligent organization of
nodes, degrees of freedom and enrichment functions is fundamental to achieve an efficient
implementation. Our aim in this paper is to provide a common reference framework for the
implementation of XFEM from a mathematical point of view, providing the readers with a set
of tools that will allow them to apply it to any kind of problem. To this aim, we present a
detailed description of XFEM implementation, with special emphasis on the terms that involve
integration over interfaces. The proposed tools are presented in a general context, and as
an example, we will apply them to a problem of solids mechanics. In particular, we will
contextualize the procedure on a Rayleigh waves propagation problem in a cracked structure
considering a Signorini contact condition on the crack sides
Palabras chave
Extended finite element method
Mathematical tools for numerical implementation
Integration over interfaces Rayleigh waves
Mathematical tools for numerical implementation
Integration over interfaces Rayleigh waves
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This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).