An explicit dynamics extended finite element method. Part 1: Mass lumping for arbitrary enrichment functions

This paper presents a general mass lumping technique for explicit dynamics simulations using the eXtended Finite Element Method with arbitrary enrichment functions. The proposed mass lumping technique is a generalization of previously published results for cracks and holes. Time step estimates are s...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2009-06, Vol.198 (30), p.2297-2317
Main Authors: Elguedj, T., Gravouil, A., Maigre, H.
Format: Article
Language:English
Subjects:
Computational techniques
Engineering Sciences
Enrichment
Exact sciences and technology
Explicit dynamics
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Mass lumping
Mathematical methods in physics
Mechanics
Physics
Solid mechanics
Structural and continuum mechanics
X-FEM
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Summary:This paper presents a general mass lumping technique for explicit dynamics simulations using the eXtended Finite Element Method with arbitrary enrichment functions. The proposed mass lumping technique is a generalization of previously published results for cracks and holes. Time step estimates are studied for crack singular enrichment functions and for hole enrichment. In both cases, we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element. The performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published X-FEM results.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2009.02.019