A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM

A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM A comparative study on finite elements for capturing strong discontinuities by means of elemental (E-FEM) or nodal enrichments (X-FEM) is presented. Based on the same constitutive model (continuum damage) and linear elements (triangles and tetrahedra) optimized implementations of both types of enrichments in the same non-linear code are tested for a representative set of 2D and 3D crack propagation examples. It is shown that both methods provide the same qualitative and quantitative results for enough refined meshes. For the performed tests, E-FEM exhibited, in general, a higher accuracy, mostly for coarse meshes, whereas, convergence rate with mesh refinement, which is super-linear, showed slightly higher for X-FEM. As for the computational costs for single crack modelling X-FEM showed, depending on the case, from 1.1 to about 2.5 times more expensive than E-FEM. For multiple cracks, the computational cost of E-FEM keeps constant, whereas the cost associated to X-FEM increases linearly with the number of modelled cracks. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computer Methods in Applied Mechanics and Engineering Elsevier

A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM

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Publisher
Elsevier
Copyright
Copyright © 2005 Elsevier B.V.
ISSN
0045-7825
eISSN
1879-2138
D.O.I.
10.1016/j.cma.2005.09.020
Publisher site
See Article on Publisher Site

Abstract

A comparative study on finite elements for capturing strong discontinuities by means of elemental (E-FEM) or nodal enrichments (X-FEM) is presented. Based on the same constitutive model (continuum damage) and linear elements (triangles and tetrahedra) optimized implementations of both types of enrichments in the same non-linear code are tested for a representative set of 2D and 3D crack propagation examples. It is shown that both methods provide the same qualitative and quantitative results for enough refined meshes. For the performed tests, E-FEM exhibited, in general, a higher accuracy, mostly for coarse meshes, whereas, convergence rate with mesh refinement, which is super-linear, showed slightly higher for X-FEM. As for the computational costs for single crack modelling X-FEM showed, depending on the case, from 1.1 to about 2.5 times more expensive than E-FEM. For multiple cracks, the computational cost of E-FEM keeps constant, whereas the cost associated to X-FEM increases linearly with the number of modelled cracks.

Journal

Computer Methods in Applied Mechanics and EngineeringElsevier

Published: Jul 15, 2006

References

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