Arbitrary discontinuities in finite elements

By Ted Belytschko, Nicolas Moës, S. Usui, Chandu Parimi. 2001

1,178 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/313c74b5aa67c4841ba7515d04b2d6fbad9d07ae

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Multiscale aggregating discontinuities: A method for circumventing loss of material stability (2008, methodology): “The XFEM method was developed in [21, 22]; recent developments are given in [23–29].”
Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3) (2014, positive): “For cracked Mindlin plates [7-9,11], the finite element approximation for enriched elements is expressed in the form of”
A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures (2008, positive): “the local partition of unity by Belytschko and his collaborators [18–21] where the crack can propagate arbitrarily in an element without remeshing.”
Non‐linear analysis of shells with arbitrary evolving cracks using XFEM (2005, positive): “The function HK( ) in (3) is a modified sign function which was employed in previous studies (see References [3, 7]) HK( ) = 1 2 ∑4L=1 NL( )dL∣∣∣∑4L=1 NL( )dL∣∣∣ − dK |dK | (4) Copyright 2004 John Wiley & Sons, Ltd. Int.”
Modeling three‐dimensional crack propagation—A comparison of crack path tracking strategies (2008, methodology): “To overcome this deficiency, Belytschko and co-workers [7, 8] introduced a technique to successfully capture smooth failure surfaces: the celebrated extended finite element method.”
Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach (2006, methodology): “The ones developed up to date are based on the X-FEM method [6,19], which, in turn, lies on the use of the partition of unity concept [6].”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “The interface of the X-FEM with level set techniques to model weak discontinuities such as material interfaces (bimaterials) was introduced in Sukumar et al. (2001), whereas the representation of tangential discontinuities was presented in Belytschko et al. (2001).”
A generalized finite element method with global-local enrichment functions for confined plasticity problems (2012, positive): “As an example, Heaviside (or Step) and Westergaard (or Branch) functions can be used as enrichment functions to accurately describe the discontinuity and singularity in the interior of a finite element caused by the presence of a crack [6, 8, 18, 29].”