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

By Javier Oliver, Alfredo Huespe, P. Sánchez. 2006

281 citations recorded by the source corpus.

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.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0ef8ef8bce57c0b3e25185d5823481e7e4cf452f

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In Mechanics of Materials

Citations in the corpus

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities (2009, background): “See Oliver et al. (2006) for a comparative study between the local element-based enhanced elements and nodally-enriched formulations, especially in terms of the associated computational costs.”
A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, methodology): “Jirásek and Belytschko (2002), Oliver et al. (2006) and Borja (2008) performed a comparative analysis between: i) a local embedded formulation, using static condensation, based on the enhanced assumed strain method (EAS) and ii) the GFEM.”
Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations (2015, background): “However, nodal enrichment requires more computing time [10–12].”
A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics (2007, result): “[41] compared embedded elements and the XFEM for three-dimensional crack problems, which showed that embedded elements can give results very comparable to the XFEM.”
Model-Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges (2021, methodology): “In [205], control inputs are numerically evaluated as the ones minimizing a weighted sum of interaction forces and error at the end effector and relying on a quasi-static FEM model.”