Partition of unity-based discontinuous elements for interface phenomena: computational issues

By A. Simone. 2004

92 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ee7b2bd7ad1c3632c3fceb4e415ff569303f0aab

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method (2009, background): “As pointed out in (Mourad, Dolbow, and Harari 2007), these oscillations were also noticed by (Simone 2004) in the context of stiff cohesive law imposed on the faces of a crack.”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, background): “A small amount of literature has addressed the problem of applying constraints to bodies across interfaces in enriched finite element methods [3–7].”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, background): “Additionally, as can be seen from Figure 7, a large value of the penalty parameter triggers non-physical oscillations in the traction field at the interface in the same way as was seen earlier for quasi-static problems [24] as well as dynamic problems [28].”
A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, methodology): “Moreover, as already stated by Simone (2004), the Newton-Cotes/Lobatto can significantly reduce the level of oscillations which are obtained with the Gaussian rule in the GFEM.”
Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids (2015, background): “For the integration over the discontinuity Se, spurious oscillations in the tractions are observed with lowerorder Gaussian rules [52,23].”
A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM (2006, background): “• Nodal enrichment [4] [5] [16] [17] [33] [35]: the support of each mode is the one of a given nodal shape function i.e.: those elements surrounding a specific node, see Fig.”
Analysis of Interacting Cracks Using the Generalized Finite Element Method With Global-Local Enrichment Functions (2008, unknown): “[24] A.”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, background): “Regarding the integration over the discontinuity segments Se , the higher-order Gaussian or low-order Newton-Cotes/Lobatto scheme [23] is recommended to suppress spurious oscillations in tractions [10, 61].”
Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, background): “Finding such interpolations is not straightforward and most naïve choices do not satisfy this condition, resulting in spurious nonphysical oscillations in the traction field at the interface (see [3, 4]).”
Towards a generalization of a discrete strong discontinuity approach (2009, methodology): “Therefore, in order to avoid spurious oscillations found with Gaussian rules, a Newton–Cotes/ Lobatto scheme is adopted [36–39].”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, methodology): “The elasticity solution u over ωα , α ∈ Ic-f, can be written as [48, 60] u = û + ̃̃ u = û +H ũ”
Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems (2009, background): “An element with a crack is subdivided into several triangular elements in order to avoid discontinuity in the integration domain [29, 33, 34].”