A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks

By Timon Rabczuk, Goangseup Zi. 2007

347 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3acf0c18bbef333cf6efcabfde6dd189e1cfbbed

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure (2016, neutral): “Alternatively, meshfree methods [36, 37] as a promising technique in recent years have been applied in modelling of fracture.”
A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures (2008, positive): “riched by the discontinuous displacement ue [ 27 , 34, 35].”
Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws (2015, background): “Reyes and Einstein (1991), Wong and Chau (1998), Yang et al.”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, background): “We redefine the x-coordinate axis to coincide with the crack orientation [40], see Figure 14b.”
Phase-field modeling of fracture in linear thin shells (2014, neutral): “However, despite the advances made in modeling fracture for solid bodies [1, 2, 3, 4, 5], fracture in thin bodies remains a challenge due to the complex interplay between cracks and the shell kinematics and geometry.”
A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates (2010, methodology): “have combined the strain smoothing technique [19] used in meshfree methods [20–27] into the finite element method using quadrilateral elements to formulate a cell/element-based smoothed finite element method (SFEM or CS-FEM) [28–30] for 2D solids.”
Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment (2008, background): “In the whole paper, we denote by X0 the body of interest in the reference configuration, and X ¼ ðX ; Y ; ZÞ 2 X0 R3 a point in the reference configuration.”
Phase field modelling of crack propagation, branching and coalescence in rocks (2018, methodology): “hod (Nanthakumar et al. 2014, Moes and Belytschko 2002), the phantom node method (Rabczuk et al. 2008a, Chau-Dinh et al. 2012, Vu-Bac et al. 2013) and specic meshfree methods (Rabczuk et al. 2007a, Rabczuk and Zi 2007, Rabczuk et al. 2007b, 2008a, Rabczuk and Samaniego 2008, Rabczuk et al. 2008b, Am”
A robust preconditioning technique for the extended finite element method (2011, background): “Several problems, such as cohesive cracks [21] and largely deformed structures [22], can now be solved using meshfree approaches.”
Extended meshfree methods without branch enrichment for cohesive cracks (2007, methodology): “[40] developed the extended element-free Galerkin (XEFG) method for cohesive cracks.”
On three-dimensional modelling of crack growth using partition of unity methods (2010, methodology): “3 is implemented in the extended element-free Galerkin method [117,118] which is based on a local partition of unity concept.”
Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies (2018, methodology): “6 2D dynamic shear loading of Kalthoff experiment We next test our method for dynamic fracture by taking advantage of the Kalthoff-Winkler experiments [52] which has been studied by several other researchers [14, 53–59].”