Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment

By Stéphane P.A. Bordas, Timon Rabczuk, Goangseup Zi. 2008

388 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/e9a3e5fd77668ab656af66fc42f0aab4d7e8707d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “Another positive feature of meshless methods is the resulting smooth stresses which can be obtained for high-stress gradients around crack tips [13] thus requiring less effort in post-processing as compared with the XFEM.”
Extended finite element method with global enrichment (2015, background): “Several other variations have also been proposed [8,9,10,11] which extend the applicability of the method.”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “to large deformation [4], crack problems [5–8] and adaptive analysis [9–11].”
On three-dimensional modelling of crack growth using partition of unity methods (2010, neutral): “[22] and Rabczuk et al.”
A smoothed finite element method for plate analysis (2008, neutral): “It is important to retain accuracy in a local region before cracking happens in order to obtain the correct crack path [46, 16 ].”
Polygon scaled boundary finite elements for crack propagation modelling (2012, methodology): “They have been applied to solve many crack propagation problems both in statics and dynamics [16–19].”
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics (2011, background): “Meshfree algorithms for fracture mechanics remain a subject of considerable research activity, with recent work focussing on locally enriched approximations for problems containing material and geometric non-linearity [21, 22].”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Formulations for dealing with conjunctions and intersections between multiple cracks is proposed for the extended EFGM using piecewise triangular facets in [18].”
Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping (2009, neutral): “Partition of unity methods are also combined with meshfree methods to analyze fracture mechanics problems [9, 10, 21].”
A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis (2011, methodology): “Future applications of NS-XFEM may include complex problem such as the failure of concrete under large deformations, multiple crack initiation and propagation [Rabczuk, Zi, Bordas, and Nguyen-Xuan (2008)] and branching in 3D [Rabczuk and Bordas (2007); Bordas, Rabczuk, and Zi (2008)].”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, methodology): “In this work, we propose a coupling of the LME shape functions with the extrinsic enrichments used in partition of unity enriched methods for fracture, such as the extended finite element method (XFEM), see [11, 12, 13].”
A robust preconditioning technique for the extended finite element method (2011, background): “Research has shown that the concept of enrichment can also be used in these methods to simulate cracked structures [20].”