Analysis of three‐dimensional crack initiation and propagation using the extended finite element method

By Pedro Areias, Ted Belytschko. 2005

399 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7e805f29f16b9eacac1492efbe679dbd87e6d53e

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics (2007, methodology): “Other researchers choose to represent the crack path completely continuously as described e.g. in Areias and Belytschko [ 3 ].”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, methodology): “According to [1, 22, 36], the use of the planar-cut approach in a mixed-mode crack growth simulation, may lead to discontinuous crack surfaces along the boundary between elements.”
Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique (2012, methodology): “The X-FEM was originally applied in mesh-independent crack propagation problems, including: the crack growth with frictional contact [33], cohesive crack propagation [34–36], stationary and growing cracks [37] and three-dimensional crack propagation [38].”
Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method (2013, methodology): “The technique has been applied in crack problems, including crack growth with frictional contact [23], cohesive crack growth [24, 25], stationary and growing cracks [26], three-dimensional crack propagation [27] and dynamic cohesive crack propagation [28].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, background): “In order to prevent these discontinuities, Areias and Belytschko [ 2 ] proposed to adjust the planar cut provided by the maximum principal stress according to the intersection points generated by the planar cuts of adjacent elements.”
Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method (2007, methodology): “Afterwards, more investigations have been carried out by researchers such as Sukumar et al. [12] and Areias and Belytschko [13]; extending the method to three dimensional domain, Sukumar and Prévost [14]; describing computer implementation of the method, Dolbow et al. [15]; using frictional contact”
A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks (2007, background): “Computations of this problem have previously been reported by Xu and Needleman [43], Falk et al. [20], Belytschko et al. [6] and Rabczuk and Belytschko [34].”
A multiscale projection method for macro/microcrack simulations (2007, positive): “Extensions to three dimensions are reported by Gravouil et al. [19, 20] and Areias and Belytschko [21].”
The numerical simulation of fatigue crack growth using extended finite element method (2012, methodology): “Till date, XFEMhas extensively used to solve the problems of fracture mechanics including crack growth with frictional contact [17], cohesive crack propagation [18–21], quasi-static crack growth [22], arbitrary branched and intersecting cracks [23], and cracks in shells [24], fatigue crack propagati”
Local enrichment of the finite cell method for problems with material interfaces (2013, background): “simulation of evolving discontinuities such as crack propagation [6–8], two-phase fluids [9,10], or fluid-structure interactions [11,12].”
Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment (2008, methodology): “12 and is similar to the results presented in [26,39,40].”
Effective 3D failure simulations by combining the advantages of embedded Strong Discontinuity Approaches and classical interface elements (2011, methodology): “A three-dimensional numerical analysis of the same specimen by applying the XFEM can be found in [1], while a crack path prediction by using classical interface elements is presented in [19].”
Towards the algorithmic treatment of 3D strong discontinuities (2006, background): “In combination with the extended finite element method, it has been applied e.g. by Wells et al. [13, 15], Möes & Belytschko [14] and Gasser & Holzapfel [17].”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, result): “We refer to, among many others, [28–32] for the application of these ideas in the context of cohesive fracture mechanics.”
Non-ordinary state-based peridynamic analysis of stationary crack problems (2014, methodology): “Consequently, computational methods involving displacement gradients or higher-order spatial derivatives in a domain containing a crack must remove the discontinuous displacement field by either redefining the discretized body so that the crack lies on the boundary, or by using other techniques for ”