On three-dimensional modelling of crack growth using partition of unity methods

By Timon Rabczuk, Stéphane P.A. Bordas, Goangseup Zi. 2010

411 citations recorded by the source corpus.

This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the crack surface are addressed. A crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG). Several three-dimensional cracking examples are compared to other results from the literature or the experimental data and show good agreement.

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

View Paper: https://www.semanticscholar.org/paper/8d716e630fbcfee8d0aba79ee308a37d0e0460e9

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

T-spline based XIGA for fracture analysis of orthotropic media (2015, methodology): “Some applications of these methods can be found in [25–31].”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2016, neutral): “We recall for instance 3 , 4 , 12 , 13 , 19 , 21 , 24 , 25 , 29 , 31 , 32 , 33 , 35 .”
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.”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “3-D crack growth modeling with partition-of-unity methods is presented in [ 57 ].”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “Some commercial software packages such as ADAPCRACK, ZENCRACK and FRANC3D have been developed based on this idea [6–8] and two recent review papers can be consulted for details [1,9].”
A review of extended/generalized finite element methods for material modeling (2009, neutral): “[85].”
An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function (2014, background): “Remarkable successes have been reported in applying these methods for analyzing challenging engineering problems, namely, fracture modelling [4–12], plate problems [13], finite deformation problem [14,15], fluid struction interaction [16] consolidation problem [17], dynamic simulation [18–20], three”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Extrinsic techniques have been developed into meshless crack ‘particle’ methods for 3D crack modelling in a number of references [15, 18, 19, 27] and shifted weight functions are used as an alternative to the asymptotic basis in (3).”
Dual-horizon peridynamics: A stable solution to varying horizons (2017, methodology): “No techniques such as smoothing the normals of the crack surfaces in order to avoid erratic crack paths is necessary in PD, while such techniques are commonly used in the extended finite element method (XFEM) [1], meshless methods [2] or”
A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields (2014, neutral): “Recently, much effort has been directed towards the application of meshless methods to crack problems to overcome the difficulties in traditional numerical methods such as meshless methods for dynamic problem, 2D fracture modelling [9–18], 3D fracture modelling [19,38–41], fluid structure integratio”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, methodology): “There is a growing interest in modeling fracture mechanics with enrichment functions combined with meshless methods [14, 15, 16], isogeometric analysis [17], or strain-smoothed FEM [18, 19].”
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “3D modeling is the area where meshless methods are expected to show more advantages over other methods; however, only limited contributions have occurred to date [13, 19–27].”