A three dimensional large deformation meshfree method for arbitrary evolving cracks

By Timon Rabczuk, Ted Belytschko. 2007

1,284 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b26e2a38daa81d4a8f493c42dee9c17ff879b11c

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis (2011, methodology): “…the meshfree method has been successful in modeling static and dynamic fracture in 2-dimensions and 3-dimensions performed in [Rabczuk and Belytschko (2004); Rabczuk and Areias (2006); Rabczuk and Eilb (2006); Rabczuk and Belytschko (2007); Rabczuk and Bordas (2007); Rabczuk and Samaniego (2008)].”
A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media (2011, neutral): “Therefore, numerical approaches such as the boundary element method (BEM) [8], the finite element method (FEM) [9], and meshless methods [10–13] have been suggested to solve the general crack problems in anisotropic media.”
Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS‐based isogeometric approach (2012, methodology): “Because of the limitation of analytical approaches, various numerical methods have been developed such as FEM [39, 40], BEM [41, 42], smoothed FEM [43–49], mesh-free methods [50–56], etc.”
T-spline based XIGA for fracture analysis of orthotropic media (2015, methodology): “Some applications of these methods can be found in [25–31].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “to large deformation [4], crack problems [5–8] and adaptive analysis [9–11].”
New strategies for some issues of numerical manifold method in simulation of crack propagation (2014, methodology): “For the same purpose as the NMM, some other numerical methods, among which are the meshfree methods such as [18] and [19], have been exhibiting powerful capability in the 3D crack analysis.”
The MLS-based numerical manifold method with applications to crack analysis (2014, neutral): “The procedure appears easy to be extended to three dimensional cases as handled in Rabczuk and Belytschko (2007) and Bordas et al. (2008).”
A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure (2016, neutral): “The development of test and trial function with a sign function can model cracks with arbitrary movement [14].”