A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

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Meshfree Methods: Progress Made after 20 Years (2017, positive): “To circumvent this issue, a cracking particle method has been proposed, where fracture is represented by a series of discontinuities located at the particles, with arbitrary orientation (Rabczuk and Belytschko 2004, 2007; Rabczuk et al. 2007a, 2010).”
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].”
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].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “to large deformation [4], crack problems [5–8] and adaptive analysis [9–11].”