A simple and robust three-dimensional cracking-particle method without enrichment

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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).”
On generation of lumped mass matrices in partition of unity based methods (2017, background): “[21] proposed to split the particles on both sides of a crack to reflect the displacement skip, which accordingly avoids the introduction of enrichment functions reflecting displacement skip across the crack.”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “A special case of partition of unity methods, meshfree methods have also been proposed with the aim of further reducing the mesh burden, for example, the element-free Galerkin (EFG) [34], the extended EFG [35,36], the cracking-particle method [37] etc.”
A new weight‐function enrichment in meshless methods for multiple cracks in linear elasticity (2012, methodology): “As a consequence, the resulting crack path is discontinuous; nonetheless the method is simple and effective and has been successfully applied to three-dimensional problems [27].”