Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations

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Boundary conditions generated by dynamic particles in SPH methods (2007, methodology): “In addition, the kernel was modified following the linear method proposed by Bonet and Kulasegaram (2000) in order to assure the normalization property, particularly near the free surface.”
Meshfree and finite element nodal integration methods (2008, methodology): “A modified form of the ‘integration correction’ [5, 13] can rectify this.”
A Smoothed Finite Element Method for Mechanics Problems (2007, methodology): “Recently, nodal integration method has been suggested in mesh-free methods with the aim to eliminate “background” mesh for integration [2, 5].”
Imposing essential boundary conditions in mesh-free methods (2004, methodology): “For example, an efficient imposition of essential boundary conditions in Galerkin based mesh-free methods, such as the EFG method [4], the RKPM [5] or the CSPH method [6], is still an open issue.”
Second‐order accurate derivatives and integration schemes for meshfree methods (2012, methodology): “This fact leads to the integration correction by Bonet and Kulasegaram [8] and the SCNI by Chen et al. [3, 4].”
A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves (2016, methodology): “Bonet and Kulasegaram (2000, 2002) adopted a variational formulation to solve Possion’s equation for their ISPH method.”