Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method

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A scaled boundary polygon formulation for elasto-plastic analyses (2014, background): “unbounded media [35, 36, 37, 38], diffusion [39], fluid-structure interaction [40], fracture [41, 42, 43, 44, 45, 46, 47], acoustics [48] electro-statics [49] and thin plates [50].”
Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method (2012, methodology): “The two-dimensional application of the SBFEM in crack and notch problems can be found in the literature (Song and Wolf 1997, 1999, 2000; Deeks 2002; Müller et al. 2004; Chidgzey and Deeks 2005; Yang and Deeks 2007; Chidgzey et al. 2008; Bird et al. 2010).”
Crack propagation modelling in functionally graded materials using scaled boundary polygons (2015, background): “Under such conditions, Chidgzey and Deeks (2005) showed that stress field in a sector covered by a line element is σ (ξ, η) = D(ξ, η)Ψ (η)ξ−Sn−IΨ −1u ub , (31) and is a power function that contains the singularand higher order terms of the Williams eigenfunction expansion around a crack tip…”
A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics (2017, methodology): “The fracture parameters, such as the stress intensity factors, T -stress and the coefficients of higher order terms are extracted directly based on their definitions [57, 12].”