Modeling of failure in composites by X-FEM and level sets within a multiscale framework

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Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids (2010, methodology): “Variational multiscale methods are nowadays also used to simulate microstructural effects on cohesive cracks [11].”
An efficient augmented finite element method for arbitrary cracking and crack interaction in solids (2014, methodology): “Another important class of numerical methods is the partition-of-unity (PoU)-based finite element methods [7], including the generalized finite element method (G-FEM) [8–11], extended finite element method (X-FEM) [12–20] and the phantom node method (PNM) [21–27].”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “XFEM has been applied to bimaterial problems by Sukumar et al [100], Hettich et al [54] and Huynh and Belytschko [56].”
A computational library for multiscale modeling of material failure (2013, background): “The work by Hettich et al. [53] is an examples in the area of crack propagation.”