An overview of the extended/generalized finite element method (GEFM/XFEM) with
emphasis on methodological issues is presented. This method enables the accurate …

The extended and generalized finite element methods are reviewed with an emphasis on
their applications to problems in material science:(1) fracture,(2) dislocations,(3) grain …

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where
the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial …

A new multi-phase-field method is developed for modeling the fracture of polycrystals at the
microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both …

This paper presents a review on the numerical manifold method (NMM), which covers the
basic theories of the NMM, such as NMM components, NMM displacement approximation …

In the numerical manifold method, there are two kinds of covers, namely mathematical cover
and physical cover. Mathematical covers are independent of the physical domain of the …

In this paper, we provide a retrospective examination of the developments and applications
of the extended finite element method (X-FEM) in computational fracture mechanics. Our …

This paper presents a procedure to build enrichment functions for partition of unity methods
like the generalized finite element method and the hp cloud method. The procedure …

In this study, an efficient polygonal finite element method (PFEM) in combination with
quadratic serendipity shape functions is proposed to study nonlinear static and dynamic …

By using the strain smoothing technique proposed by Chen et al.(Comput. Mech. 2000; 25:
137–156) for meshless methods in the context of the finite element method (FEM), Liu et …