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

An overview of computational methods to model fracture in brittle and quasi‐brittle materials
is given. The overview focuses on continuum models for fracture. First, numerical difficulties …

This paper reviews different crack tracking techniques in three-dimensions applicable in the
context of partition of unity methods, especially meshfree methods. Issues such as …

This paper presents new finite elements that incorporate strong discontinuities with linear
interpolations of the displacement jumps for the modeling of failure in solids. The cases of …

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 …

Rock mass failure is a particularly complex process that involves the opening and sliding of
existing discontinuities and the fracturing of the intact rock. This paper adopts an advanced …

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 …

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 …

The extended finite element method (XFEM) enables the accurate approximation of
solutions with jumps or kinks within elements. Optimal convergence rates have frequently …

Large underground caverns are characterized by high geostress, high sidewalls and
complex geological conditions, which make the rock masses suffer a series of failures in the …