The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns

By Thomas-Peter Fries, Ted Belytschko. 2006

209 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e4ec7a763e3d0d42421a0aec8bb4626d7e343926

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “[22] and later Fries [78], it is shown that in order to obtain optimal accuracy for the singular problem of elastic fracture mechanics, (i) the crack tip enrichment should be applied in a fixed area around the crack tip as the mesh is refined (section 5.”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, result): “This is similar in principle to the work of the intrinsic XFEM [20].”
An improved finite element space for discontinuous pressures (2010, methodology): “The proposed space is much simpler than the one proposed by Gross and Reusken [2], which is based on XFEM enrichment, and also to the one proposed by Fries and Belytschko [26], which avoids introducing additional unknowns by switching to a moving-least-squares approximation in the vicinity of Γ.”
Multiscale aggregating discontinuities: A method for circumventing loss of material stability (2008, methodology): “The XFEM method was developed in [21, 22]; recent developments are given in [23–29].”
Level set topology optimization of structural problems with interface cohesion (2017, background): “The reader is referred to [13] and [14] for an introduction and general overview of the XFEM.”
A review of extended/generalized finite element methods for material modeling (2009, background): “Fries and Belytschko [46] proposed a discontinuity enrichment that does not require additional degrees of freedom at nodes whose elements are crossed by the discontinuity.”
Simulations of instability in dynamic fracture by the cracking particles method (2009, unknown): “[14]; recent developments are given in [15–23].”
An augmented finite element method for modeling arbitrary discontinuities in composite materials (2009, methodology): “This combination was first reported by ( Belytschko and Black 1999 ) and extended by (Moes et al. 1999).”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “Numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques.”