4.4 Review

A review of extended/generalized finite element methods for material modeling

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The extended finite element method for fracture in composite materials

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Analysis and applications of a generalized finite element method with global-local enrichment functions

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Parametric enrichment adaptivity by the extended finite element method

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A corrected XFEM approximation without problems in blending elements

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The rs-method for material failure simulations

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Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods

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A regularized XFEM model for the transition from continuous to discontinuous displacements

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Robust and direct evaluation of J2 in linear elastic fracture mechanics with the X-FEM

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Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method

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Quadrature rules for triangular and tetrahedral elements with generalized functions

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On a new extended finite element method for dislocations: Core enrichment and nonlinear formulation

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A consistent partly cracked XFEM element for cohesive crack growth

J. L. Asferg et al.

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A multiscale projection method for macro/microcrack simulations

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An extended finite element library

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Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems

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Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM

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Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method

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An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation

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A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces

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A new fast finite element method for dislocations based on interior discontinuities

Robert Gracie et al.

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Derivative recovery and a posteriori error estimate for extended finite elements

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On XFEM applications to dislocations and interfaces

Ted Belytschko et al.

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Modelling of cohesive crack growth in concrete structures with the extended finite element method

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Extended finite element simulation of quasi-brittle fracture in functionally graded materials

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

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Modelling dendritic solidification with melt convection using the extended finite element method

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A method for dynamic crack and shear band propagation with phantom nodes

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A quasi-optimal convergence result for fracture mechanics with XFEM

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Mesh-independent discrete numerical representations of cohesive-zone models

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Improved implementation and robustness study of the X-FEM for stress analysis around cracks

E Béchet et al.

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Strong and weak arbitrary discontinuities in spectral finite elements

A Legay et al.

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High-order extended finite element method for cracked domains

P Laborde et al.

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A combined space-time extended finite element method

J Réthoré et al.

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Analysis of three-dimensional crack initiation and propagation using the extended finite element method

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An energy-conserving scheme for dynamic crack growth using the eXtended finite element method

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Multiscale enrichment based on partition of unity

J Fish et al.

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Modeling 3D crack propagation in unreinforced concrete using PUFEM

TC Gasser et al.

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Combined extended and superimposed finite element method for cracks

SH Lee et al.

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XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials

XY Liu et al.

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Partition of unity enrichment for bimaterial interface cracks

N Sukumar et al.

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On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method

H Ji et al.

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A bridging domain method for coupling continua with molecular dynamics

SP Xiao et al.

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A finite element method for the simulation of strong and weak discontinuities in solid mechanics

A Hansbo et al.

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A method for multiple crack growth in brittle materials without remeshing

É Budyn et al.

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A superposition framework for discrete dislocation plasticity

MP O'Day et al.

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Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis

R de Borst et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2004)

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An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension

J Chessa et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2003)

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Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

T Belytschko et al.

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Vector level sets for description of propagating cracks in finite elements

G Ventura et al.

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Finite cover method for linear and non-linear analyses of heterogeneous solids

K Terada et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2003)

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Extended finite element method for quasi-brittle fracture

S Mariani et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2003)

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New crack-tip elements for XFEM and applications to cohesive cracks

G Zi et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2003)

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On the construction of blending elements for local partition of unity enriched finite elements

J Chessa et al.

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An extended finite element method with higher-order elements for curved cracks

FL Stazi et al.

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Process zone resolution by extended finite elements

B Patzák et al.

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Stress intensity factor analysis of interface cracks using X-FEM

T Nagashima et al.

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Mesh independent modelling of cracks by using higher order shape functions

EV Iarve

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Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review

BL Karihaloo et al.

COMPUTERS & STRUCTURES (2003)

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Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

N Sukumar et al.

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES (2003)

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Coupling Methods for Continuum Model with Molecular Model

T. Belytschko et al.

INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING (2003)

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From continuous to discontinuous failure in a gradient-enhanced continuum damage model

A Simone et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2003)

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A hybrid extended finite element/level set method for modeling phase transformations

H Ji et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2002)

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Extended finite element method for cohesive crack growth

N Moës et al.

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Solving thermal and phase change problems with the eXtended finite element method

R Merle et al.

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Non-planar 3D crack growth by the extended finite element and level sets -: Part II:: Level set update

A Gravouil et al.

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Non-planar 3D crack growth by the extended finite element and level sets -: Part I:: Mechanical model

N Moës et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2002)

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The extended finite element method (XFEM) for solidification problems

J Chessa et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2002)

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Simulating the propagation of displacement discontinuities in a regularized strain-softening medium

GN Wells et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2002)

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Grain level analysis of crack initiation and propagation in brittle materials

PD Zavattieri et al.

ACTA MATERIALIA (2001)

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Modelling crack growth by level sets in the extended finite element method

M Stolarska et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2001)

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Discontinuous analysis of softening solids under impact loading

GN Wells et al.

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS (2001)

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A new method for modelling cohesive cracks using finite elements

GN Wells et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2001)

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Modeling holes and inclusions by level sets in the extended finite-element method

N Sukumar et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

Article Engineering, Multidisciplinary

An extended finite element method for modeling crack growth with frictional contact

J Dolbow et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

Article Engineering, Multidisciplinary

A generalized finite element method for the simulation of three-dimensional dynamic crack propagation

CA Duarte et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

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Discontinuous enrichment in finite elements with a partition of unity method

J Dolbow et al.

FINITE ELEMENTS IN ANALYSIS AND DESIGN (2000)

Article Mechanics

Modeling fracture in Mindlin-Reissner plates with the extended finite element method

J Dolbow et al.

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES (2000)

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Generalized finite element methods for three-dimensional structural mechanics problems

CA Duarte et al.

COMPUTERS & STRUCTURES (2000)

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The design and analysis of the Generalized Finite Element Method

T Strouboulis et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2000)