Extended finite element method for three-dimensional crack modelling

From MaRDI portal
Publication:4506058

DOI<1549::AID-NME955>3.0.CO;2-A 10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-AzbMath0963.74067OpenAlexW1974288061MaRDI QIDQ4506058

N. Sukumar, Ted Beltytschko, Brian Moran, Nicolas Moës

Publication date: 18 June 2001

Full work available at URL: https://doi.org/10.1002/1097-0207(20000820)48:11<1549::aid-nme955>3.0.co;2-a


zbMATH Keywords

stress intensity factorselastostaticsextended finite element methodpartition of unitylocal enrichmentcrack representationthree-dimensional crack modellingtwo-dimensional asymptotic crack-tip displacement fields


Mathematics Subject Classification ID

Brittle fracture (74R10) Stress concentrations, singularities in solid mechanics (74G70) Finite element methods applied to problems in solid mechanics (74S05)


Related Items

A hybrid extended finite element/level set method for modeling phase transformations ⋮ Adaptive hierarchical enrichment for delamination fracture using a decohesive zone model ⋮ Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model ⋮ A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM ⋮ Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum ⋮ A Global-Local Approach for the Construction of Enrichment Functions for the Generalized FEM and Its Application to Three-Dimensional Cracks ⋮ Study of Some Optimal XFEM Type Methods ⋮ A stabilized formulation for the advection-diffusion equation using the Generalized Finite Element Method ⋮ A ‘pure’ boundary node method for potential theory ⋮ Mixed Aggregated Finite Element Methods for the Unfitted Discretization of the Stokes Problem ⋮ Meshfree Methods: A Comprehensive Review of Applications ⋮ XFEM Analyses Using Two-Dimensional Quadrilateral Elements Enriched with Only the Heaviside Step Function ⋮ Hybrid of monolithic and staggered solution techniques for the computational analysis of fracture, assessed on fibrous network mechanics ⋮ A new strategy for 3D non-persistent crack propagation by the numerical manifold method with tetrahedral meshes ⋮ Computational multiphase periporomechanics for unguided cracking in unsaturated porous media ⋮ A neural network‐enhanced reproducing kernel particle method for modeling strain localization ⋮ 3D simulation of complex fractures with a simple mesh ⋮ Considerations on the identifiability of fracture and bond properties of reinforced concrete ⋮ A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads ⋮ Nonlocal geometric fracture theory: A nonlocal‐local asymptotically compatible framework for continuous–discontinuous deformation of solid materials ⋮ Robust, strong form mechanics on an adaptive structured grid: efficiently solving variable-geometry near-singular problems with diffuse interfaces ⋮ DOF‐gathering stable generalized finite element methods for crack problems ⋮ 3D phase field simulations of ductile fracture ⋮ An object‐oriented geometric engine design for discontinuities in unfitted/immersed/enriched finite element methods ⋮ An extended peridynamic model equipped with a new bond-breakage criterion for mixed-mode fracture in rock-like materials ⋮ Past, current and future trends and challenges in non-deterministic fracture mechanics: a review ⋮ Field-enriched finite element method for simulating of three-dimensional crack propagation ⋮ Bond-based nonlocal models by nonlocal operator method in symmetric support domain ⋮ A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks ⋮ A neural network-based enrichment of reproducing kernel approximation for modeling brittle fracture ⋮ Robust numerical integration of embedded solids described in boundary representation ⋮ GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE ⋮ Multiscale Methods for Fracturing Solids ⋮ An extended finite element method with analytical enrichment for cohesive crack modeling ⋮ Error estimation and adaptivity for discontinuous failure ⋮ A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method ⋮ Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems ⋮ Analysis of three-dimensional fracture mechanics problems: A two-scale approach using coarse-generalized FEM meshes ⋮ High–order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations ⋮ The extended finite element method for fracture in composite materials ⋮ Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms ⋮ Higher-order XFEM for curved strong and weak discontinuities ⋮ Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations ⋮ The generalized finite element method ⋮ Crack tip enrichment in the XFEM using a cutoff function ⋮ A recovery-type error estimator for the extended finite element method based onsingular+smoothstress field splitting ⋮ Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method ⋮ Contact with friction in multi-material arbitrary Lagrangian-Eulerian formulations using X-FEM ⋮ A posteriorierror estimation for extended finite elements by an extended global recovery ⋮ Modeling three-dimensional crack propagation-A comparison of crack path tracking strategies ⋮ Singularity enrichment for complete sliding contact using the partition of unity finite element method ⋮ Robust and direct evaluation ofJ2in linear elastic fracture mechanics with the X-FEM ⋮ A contact algorithm for frictional crack propagation with the extended finite element method ⋮ A smeared-embedded mesh-corrected damage model for tensile cracking ⋮ Fast integration and weight function blending in the extended finite element method ⋮ Enhanced blending elements for XFEM applied to linear elastic fracture mechanics ⋮ Modeling holes and inclusions by level sets in the extended finite element method ⋮ STRESS ANALYSES OF COMPOSITE LAMINATE WITH DELAMINATION USING X-FEM ⋮ The extended/generalized finite element method: An overview of the method and its applications ⋮ Crack identification by ‘arrival time’ using XFEM and a genetic algorithm ⋮ hp-Generalized FEM and crack surface representation for non-planar 3-D cracks ⋮ New development in extended finite element modeling of large elasto-plastic deformations ⋮ Brittle fracture in polycrystalline microstructures with the extended finite element method ⋮ The contour integral method for loaded cracks ⋮ A note on enrichment functions for modelling crack nucleation ⋮ An enriched element-failure method (REFM) for delamination analysis of composite structures ⋮ Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods ⋮ Numerical Study of SIF for a Crack in P265GH Steel by XFEM ⋮ Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities ⋮ The Aggregated Unfitted Finite Element Method on Parallel Tree-Based Adaptive Meshes ⋮ Towards the algorithmic treatment of 3D strong discontinuities ⋮ Modelling of damage of a liquid-core microcapsule in simple shear flow until rupture ⋮ A Precise Time-Domain Expanding Crack-Tip Element for 3D Planar and Axial Dynamic Cracks ⋮ A local integral-generalized finite difference method with mesh-meshless duality and its application ⋮ Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method ⋮ Delamination analysis of composites by new orthotropic bimaterial extended finite element method ⋮ A level set-based topology optimization method targeting metallic waveguide design problems ⋮ Embedded interfaces by polytope FEM ⋮ Efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach ⋮ An XFEM method for modeling geometrically elaborate crack propagation in brittle materials ⋮ An interface-enriched generalized FEM for problems with discontinuous gradient fields ⋮ Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description ⋮ Lower-dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media ⋮ Cohesive and non-cohesive fracture by higher-order enrichment of XFEM ⋮ Directly resolving particles in an electric field: local charge, force, torque, and applications ⋮ A weighted Nitsche's method for interface problems with higher-order simplex elements ⋮ Well-conditioned and optimally convergent second-order generalized/extended FEM formulations for linear elastic fracture mechanics ⋮ Blended isogeometric-finite element analysis for large displacements linear elastic fracture mechanics ⋮ A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted finite element method ⋮ Graph neural networks for simulating crack coalescence and propagation in brittle materials ⋮ An orthotropic mesh-corrected crack model ⋮ Application of an elastoplastic spectral-element method to 3D slope stability analysis ⋮ Polygon scaled boundary finite elements for crack propagation modelling ⋮ A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities ⋮ 3D fluid-structure interaction with fracturing: a new method with applications ⋮ A 3D locking-free XFEM formulation for the von Mises elasto-plastic analysis of cracks ⋮ Arbitrary discontinuities in finite elements ⋮ Distributed-memory parallelization of the aggregated unfitted finite element method ⋮ A stable generalized/extended \(p\)-hierarchical FEM for three-dimensional linear elastic fracture mechanics ⋮ Structural fatigue life prediction considering model uncertainties through a novel digital twin-driven approach ⋮ From diffuse damage to sharp cohesive cracks: a coupled XFEM framework for failure analysis of quasi-brittle materials ⋮ A concurrent multiscale study of dynamic fracture ⋮ Stable generalized finite element method (SGFEM) for three-dimensional crack problems ⋮ Fracture modeling using meshless methods and level sets in 3D: Framework and modeling ⋮ Three-dimensional integration strategies of singular functions introduced by the XFEM in the LEFM ⋮ Convergence of domain integrals for stress intensity factor extraction in 2-D curved cracks problems with the extended finite element method ⋮ Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm ⋮ Improvements of explicit crack surface representation and update within the generalized finite element method with application to three-dimensional crack coalescence ⋮ An explicit application of partition of unity approach to XFEM approximation for precise reproduction ofa prioriknowledge of solution ⋮ Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes ⋮ A multiscale flaw detection algorithm based on XFEM ⋮ A fast weakly intrusive multiscale method in explicit dynamics ⋮ Three-dimensional simulation of crack with curved front with direct estimation of stress intensity factors ⋮ Multi-scale computational homogenization-localization for propagating discontinuities using X-FEM ⋮ Extraction of stress intensity factors from Irwin's integral using high-order XFEM on triangular meshes ⋮ A conservative embedded boundary method for an inviscid compressible flow coupled with a fragmenting structure ⋮ Adaptive delamination analysis ⋮ Adaptive quadrature/cubature rule: application to polytopes ⋮ An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction ⋮ Interfacial coupling across incompatible meshes in a monolithic finite-strain thermomechanical formulation ⋮ Adaptive fourth-order phase-field modeling of ductile fracture using an isogeometric-meshfree approach ⋮ Three-dimensional fracture analysis using tetrahedral enriched elements and fully unstructured mesh ⋮ Immersed volume method for solving natural convection, conduction and radiation of a hat‐shaped disk inside a 3D enclosure ⋮ Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting ⋮ Shape optimization approach based on the extended finite element method ⋮ An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities ⋮ Effect of interfacial delamination on coating crack in thick diamond-like carbon coatings under indentation ⋮ Strong tangential discontinuity modeling of shear bands using the extended finite element method ⋮ Fracture and impulse based finite-discrete element modeling of fragmentation ⋮ Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods ⋮ Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method ⋮ A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics ⋮ Mesh based construction of flat-top partition of unity functions ⋮ Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique ⋮ ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles ⋮ Constrained optimization for interface cracks in composite materials subject to non-penetration conditions ⋮ 3D corrected XFEM approach and extension to finite deformation theory ⋮ Multiscale XFEM-modelling and simulation of the inelastic material behaviour of textile-reinforced polymers ⋮ Robust and scalable \(h\)-adaptive aggregated unfitted finite elements for interface elliptic problems ⋮ Consistent immersed volumetric Nitsche methods for composite analysis ⋮ A novel micromechanics-enhanced phase-field model for frictional damage and fracture of quasi-brittle geomaterials ⋮ A three-dimensional generalized finite element method for the simulation of wave propagation in fluid-filled fractures ⋮ A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM ⋮ Generalized boundary element method for Galerkin boundary integrals ⋮ A novel algorithmic framework for the numerical implementation of locally embedded strong discontinuities ⋮ Appropriate extended functions for X-FEM simulation of plastic fracture mechanics ⋮ Numerical analyses of discontinuous material bifurcation: strong and weak discontinuities ⋮ On the modeling of highly localized deformations induced by material failure: the strong discontinuity approach ⋮ Generalized finite element analysis using the preconditioned conjugate gradient method ⋮ 3D multiscale crack propagation using the XFEM applied to a gas turbine blade ⋮ A meshless method using local exponential basis functions with weak continuity up to a desired order ⋮ A stabilization technique for the regularization of nearly singular extended finite elements ⋮ Mixed virtual element methods for general second order elliptic problems on polygonal meshes ⋮ An \(h\)-adaptive meshfree-enriched finite element method based on convex approximations for the three-dimensional ductile crack propagation simulation ⋮ A combined virtual element method and the scaled boundary finite element method for linear elastic fracture mechanics ⋮ A hybrid FEMM-phase field method for fluid-driven fracture propagation in three dimension ⋮ Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack singularities ⋮ A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography ⋮ 3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks ⋮ High order boundary and finite elements for 3D fracture propagation in brittle materials ⋮ Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth ⋮ Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture ⋮ A general algorithm for numerical integration of three-dimensional crack singularities in PU-based numerical methods ⋮ Concurrently coupled solid shell-based adaptive multiscale method for fracture ⋮ A modification of the phase-field model for mixed mode crack propagation in rock-like materials ⋮ Material point method with enriched shape function for crack problems ⋮ An implicit surface tension model for the analysis of droplet dynamics ⋮ A continuum consistent discrete particle method for continuum-discontinuum transitions and complex fracture problems ⋮ Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations ⋮ On the implementation of a hydro-mechanical coupling model in the numerical manifold method ⋮ Strain localization due to crack--microcrack interactions: X-FEM for a multifield approach ⋮ Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer ⋮ A multiscale method coupling peridynamic and boundary element models for dynamic problems ⋮ An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces. ⋮ Computational aspects of the mechanics of complex materials ⋮ A two-scale generalized finite element method for fatigue crack propagation simulations utilizing a fixed, coarse hexahedral mesh ⋮ An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems ⋮ Multiple crack detection in 3D using a stable XFEM and global optimization ⋮ An enrichment-based approach for the simulation of fretting problems ⋮ Numerical integration of discontinuities on arbitrary domains based on moment fitting ⋮ Size effect and localization in J2 plasticity ⋮ Analysis and applications of a generalized finite element method with global-local enrichment functions ⋮ Extended finite element method for three-dimensional large plasticity deformations on arbitrary interfaces ⋮ Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods ⋮ An embedded strong discontinuity model for cracking of plain concrete ⋮ Three-dimensional fracture propagation with numerical manifold method ⋮ A high-order three-dimensional numerical manifold method enriched with derivative degrees of freedom ⋮ Stress intensity factor analyses of three-dimensional interface cracks using tetrahedral finite elements ⋮ Stefan problem through extended finite elements: review and further investigations ⋮ Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method ⋮ Propagation and bifurcation of cracks based on implicit surfaces and discontinuous velocities ⋮ Dynamic crack propagation analysis of orthotropic media by the extended finite element method ⋮ A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements ⋮ Modeling complex crack problems using the numerical manifold method ⋮ Levelset based fluid topology optimization using the extended finite element method ⋮ Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization ⋮ A generalized finite element method with global-local enrichment functions for confined plasticity problems ⋮ Crack face contact for a hexahedral-based XFEM formulation ⋮ On the necessity of Nitsche term. II: An alternative approach ⋮ A three-dimensional self-adaptive cohesive zone model for interfacial delamination ⋮ Stable generalized finite element method (SGFEM) ⋮ Formulation and implementation of a high-order 3-D domain integral method for the extraction of energy release rates ⋮ Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials ⋮ Modeling localized failure with arbitrary Lagrangian Eulerian methods ⋮ Gradient-enhanced damage modeling of cracked bodies by reproducing kernel element method ⋮ Meshless fracture analysis of 3D planar cracks with generalized thermo-mechanical stress intensity factors ⋮ A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics ⋮ A particle-level set-based sharp interface Cartesian grid method for impact, penetration, and void collapse. ⋮ Finite element analysis on implicitly defined domains: an accurate representation based on arbitrary parametric surfaces ⋮ A two-scale extended finite element method for modelling 3D crack growth with interfacial contact ⋮ A hybrid finite element-scaled boundary finite element method for crack propagation modelling ⋮ A computational framework of three-dimensional configurational-force-driven brittle crack propagation ⋮ Three dimensional experimental and numerical multiscale analysis of a fatigue crack ⋮ An extended finite element method for dislocations in complex geometries: thin films and nanotubes ⋮ The numerical simulation of the crack elastoplastic extension based on the extended finite element method ⋮ Extended finite element method for predicting productivity of multifractured horizontal wells ⋮ Archetype-blending continuum theory ⋮ An explicit dynamics extended finite element method. I: Mass lumping for arbitrary enrichment functions ⋮ Studied X-FEM enrichment to handle material interfaces with higher order finite element ⋮ Mixed stabilized finite element methods in nonlinear solid mechanics. II: Strain localization ⋮ A nitsche-extended finite element method for earthquake rupture on complex fault systems ⋮ Modeling cohesive crack growth via a truly-mixed formulation ⋮ Extended particle difference method for moving boundary problems ⋮ Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model ⋮ Benchmarking on bifurcation and localization in \(\mathrm{J}_{2}\) plasticity for plane stress and plane strain conditions ⋮ An exact and efficient X-FEM-based reanalysis algorithm for quasi-static crack propagation ⋮ XFEM with hanging nodes for two-phase incompressible flow ⋮ How to control the crack to propagate along the specified path feasibly? ⋮ A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics ⋮ Three-dimensional improved XFEM (IXFEM) for static crack problems ⋮ Equivalent Legendre polynomials: numerical integration of discontinuous functions in the finite element methods ⋮ A stable generalized/extended FEM with discontinuous interpolants for fracture mechanics ⋮ Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization ⋮ A structured grid based B-spline finite elements method combining local isogeometry analysis technique for crack problems ⋮ A novel multi-grid based reanalysis approach for efficient prediction of fatigue crack propagation ⋮ A stable discontinuity-enriched finite element method for 3-D problems containing weak and strong discontinuities ⋮ Loaded crack surfaces in two and three dimensions with XFEM ⋮ Discontinuous cellular automaton method for crack growth analysis without remeshing ⋮ Numerical integration of discontinuous functions: moment fitting and smart octree ⋮ On the enrichment zone size for optimal convergence rate of the generalized/extended finite element method ⋮ 3D ductile crack propagation within a polycrystalline microstructure using XFEM ⋮ Meshless methods: a review and computer implementation aspects ⋮ Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method ⋮ A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries ⋮ An implicit geometrical approach to level sets update for 3D non planar X-FEM crack propagation ⋮ Error estimates in weighted Sobolev norms for finite element immersed interface methods ⋮ Criterion for initiation of cracks under mixed-mode I + III loading ⋮ Analysis of three-dimensional interface cracks using enriched finite element ⋮ A generalized bond-based peridynamic model for quasi-brittle materials enriched with bond tension-rotation-shear coupling effects ⋮ Arbitrary 3D crack propagation with improved XFEM: accurate and efficient crack geometries ⋮ Three-dimensional crack growth with \(hp\)-generalized finite element and face offsetting methods ⋮ On the necessity of Nitsche term ⋮ Fracture and singularities of the mass-density gradient field ⋮ A node-splitting discrete element model for fluid-structure interaction ⋮ Implementation of the extended finite element method for dynamic thermoelastic fracture initiation ⋮ An interaction integral method for 3D curved cracks in nonhomogeneous materials with complex interfaces ⋮ Stability of incompressible formulations enriched with X-FEM ⋮ Quasi-brittle damage modeling based on incremental energy relaxation combined with a viscous-type regularization ⋮ An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: application to embedded interface methods ⋮ A state-of-the-art review of the X-FEM for computational fracture mechanics ⋮ The orthonormalized generalized finite element method-OGFEM: efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions ⋮ Strong discontinuity embedded approach with standard SOS formulation: element formulation, energy-based crack-tracking strategy, and validations ⋮ Higher order stable generalized finite element method ⋮ On local tracking algorithms for the simulation of three-dimensional discontinuities ⋮ Kinetic friction for multi-material arbitrary Lagrangian Eulerian extended finite element formulations ⋮ Generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems ⋮ A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method ⋮ Derivative recovery and a posteriori error estimate for extended finite elements ⋮ Extended finite element simulation of quasi-brittle fracture in functionally graded materials ⋮ Energy-based modeling of cohesive and cohesionless cracks via X-FEM ⋮ A unified non-local fluid transport model for heterogeneous saturated porous media ⋮ A continuous-discontinuous localizing gradient damage framework for failure analysis of quasi-brittle materials ⋮ Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture


Uses Software


Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:4506058&oldid=18600627"
Powered by MediaWiki