Modeling crack discontinuities without element-partitioning in the extended finite element method

DOI10.1002/NME.5436zbMATH Open1548.74698MaRDI QIDQ6556859

Jean B. Lasserre, N. Sukumar, Eric B. Chin

Publication date: 17 June 2024

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

zbMATH Keywords

numerical integrationweakly singular integralshomogeneous polynomialsstrong discontinuitiesX-FEMEuler's homogeneous function theorem

Mathematics Subject Classification ID

Brittle fracture (74R10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

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• Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method
• Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
• The partition of unity finite element method: basic theory and applications
• A new method for numerical integration of singular functions on the plane
• Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods
• Equivalent polynomials for quadrature in Heaviside function enriched elements
• Improved implementation and robustness study of the X-FEM for stress analysis around cracks
• On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method
• Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
• Quadrature rules for triangular and tetrahedral elements with generalized functions
• A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity
• Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
• On the use of isoparametric finite elements in linear fracture mechanics
• Integration and homogeneous functions
• Integration on a convex polytope
• A finite element method for crack growth without remeshing
• High-order extended finite element method for cracked domains

Related Items (8)

Gradient plasticity crack tip characterization by means of the extended finite element method ⋮ Linear smoothed extended finite element method ⋮ Modeling curved interfaces without element-partitioning in the extended finite element method ⋮ An adaptive material point method coupled with a phase-field fracture model for brittle materials ⋮ A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities ⋮ Erratum to: ``Modeling crack discontinuities without element-partitioning in the extended finite element method ⋮ Erratum to: ``Modeling crack discontinuities without element-partitioning in the extended finite element method ⋮ An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition

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