A quasi-optimal convergence result for fracture mechanics with XFEM
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Chahine et al. as discussed by the authors gave a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area.About:
This article is published in Comptes Rendus Mathematique.The article was published on 2006-04-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Extended finite element method & Rate of convergence.read more
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Journal ArticleDOI
A review of extended/generalized finite element methods for material modeling
TL;DR: In this article, the extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: fracture, dislocations, grain boundaries and phase interfaces.
Book
Extended finite element method for fracture analysis of structures
TL;DR: In this paper, the authors present a review of the literature on finite element fracture models and their application in the field of finite element finite element models (FEM) and fracture mechanics.
Journal ArticleDOI
Review: A survey of the extended finite element
TL;DR: In this article, the authors present an overview and recent progress of the extended finite element method X-FEM in the analysis of crack growth modeling, and summarize the important milestones achieved by the finite element community in the arena of computational fracture mechanics.
Journal ArticleDOI
A state-of-the-art review of the X-FEM for computational fracture mechanics
TL;DR: In this paper, the authors present a review of the extended finite element method X-FEM for computational fracture mechanics, and discuss the basic ideas and formulation for the newly developed XFEM method.
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An XFEM method for modeling geometrically elaborate crack propagation in brittle materials
Casey L. Richardson,Casey L. Richardson,Jan Hegemann,Eftychios Sifakis,Jeffrey Lee Hellrung,Joseph Teran +5 more
TL;DR: In this paper, the authors present a method for simulating quasistatic crack propagation in 2D which combines the extended finite element method (XFEM) with a general algorithm for cutting triangulated domains, and introduce a simple yet general and flexible quadrature rule based on the same geometric algorithm.
References
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Mechanics of Solid Materials
TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
Book
Singularities in Boundary Value Problems
TL;DR: In this paper, the authors studied the solutions of a boundary problem near corner edges and vertices and highlighted the singular solutions which carry the main physical information and which are given in their most explicit form to help potential users.
Journal ArticleDOI
A finite element method for the simulation of strong and weak discontinuities in solid mechanics
Anita Hansbo,Peter Hansbo +1 more
TL;DR: This paper introduces and analyze a finite element method for elasticity problems with interfaces and proposes a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code.
Journal ArticleDOI
Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model
TL;DR: In this paper, a methodology for solving three-dimensional crack problems with geometries independent of the mesh is described, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity.
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Non-planar 3d crack growth by the extended finite element and level sets- part ii: level set update
TL;DR: In this article, a level set method for treating the growth of non-planar 3D cracks is presented, where the crack is defined by two almost-orthogonal level sets (signed distance functions) and the Hamilton-Jacobi equation is used to update the level sets.
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The partition of unity finite element method: Basic theory and applications
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