Journal ArticleDOI
A generalized finite element method for the simulation of three-dimensional dynamic crack propagation
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TLDR
In this article, a partition of unity finite element method and hp-cloud method for dynamic crack propagation is presented, where the approximation spaces are constructed using a partition-of-unity (PU) and local enrichment functions.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2001-01-05. It has received 372 citations till now. The article focuses on the topics: Extended finite element method & Mixed finite element method.read more
Citations
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Journal ArticleDOI
The extended/generalized finite element method: An overview of the method and its applications
TL;DR: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.
Journal ArticleDOI
A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering
TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.
Journal ArticleDOI
Arbitrary branched and intersecting cracks with the eXtended Finite Element Method
TL;DR: In this paper, a new technique for the finite element modeling of cracks with multiple branches, multiple holes and cracks emanating from holes is presented, which allows the representation of crack discontinuities and voids independently of the mesh.
Journal ArticleDOI
Modelling crack growth by level sets in the extended finite element method
TL;DR: An algorithm which couples the level set method (LSM) with the extended finite element method (X‐FEM) to model crack growth is described, which requires no remeshing as the crack progresses, making the algorithm very efficient.
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.
References
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Journal ArticleDOI
A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Book
The stress analysis of cracks handbook
TL;DR: The Stress Analysis of Cracks Handbook as mentioned in this paper provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations, along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
Elastic crack growth in finite elements with minimal remeshing
Ted Belytschko,T. Black +1 more
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
Proceedings ArticleDOI
A two-dimensional interpolation function for irregularly-spaced data
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
Related Papers (5)
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more