Journal ArticleDOI
Extended finite element method in computational fracture mechanics: a retrospective examination
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In this paper, the authors provide a retrospective examination of the developments and applications of the extended finite element method (X-FEM) in computational fracture mechanics, focusing on the modeling of cracks (strong discontinuities) for quasistatic crack growth simulations in isotropic linear elastic continua.Abstract:
In this paper, we provide a retrospective examination of the developments and applications of the extended finite element method (X-FEM) in computational fracture mechanics. Our main attention is placed on the modeling of cracks (strong discontinuities) for quasistatic crack growth simulations in isotropic linear elastic continua. We provide a historical perspective on the development of the method, and highlight the most important advances and best practices as they relate to the formulation and numerical implementation of the X-FEM for fracture problems. Existing challenges in the modeling and simulation of dynamic fracture, damage phenomena, and capturing the transition from continuum-to-discontinuum are also discussed.read more
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Book ChapterDOI
Phase-field modeling of fracture
TL;DR: This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician.
Journal ArticleDOI
Discrete and phase field methods for linear elastic fracture mechanics: A comparative study and state-of-the-art review
Adrian Egger,Udit Pillai,Konstantinos Agathos,Emmanouil G. Kakouris,Eleni Chatzi,Ian A. Aschroft,Savvas P. Triantafyllou +6 more
TL;DR: In this paper, the authors provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.
Journal ArticleDOI
Phase-field material point method for brittle fracture
TL;DR: In this paper, the material point method is revisited and originally upgraded to simulate crack propagation in brittle media, and a phase field model is introduced to resolve the crack path geometry following a particle in cell approach.
Journal ArticleDOI
An overview on advances in computational fracture mechanics of rock
M. Mohammadnejad,M. Mohammadnejad,Hongyuan Liu,Andrew Chan,Sevda Dehkhoda,Daisuke Fukuda,Daisuke Fukuda +6 more
TL;DR: This paper provided a review of recent advances in computational analysis of the rock fracture process, which is built upon a number of literature on numerical modelling of mechanics of failure in rock and other brittle materials.
Journal ArticleDOI
Modeling crack discontinuities without element-partitioning in the extended finite element method
TL;DR: This paper model crack discontinuities in two‐dimensional linear elastic continua using the extended finite element method without the need to partition an enriched element into a collection of triangles or quadrilaterals and demonstrates the flexibility of the approach and its excellent accuracy in stress intensity factor computations for two-dimensional crack problems.
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.
Journal ArticleDOI
On the Crack Extension in Plates Under Plane Loading and Transverse Shear
Fazil Erdogan,G.C. Sih +1 more
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.
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