Strain smoothing in FEM and XFEM
TL;DR: The numerical results indicate that for 2D and 3D continuum, locking can be avoided and the principle is extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method.
About: This article is published in Computers & Structures.The article was published on 2010-12-01. It has received 294 citations till now. The article focuses on the topics: Extended finite element method & Finite element method.
Citations
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TL;DR: An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed in this article, where the discretization is based on Non-Uniform Rational B-Splines (NURBS).
320 citations
01 Jan 2020
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.
Abstract: Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, a major concern in structural designs. Computational modeling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights into understanding the fracture processes of many materials such as concrete, rock, ceramic, metals, and biological soft tissues. 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. PFMs are the regularized versions of the variational approach to fracture which generalizes Griffith's theory for brittle fracture. They can handle topologically complex fractures such as initiation, intersecting, and branching cracks in both two and three dimensions with a quite straightforward implementation. One of our aims is to justify the gaining popularity of PFMs. To this end, both theoretical and computational aspects are discussed and extensive benchmark problems (for quasi-static and dynamic brittle/cohesive fracture) that are successfully and unsuccessfully solved with PFMs are presented. Unresolved issues for further investigations are also documented.
290 citations
TL;DR: In this article, the authors proposed an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasi-brittle and ductile materials based on edge rotations.
223 citations
Cites methods from "Strain smoothing in FEM and XFEM"
...In particular, the extended finite element method (XFEM) by Moës, Belytschko and co-workers [47, 20, 46, 15, 63, 23, 24] was used previously but still poses challenges for large amplitude displacements (this is particularly critical for quasi-adiabatic shear bands)....
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TL;DR: In this article, a strain smoothing procedure for the extended finite element method (XFEM) is presented, which is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM.
210 citations
TL;DR: In this paper, a coarse-graining technique is proposed to reduce a given atomistic model into an equivalent coarse grained continuum model, tailored for problems involving complex crack patterns in 2D and 3D including crack branching and coalescence.
210 citations
References
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Book•
01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08
17,327 citations
"Strain smoothing in FEM and XFEM" refers background in this paper
...g, in the textbooks [108,7], among other reference texts....
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Book•
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Abstract: 1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4. Formulation of the Finite Element Method -- Linear Analysis in Solid and Structural Mechanics. 5. Formulation and Calculation of Isoparametric Finite Element Matrices. 6. Finite Element Nonlinear Analysis in Solid and Structural Mechanics. 7. Finite Element Analysis of Heat Transfer, Field Problems, and Incompressible Fluid Flows. 8. Solution of Equilibrium Equations in State Analysis. 9. Solution of Equilibrium Equations in Dynamic Analysis. 10. Preliminaries to the Solution of Eigenproblems. 11. Solution Methods for Eigenproblems. 12. Implementation of the Finite Element Method. References. Index.
8,068 citations
"Strain smoothing in FEM and XFEM" refers background in this paper
...g, in the textbooks [108,7], among other reference texts....
[...]
Book•
01 Jan 1950
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy
7,810 citations
"Strain smoothing in FEM and XFEM" refers background or result in this paper
...Also, the proposed method agrees well with the exact solution [41] and other published results [68,27]....
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...Hill [41] shows the exact solution for this problem....
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TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.
7,468 citations
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.
Abstract: SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard 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. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright ? 1999 John Wiley & Sons, Ltd.
5,815 citations
"Strain smoothing in FEM and XFEM" refers background or methods in this paper
...4 We choose here the extended finite element method, XFEM [11,57]....
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...[57] is the first to propose the use of discontinuous enrichment....
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