Modeling holes and inclusions by level sets in the extended finite-element method

Sukumar, N.; Chopp, David L.; Moës, Nicolas; Belytschko, Ted

doi:10.1016/s0045-7825(01)00215-8

Cited by 1,005 publications

(852 citation statements)

References 16 publications

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“…For problems with discontinuities in the primal dependent variable (cracks [29,28,13], fluid-structure interaction [26]), discontinuous functions are added. To handle discontinuities in the dual unknown (multi-materials [41], solidification [16], biofilms [35], multi-phase flow [15], Stokes flow [47]), functions with discontinuous derivatives enhance the standard basis. These additional functions allow to model the discontinuous features without recourse to a conforming mesh, while retaining an exact representation of the discontinuities, to which the mesh need not conform.…”

Section: Introductionmentioning

confidence: 99%

Derivative recovery and a posteriori error estimate for extended finite elements

Bordas

Duflot

2007

Computer Methods in Applied Mechanics and Engineering

130

102

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The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM). In each element, the local estimator is the L2 norm of the difference between the raw XFEM strain field and an enhanced strain field computed by extended moving least squares (XMLS) derivative recovery obtained from the raw nodal XFEM displacements. The XMLS construction is taylored to the nature of the solution. The technique is applied to linear elastic fracture mechanics, in which near-tip asymptotic functions are added to the MLS basis. The XMLS shape functions are constructed from weight functions following the diffraction criterion to represent the discontinuity. The result is a very smooth enhanced strain solution including the singularity at the crack tip. Results are shown for two and three dimensional linear elastic fracture mechanics problems in mode I and mixed mode. The effectivity index of the estimator is always close to 1. and improves upon mesh refinement. It is also shown that for the linear elastic fracture mechanics problems treated, the proposed estimator outperforms one of the superconvergent patch recovery technique of Zienkiewicz and Zhu, which is only C0. Parametric studies of the general performance of the estimator are also carried out.

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Section: Introductionmentioning

confidence: 99%

Derivative recovery and a posteriori error estimate for extended finite elements

Bordas

Duflot

2007

Computer Methods in Applied Mechanics and Engineering

130

102

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“…The modeling of material-void interfaces with X-FEM [12] differs only marginaly from the cracked structure case. Hence, for void inclusions and holes, the displacement field is now approximated by:…”

Section: Representing Holesmentioning

confidence: 99%

Stress Constrained Optimization using X-FEM and Level Set Description

Miegroet

Jacobs

Lemaire

et al. 2006

III European Conference on Computational Mechanics

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Abstract. This paper presents and describes an intermediate approach which takes its place between the two classical methods of shape and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (X-FEM). The method benefits from the fixed mesh work using X-FEM and from the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation remains small whereas various global and local constraints can be considered. A key problem which is investigated here is the sensitivity analysis and the way it can be carried out precisely and efficiently. Numerical applications revisit some classical 2D (academic) benchmarks from shape optimization and illustrate the great interest of using X-FEM and Level Set description together. The paper presents the results of stress constrained problems using the proposed X-FEM and Level Set based formulation. A central issue is the sensitivity analysis (related to the compliance and/or the stresses) and the way it can be carried out efficiently.A special attention is also paid to stress constrained problems which are often neglected in other Level Set Methods works.

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“…The principle idea lies in decoupling the discontinuities, both weak (material interfaces) and strong (cracks), from the mesh. This is achieved via adoption of the level set method (LSM) [4] for tracking discontinuities in conjunction with the seeding of jump and crack tip enrichments to the displacement solution, thus extending the standard FEM procedure. Leaving intact the core concepts and steps of FEM is in large responsible for its success and inclusion in most major commercial FEM software packages.…”

Section: Introductionmentioning

confidence: 99%

The Scaled Boundary Finite Element Method for the Efficient Modelling of Linear Elastic Fracture

Egger¹,

Triantafyllou²,

Chatzi³

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM's potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed.

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Modeling holes and inclusions by level sets in the extended finite-element method

Abstract: A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (S.

Cited by 1,005 publications

References 16 publications

Derivative recovery and a posteriori error estimate for extended finite elements

Derivative recovery and a posteriori error estimate for extended finite elements

Stress Constrained Optimization using X-FEM and Level Set Description

The Scaled Boundary Finite Element Method for the Efficient Modelling of Linear Elastic Fracture

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