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Article
Publication date: 2 May 2017

A computational framework for a two-scale generalized/extended finite element method: Generic imposition of boundary conditions

Mohammad Malekan, Felício Barros, Roque Luiz da Silva Pitangueira, Phillipe Daniel Alves and Samuel Silva Penna

This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local…

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Abstract

Purpose

This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

Design/methodology/approach

The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized.

Findings

The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated.

Originality/value

This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

Details

Engineering Computations, vol. 34 no. 3
Type: Research Article
DOI: https://doi.org/10.1108/EC-02-2016-0050
ISSN: 0264-4401

Keywords

  • Boundary condition
  • Extended FEM
  • Generalized FEM
  • Object-oriented design
  • Two-scale analysis

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Article
Publication date: 5 April 2011

The extended finite element method (XFEM) for discontinuous rock masses

T.T. Yu

The purpose of this paper is to achieve numerical simulation of discontinuous rock masses.

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Abstract

Purpose

The purpose of this paper is to achieve numerical simulation of discontinuous rock masses.

Design/methodology/approach

The extended finite element method (XFEM) was used. Discontinuities (such as joints, faults, and material interfaces) are contained in the elements, thus the mesh can be generated without taking into account the existence of discontinuities. When one element contains no discontinuity, the displacement function is degenerated into that of the conventional finite element. For the element containing discontinuities, the standard displacement‐based approximation is enriched by incorporating level‐set‐based enrichment functions that model the discontinuities, and an element subdivision procedure is used to integrate the domain of the element.

Findings

Mesh generation can be simplified considerably and high‐quality meshes can be obtained. A solution with good precision can also be achieved. It is concluded that the XFEM technique is especially suitable in simulating discontinuous rock masses problems.

Research limitations/implications

Crack initiation and propagation should be considered in further studies.

Practical implications

The paper presents a very useful numerical method for a geotechnical engineering problem that has the ability to simulate the failure process of discontinuous rock masses. The method is expected to be used widely in the deformation and stability analysis of complicated rock masses.

Originality/value

The paper provides a new numerical method for discontinuous rock masses that is very convenient for pre‐processing.

Details

Engineering Computations, vol. 28 no. 3
Type: Research Article
DOI: https://doi.org/10.1108/02644401111118178
ISSN: 0264-4401

Keywords

  • Rocks
  • Mechanical behaviour of materials
  • Numerical analysis
  • Simulation

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Article
Publication date: 2 March 2015

The XFEM for nonlinear thermal and phase change problems

Pawel Stapór

Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing…

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Abstract

Purpose

Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing or moving-mesh algorithms for a physically nonlinear phase change problem. The paper aims to discuss this issue.

Design/methodology/approach

The XFEM is applied to solve nonlinear transient problems with a phase change. Thermal conductivity and volumetric heat capacity are assumed to be dependent on temperature. The nonlinearities in the governing equations make it necessary to employ an effective iterative approach to solve the problem. The Newton-Raphson method is used and the incremental discrete XFEM equations are derived.

Findings

The robustness and utility of the method are demonstrated on several one-dimensional benchmark problems.

Originality/value

The novel procedure based on the XFEM is developed to solve physically nonlinear phase change problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
DOI: https://doi.org/10.1108/HFF-02-2014-0052
ISSN: 0961-5539

Keywords

  • XFEM
  • Newton-Raphson method
  • Stefan-like problem

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Article
Publication date: 2 March 2012

Shape optimization approach based on the extended finite element method

Vasile Topa, Marius Purcar, Calin Munteanu, Laura Grindei, Claudia Pacurar and Ovidiu Garvasiuc

This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on…

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Abstract

Purpose

This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described.

Design/methodology/approach

The proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step.

Findings

This approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods.

Research limitations/implications

This research is limited to shape optimization of two‐dimensional electric structures, however, the work can be extended to 3D ones too.

Practical implications

The implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described.

Originality/value

The main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 2
Type: Research Article
DOI: https://doi.org/10.1108/03321641211200545
ISSN: 0332-1649

Keywords

  • Shape optimization
  • Level set method
  • Extended finite element method
  • Electric structures

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Article
Publication date: 19 June 2020

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

Bruna Caroline Campos, Felício Bruzzi Barros and Samuel Silva Penna

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic…

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Abstract

Purpose

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.

Design/methodology/approach

Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.

Findings

Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.

Originality/value

This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
DOI: https://doi.org/10.1108/EC-02-2020-0067
ISSN: 0264-4401

Keywords

  • Computational mechanics
  • Fracture mechanics
  • Generalized/extended finite element method
  • Numerical integration
  • Partition of unity methods

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Article
Publication date: 29 March 2020

Fracture mechanics testing and crack propagation modelling in polypropylene pipes

Imad Barsoum, Hamda Almansoori, Aaesha Ahmed Almazrouei and Ebru Gunister

The main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension…

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Abstract

Purpose

The main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension accurately in polypropylene subsea pipes subjected to internal pressure.

Design/methodology/approach

Tensile test was performed following the ISO 527–1 standard. An elastic-plastic constitutive model was developed based on the tensile test results, and it is implemented in the FEA model to describe the constitutive behaviour of the polypropylene material. Three-point bend tests with linear-elastic fracture mechanics (LEFM) approach were conducted following ISO-13586 standard, from which the average fracture toughness of the polypropylene pipe material in crack-opening mode was found as KIc = 3.3 MPa√m. A numerical model of the experiments is developed based on the extended finite element method (XFEM), which showed markedly good agreement with the experimental results.

Findings

The validated XFEM modelling approach is utilised to illustrate its capabilities in predicting fracture initiation and crack propagation in a polypropylene subsea pipe subjected to an internal pressure containing a semi-elliptical surface crack, which agrees well with existing analytical solutions. The XFEM model is capable of predicting the crack initiation and propagation in the polypropylene pipe up to the event of leakage.

Originality/value

The methodology proposed herein can be utilised to assess the structural integrity and resistance to fracture of subsea plastic pipes subjected to operational loads (e.g. internal pressure).

Details

International Journal of Structural Integrity, vol. ahead-of-print no. ahead-of-print
Type: Research Article
DOI: https://doi.org/10.1108/IJSI-01-2020-0006
ISSN: 1757-9864

Keywords

  • Fracture mechanics testing
  • Polypropylene pipes
  • XFEM
  • Crack propagation
  • Leakage prediction

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Article
Publication date: 20 April 2015

A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures

Xiaodong Zhang and Tinh Quoc Bui

– The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

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Abstract

Purpose

The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

Design/methodology/approach

The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming.

Findings

The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures.

Research limitations/implications

Multiple cracks and crack growth in reinforced concretes should be considered in further studies.

Practical implications

The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures.

Originality/value

The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.

Details

Engineering Computations, vol. 32 no. 2
Type: Research Article
DOI: https://doi.org/10.1108/EC-08-2013-0203
ISSN: 0264-4401

Keywords

  • Concrete
  • Cohesive crack
  • Crack growth
  • Extended finite element method
  • Fictitious crack model
  • Fracture mechanics

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Article
Publication date: 9 November 2012

On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods

Octavio Andrés González‐Estrada, Juan José Ródenas, Stéphane Pierre Alain Bordas, Marc Duflot, Pierre Kerfriden and Eugenio Giner

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the…

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Abstract

Purpose

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).

Design/methodology/approach

The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.

Findings

Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.

Originality/value

The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.

Details

Engineering Computations, vol. 29 no. 8
Type: Research Article
DOI: https://doi.org/10.1108/02644401211271609
ISSN: 0264-4401

Keywords

  • Finite element analysis
  • Error analysis
  • Extended finite element method
  • Error estimation
  • Linear elastic fracture mechanics
  • Statical admissibility
  • Extended recovery

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Article
Publication date: 10 July 2020

Modeling of crack repair using piezoelectric material: XFEM approach

Ritesh Kumar, Himanshu Pathak, Akhilendra Singh and Mayank Tiwari

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the…

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Abstract

Purpose

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

Design/methodology/approach

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

Findings

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

Originality/value

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
DOI: https://doi.org/10.1108/EC-01-2020-0001
ISSN: 0264-4401

Keywords

  • Piezoelectric
  • Stress intensity factor
  • J-integral
  • Thermo-mechanical loading
  • XFEM

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Article
Publication date: 8 May 2018

Extended finite element method for analysis of the acoustic emission response by a crack under moving heat source

Kuanfang He, Wei Lu, Xiangnan Liu, Siwen Xiao and Xuejun Li

This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for…

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Abstract

Purpose

This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the actual crack detection during welding process.

Design/methodology/approach

The paper studied the AE characteristics in welding using thermoelastic theory, which investigates the dynamical displacement field caused by a crack and the welding heating effect. In the calculation model, the crack initiation and extension are represented by moment tensor as the AE source, and the welding heat source is the Gauss heat flux distribution. The extended finite element method (XFEM) is implemented to calculate and solve the AE response of a thermoelastic plate with a crack during the welding heating effect. The wavelet transform is applied to the time–frequency analysis of the AE signals.

Findings

The paper provides insights about the changing rule of the acoustic radiation patterns influenced by the heating effect of the moving heat source and the AE signal characteristics in thermoelastic plate by different crack lengths and depths. It reveals that the time–frequency characteristics of the AE signals from the simulation are in good agreement with the theoretical ones. The energy ratio of the antisymmetric mode A0 to symmetric mode S0 is a valuable quantitative inductor to estimate the crack depth with a certain regularity.

Research limitations/implications

This paper mainly discusses the application of XFEM to calculate and analyze thermoelastic problems, and has presented few cases based on a specified configuration. Further work will focus on the calculation and analysis under different plate configurations and conditions, which is to obtain more interesting and general conclusions for guiding practice.

Originality/value

The paper is a successful application of XFEM to solve the problem of AE response of a crack in the dynamic welding inhomogeneous heating effect. The paper provides an effective way to obtain the AE signal characteristics in monitoring the welding crack.

Details

Engineering Computations, vol. 35 no. 3
Type: Research Article
DOI: https://doi.org/10.1108/EC-03-2017-0101
ISSN: 0264-4401

Keywords

  • XFEM
  • Crack
  • Acoustic emission response
  • Moving heat source
  • Thermoelasticity plate
  • Time–frequency characteristics
  • AE response

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