Extended Finite Element and Meshfree Methods

Extended Finite Element and Meshfree Methods

1st Edition - November 13, 2019

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  • Authors: Timon Rabczuk, Jeong-Hoon Song, Xiaoying Zhuang, Cosmin Anitescu
  • Paperback ISBN: 9780128141069
  • eBook ISBN: 9780128141076

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Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications.

Key Features

  • Explains all the important theory behind XFEM and meshfree methods
  • Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes
  • Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods
  • Introduces alternative modeling methods to help readers decide what is most appropriate for their work


Advanced students, researchers, and engineers interested in learning about and coding using meshfree methods, particularly for applications in solid mechanics

Table of Contents

  • 1. Introduction
    2. Weak forms and governing equations
    3. Extended Finite Element Method
    4. Phantom Node Method
    5. Extended Meshfree Methods
    6. Extended Isogeometric Analysis
    7. Fracture in plates and shells
    8. Fracture criteria and crack tracking procedures
    9. Multiscale methods for fracture
    10. A short overview of alternatives
    11. Implementation details

Product details

  • No. of pages: 638
  • Language: English
  • Copyright: © Academic Press 2019
  • Published: November 13, 2019
  • Imprint: Academic Press
  • Paperback ISBN: 9780128141069
  • eBook ISBN: 9780128141076

About the Authors

Timon Rabczuk

Timon Rabczuk is Professor of Modeling and Simulation, and Chair of Computational Mechanics at the Bauhaus Universität Weimar, Germany. He has published more than 450 SCI papers, many of them on extended finite element and meshfree methods, multiscale methods and isogeometric analysis. He is editor-in-chief of CMC-Computers, Materials and Continua, associated editor of International Journal of Impact Engineering, assistant editor of Computational Mechanics, and executive editor of FSCE-Frontiers of Structural and Civil Engineering. He was listed as one of ISI Highly Cited Researchers in Computer Science and Engineering from 2014 up to now.

Affiliations and Expertise

Professor of Modeling and Simulation and Chair of Computational Mechanics, Bauhaus Universitat Weimar, Germany

Jeong-Hoon Song

Jeong-Hoon Song is Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and Engineering Program at the University of Colorado, Boulder, USA. He received a Ph.D. in Theoretical and Applied Mechanics at Northwestern University in 2008 and has worked in the area of computational mechanics and physics of solids to develop new computational methods and algorithms for various multiscale/multiphysics phenomena. He has authored over 45 peer-reviewed journal publications and two book chapters and has presented over 70 research lectures at national and international conferences, seminars, and workshops.

Affiliations and Expertise

Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and Engineering Program at the University of Colorado, Boulder, USA.

Xiaoying Zhuang

Xiaoying Zhuang is Associate Professor at the Institute of Continuum Mechanics at Leibniz Universität Hannover, Germany. She has been developing computational methods for two-dimensional and three-dimensional fracture problems using partition-of-unity methods, including meshfree methods, the extended finite element method (XFEM), the phantom node and finite cover method, and multiscale methods. She is on the editorial boards of international journals including Theoretical and Applied Fracture Mechanics, KSCE Journal of Civil Engineering, and Engineering Geology.

Affiliations and Expertise

Associate Professor, Institute of Continuum Mechanics, Leibniz Universitat Hannover, Germany

Cosmin Anitescu

Cosmin Anitescu is a researcher at the Institute for Structural Mechanics of the Bauhaus Universität Weimar, Germany. His research focuses on the theory and application of extended finite elements, meshfree methods, and isogeometric analysis to engineering problems. He is currently the main contributor and maintainer of IGAFEM, an educational software package written in Matlab for solving computational mechanics problems.

Affiliations and Expertise

Researcher, Institute for Structural Mechanics, Bauhaus Universitat Weimar, Germany

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