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Extended Finite Element Method - 1st Edition - ISBN: 9780124077171, 9780124078567

Extended Finite Element Method

1st Edition

Tsinghua University Press Computational Mechanics Series

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Editors: Zhuo Zhuang Zhanli Liu Binbin Cheng Jianhui Liao
Hardcover ISBN: 9780124077171
eBook ISBN: 9780124078567
Imprint: Academic Press
Published Date: 31st March 2014
Page Count: 286
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Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems.

The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials.

Key Features

  • Authored by an expert team from one of China's leading academic and research institutions
  • Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples
  • Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems


Graduate students, engineers and researchers in mechanical, aerospace and civil engineering.

Table of Contents

  • Preface
  • Chapter 1. Overview of Extended Finite Element Method
    • 1.1. Significance of Studying Computational Fracture Mechanics
    • 1.2. Introduction to X-FEM
    • 1.3. Research Status and Development of X-FEM
    • 1.4. Organization of this Book
  • Chapter 2. Fundamental Linear Elastic Fracture Mechanics
    • 2.1. Introduction
    • 2.2. Two-Dimensional Linear Elastic Fracture Mechanics
    • 2.3. Material Fracture Toughness
    • 2.4. Fracture Criterion of Linear Elastic Material
    • 2.5. Complex Fracture Criterion
    • 2.6. Interaction Integral
    • 2.7. Summary
  • Chapter 3. Dynamic Crack Propagation
    • 3.1. Introduction to Dynamic Fracture Mechanics
    • 3.2. Linear Elastic Dynamic Fracture Theory
    • 3.3. Crack Driving Force Computation
    • 3.4. Crack Propagation in Steady State
    • 3.5. Engineering Applications of Dynamic Fracture Mechanics
    • 3.6. Summary
  • Chapter 4. Fundamental Concept and Formula of X-FEM
    • 4.1. X-FEM Based on the Partition of Unity
    • 4.2. Level Set Method
    • 4.3. Enriched Shape Function
    • 4.4. Governing Equation and Weak Form
    • 4.5. Integration on Spatial Discontinuity Field
    • 4.6. Time Integration and Lumped Mass Matrix
    • 4.7. Postprocessing Demonstration
    • 4.8. One-Dimensional X-FEM
    • 4.9. Summary
  • Chapter 5. Numerical Study of Two-Dimensional Fracture Problems with X-FEM
    • 5.1. Numerical Study and Precision Analysis of X-FEM
    • 5.2. Two-Dimensional High-Order X-FEM
    • 5.3. Crack Branching Simulation
    • 5.4. Summary
  • Chapter 6. X-FEM on Continuum-Based Shell Elements
    • 6.1. Introduction
    • 6.2. Overview of Plate and Shell Fracture Mechanics
    • 6.3. Plate and Shell Theory Applied In Finite Element Analysis
    • 6.4. Brief Introduction to General Shell Elements
    • 6.5. X-FEM on CB Shell Elements
    • 6.6. Crack Propagation Criterion
    • 6.7. Numerical Examples
    • 6.8. Summary
  • Chapter 7. Subinterfacial Crack Growth in Bimaterials
    • 7.1. Introduction
    • 7.2. Theoretical Solutions of Subinterfacial Fracture
    • 7.3. Simulation of Subinterfacial Cracks Based On X-FEM
    • 7.4. Equilibrium State of Subinterfacial Mode I Cracks
    • 7.5. Effect on Subinterfacial Crack Growth from a Tilted Interface
    • 7.6. Summary
  • Chapter 8. X-FEM Modeling of Polymer Matrix Particulate/Fibrous Composites
    • 8.1. Introduction
    • 8.2. Level Set Method for Composite Materials
    • 8.3. Microstructure Generation
    • 8.4. Material Constitutive Model
    • 8.5. Numerical Examples
    • 8.6. Summary
  • Chapter 9. X-FEM Simulation of Two-Phase Flows
    • 9.1. Governing Equations and Interfacial Conditions
    • 9.2. Interfacial Description of Two-Phase Flows
    • 9.3. X-FEM and Unknown Parameters Discretization
    • 9.4. Discretization of Governing Equations
    • 9.5. Numerical Integral Method
    • 9.6. Examples and Analyses
    • 9.7. Summary
  • Chapter 10. Research Progress and Challenges of X-FEM
    • 10.1. Research on Micro-Scale Crystal Plasticity
    • 10.2. Application of Multi-Scale Simulation
    • 10.3. Modeling of Deformation Localization
    • 10.4. Summary
  • Appendix A: Westergaard Stress Function Method
  • Appendix B: J Integration
  • References
  • Index


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© Academic Press 2014
31st March 2014
Academic Press
Hardcover ISBN:
eBook ISBN:

About the Editors

Zhuo Zhuang

Zhuo Zhuang is Professor and Co-director of the Advanced Mechanics and Materials Center in the School of Aerospace Engineering, at Tsinghua University in China. He has published over 260 papers in leading scientific journals. He is General Council member for IACM, and APACM, and President of the Chinese Association of Computation Mechanics (CACM), Vice-director of the Supervision Committee on Mechanics at the Ministry of Education, and serves as an editor on both national and international journals. He received his PhD from University College Dublin in Ireland, and an Honorary Doctorate Degree (EngD) from Swansea University in the UK.

Affiliations and Expertise

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Zhanli Liu

Zhanli Liu is Associate Professor in the School of Aerospace Engineering at Tsinghua University in China. He has published over 60 papers, mostly relating to computational multi-scale mechanics, plasticity, damage and fracture mechanics. He received his PhD from Tsinghua University, and was a winner of the prestigious China Thousand Young Talents Program.

Affiliations and Expertise

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Binbin Cheng

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Affiliations and Expertise

Tsinghua University, Beijing, China

Jianhui Liao

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Affiliations and Expertise

Tsinghua University, Beijing, China

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