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 Element


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© 2014
Academic Press
Electronic ISBN:
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About the editors

Zhuo Zhuang

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Zhanli Liu

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Binbin Cheng

Department of Engineering Mechanics, Tsinghua University, Beijing, China

Jianhui Liao

Department of Engineering Mechanics, Tsinghua University, Beijing, China