book

Extended Finite Element Method

by Zhuo Zhuang, Zhanli Liu, Binbin Cheng, Jianhui Liao

March 2014

Intermediate to advanced

286 pages

8h 16m

English

Academic Press

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1.1. Significance of Studying Computational Fracture Mechanics1.2. Introduction to X-FEM1.3. Research Status and Development of X-FEM1.4. Organization of this Book
2.1. Introduction2.2. Two-Dimensional Linear Elastic Fracture Mechanics2.3. Material Fracture Toughness2.4. Fracture Criterion of Linear Elastic Material2.5. Complex Fracture Criterion2.6. Interaction Integral2.7. Summary
3.1. Introduction to Dynamic Fracture Mechanics3.2. Linear Elastic Dynamic Fracture Theory3.3. Crack Driving Force Computation3.4. Crack Propagation in Steady State3.5. Engineering Applications of Dynamic Fracture Mechanics3.6. Summary
4.1. X-FEM Based on the Partition of Unity4.2. Level Set Method4.3. Enriched Shape Function4.4. Governing Equation and Weak Form4.5. Integration on Spatial Discontinuity Field4.6. Time Integration and Lumped Mass Matrix4.7. Postprocessing Demonstration4.8. One-Dimensional X-FEM4.9. Summary
5.1. Numerical Study and Precision Analysis of X-FEM5.2. Two-Dimensional High-Order X-FEM5.3. Crack Branching Simulation5.4. Summary

6.1. Introduction
7.1. Introduction7.2. Theoretical Solutions of Subinterfacial Fracture7.3. Simulation of Subinterfacial Cracks Based On X-FEM7.4. Equilibrium State of Subinterfacial Mode I Cracks7.5. Effect on Subinterfacial Crack Growth from a Tilted Interface7.6. Summary
8.1. Introduction8.2. Level Set Method for Composite Materials8.3. Microstructure Generation8.4. Material Constitutive Model8.5. Numerical Examples8.6. Summary
9.1. Governing Equations and Interfacial Conditions9.2. Interfacial Description of Two-Phase Flows9.3. X-FEM and Unknown Parameters Discretization9.4. Discretization of Governing Equations9.5. Numerical Integral Method9.6. Examples and Analyses9.7. Summary
10.1. Research on Micro-Scale Crystal Plasticity10.2. Application of Multi-Scale Simulation10.3. Modeling of Deformation Localization10.4. Summary

Content preview from Extended Finite Element Method

6.6. Crack Propagation Criterion

6.6.1. Stress Intensity Factor Computation

The calculation of the stress intensity factors (SIFs) is based on the work of Nikishkov and Atluri (1987), who proposed an equivalent domain integral method for calculating the fracture parameter SIF of a 3D arbitrary crack. This method has been widely used in standard FEM and in this subsection it has been introduced into the CB shell element of X-FEM.

FIGURE 6.17 A local coordinate system at the crack tip.

A local coordinate system (x₁, x₂, x₃) is established at the crack tip as illustrated in Figure 6.17, where x₁ is located on the crack surface perpendicular to the crack ...