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Extended finite element method for crack propagation /

Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the...

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Bibliographic Details
Other Authors: Pommier, Sylvie
Format: eBook
Language:English
Language Notes:English.
Published: London, UK : Hoboken, NJ : ISTE ; Wiley, 2011.
Series:ISTE.
Subjects:
Fracture mechanics > Mathematics.
Finite element method.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1.1. Introduction
  • 1.2. Superposition principle
  • 1.3. Modes of crack straining
  • 1.4. Singular fields at cracking point
  • 1.4.1. Asymptotic solutions in Mode I
  • 1.4.2. Asymptotic solutions in Mode II
  • 1.4.3. Asymptotic solutions in Mode III
  • 1.4.4. Conclusions
  • 1.5. Crack propagation criteria
  • 1.5.1. Local criterion
  • 1.5.2. Energy criterion
  • 1.5.2.1. Energy release rate G
  • 1.5.2.2. Relationship between G and stress intensity factors
  • 1.5.2.3. How the crack is propagated
  • 1.5.2.4. Propagation velocity
  • 1.5.2.5. Direction of crack propagation
  • 2.1. Geometric representation of a crack: a scale problem
  • 2.1.1. Link between the geometric representation of the crack and the crack model
  • 2.1.2. Link between the geometric representation of the crack and the numerical method used for crack growth simulation
  • 2.2. Crack representation by level sets
  • 2.2.1. Introduction.
  • 2.2.2. Definition of level sets
  • 2.2.3. Level sets discretization
  • 2.2.4. Initialization of level sets
  • 2.3. Simulation of the geometric propagation of a crack
  • 2.3.1. Some examples of strategies for crack propagation simulation
  • 2.3.2. Crack propagation modeled by level sets
  • 2.3.3. Numerical methods dedicated to level set propagation
  • 2.4. Prospects of the geometric representation of cracks
  • 3.1. Introduction
  • 3.2. Going back to discretization methods
  • 3.2.1. Formulation of the problem and notations
  • 3.2.2. The Rayleigh-Ritz approximation
  • 3.2.3. Finite element method
  • 3.2.4. Meshless methods
  • 3.2.5. The partition of unity
  • 3.3. X-FEM discontinuity modeling
  • 3.3.1. Introduction, case of a cracked bar
  • 3.3.1.1. Case a: crack positioned on a node
  • 3.3.1.2. Case b: crack between two nodes
  • 3.3.2. Variants
  • 3.3.3. Extension to two-dimensional and three-dimensional cases
  • 3.3.4. Level sets within the framework of the eXtended finite element method.
  • 3.4. Technical and mathematical aspects
  • 3.4.1. Integration
  • 3.4.2. Conditioning
  • 3.5. Evaluation of the stress intensity factors
  • 3.5.1. The Eshelby tensor and the J integral
  • 3.5.2. Interaction integrals
  • 3.5.3. Considering volumic forces
  • 3.5.4. Considering thermal loading
  • 4.1. Introduction
  • 4.2. Fatigue and non-linear fracture mechanics
  • 4.2.1. Mechanisms of crack growth by fatigue
  • 4.2.1.1. Crack growth mechanism at low AK
  • 4.2.1.2. Crack growth mechanisms at average or high AK!
  • 4.2.1.3. Macroscopic crack growth rate and striation formation
  • 4.2.1.4. Fatigue crack growth rate of long cracks, Paris law
  • 4.2.1.5. Brief conclusions
  • 4.2.2. Confined plasticity and consequences for crack growth
  • 4.2.2.1. Irwin's plastic zones
  • 4.2.2.2. Role of the T stress
  • 4.2.2.3. Role of material hardening
  • 4.2.2.4. Cyclic plasticity
  • 4.2.2.5. Effect of residual stress on crack propagation
  • 4.3. eXtended constitutive law
  • 4.3.1. Scale-up method for fatigue crack growth.
  • 4.3.1.1. Procedure
  • 4.3.1.2. Scaling
  • 4.3.1.3. Assessment
  • 4.3.2. eXtended constitutive law
  • 4.3.2.1. Damage law
  • 4.3.2.2. Plasticity threshold
  • 4.3.2.3. Plastic flow rule
  • 4.3.2.4. Evolution law of the center of the elastic domain
  • 4.3.2.5. Model parameters
  • 4.3.2.6. Comparisons
  • 4.4. Applications
  • 4.4.1. Mode I crack growth under variable loading
  • 4.4.2. Effect of the T stress
  • 5.1. Energy conservation: an essential ingredient
  • 5.1.1. Proof of energy conservation
  • 5.1.1.1. X-FEM approach
  • 5.1.1.2. Cohesive zone models
  • 5.1.1.3. Energy conservation for adaptive cohesive zones
  • 5.1.2. Case where the material behavior depends on history
  • 5.2. Examples of crack growth by fatigue simulations
  • 5.2.1. Calculation of linear fatigue crack growth simulation
  • 5.2.2. Two-dimensional fatigue tests
  • 5.2.2.1. Test-piece CTS: crack growth in mode 1
  • 5.2.2.2. Arcan test piece: crack growth in mixed mode
  • 5.2.3. Three-dimensional fatigue cracks. Propavanfiss project.