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Author Pommier, Sylvie
Title Extended Finite Element Method for Crack Propagation
Imprint Somerset : John Wiley & Sons, Incorporated, 2011
©2010
book jacket
Edition 1st ed
Descript 1 online resource (280 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Cover -- Title Page -- Copyright Page -- Table of Contents -- Foreword -- Acknowledgements -- List of Symbols -- Introduction -- Chapter 1. Elementary Concepts of Fracture Mechanics -- 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 -- Chapter 2. Representation of Fixed and Moving Discontinuities -- 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 -- Chapter 3. Extended Finite Element Method X-FEM -- 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 -- Chapter 4. Non-linear Problems, Crack Growth by Fatigue -- 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 ΔKI -- 4.2.1.2. Crack growth mechanisms at average or high ΔKI -- 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
Chapter 5. Applications: Numerical Simulation of Crack Growth -- 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 -- 5.2.3.1. Internal crack growth rate -- 5.2.4. Propagation of corner cracks -- 5.3. Dynamic fracture simulation -- 5.3.1. Effects of crack speed ȧ and crack growth criteria -- 5.3.2. Analytical solution: rectilinear crack propagation on a reference problem -- 5.3.3. Kalthoff experiment -- 5.3.4. Tests on test pieces CCS of Maigre-Rittel -- 5.3.5. Réthoré, Gregoire and Maigre tests -- 5.3.6. X-FEM method in explicit dynamics -- 5.4. Simulation of ductile fracture -- 5.4.1. Characteristics of material 16MND5 -- 5.4.1.1. Dynamic characterization of the material -- 5.4.1.2. Fracture tests -- 5.4.1.3. Crack advancement measurement device -- 5.4.1.4. Description of tests on CT test pieces -- 5.4.1.5. Numerical simulation -- 5.4.2. Ring test and interpretation -- 5.4.2.1. Geometry, mesh, and loading -- 5.4.2.2. Interpretation of the test in Mode I -- 5.4.2.3. Interpretation of the test in mixed mode -- Conclusions and Open Problems -- Summary -- Bibliography -- Index
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 crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Pommier, Sylvie Extended Finite Element Method for Crack Propagation Somerset : John Wiley & Sons, Incorporated,c2011 9781848212091
Subject Fracture mechanics -- Mathematics.;Finite element method
Electronic books
Alt Author Gravouil, Anthony
Moes, Nicolas
Combescure, Alain
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