LEADER 05478nam 2200685 a 450 001 9910808334803321 005 20240313173812.0 010 $a1-118-62265-0 010 $a1-299-31564-X 010 $a1-118-62184-0 035 $a(CKB)2560000000100645 035 $a(EBL)1143632 035 $a(OCoLC)830161622 035 $a(SSID)ssj0000833189 035 $a(PQKBManifestationID)11462172 035 $a(PQKBTitleCode)TC0000833189 035 $a(PQKBWorkID)10935358 035 $a(PQKB)10079437 035 $a(OCoLC)842854713 035 $a(MiAaPQ)EBC1143632 035 $a(Au-PeEL)EBL1143632 035 $a(CaPaEBR)ebr10671567 035 $a(CaONFJC)MIL462814 035 $a(PPN)188554025 035 $a(EXLCZ)992560000000100645 100 $a20101214d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aExtended finite element method for crack propagation /$fSylvie Pommier ... [et al.] 205 $a1st ed. 210 $aLondon, U.K. $cISTE ;$aHoboken, N.J. $cWiley$d2011 215 $a1 online resource (280 p.) 225 1 $aISTE 300 $aAdapted and updated from La simulation nume?rique de la propagation des fissures : milieux tridimensionnels, fonctions de niveau, e?le?ments finis e?tendus et crite?res e?nerge?tiques published 2009 in France by Hermes Science/Lavoisier. 311 $a1-84821-209-7 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $a1.5.2.2. Relationship between G and stress intensity factors1.5.2.3. 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 327 $a2.2.3. Level sets discretization2.2.4. 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 327 $a3.2.4. 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 327 $a3.5.3. Considering volumic forces3.5.4. 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 ?KI; 4.2.1.2. Crack growth mechanisms at average or high ?KI; 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 327 $a4.2.2.2. Role of the T stress 330 $aNovel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided. 410 0$aISTE 606 $aFracture mechanics$xMathematics 606 $aFinite element method 615 0$aFracture mechanics$xMathematics. 615 0$aFinite element method. 676 $a620.1/1260151825 701 $aPommier$b Sylvie$01654333 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910808334803321 996 $aExtended finite element method for crack propagation$94006085 997 $aUNINA