Boundary elements in nonlinear fracture mechanics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Southampton u.a.
Computational Mechanics Publ.
1994
|
| Series: | Topics in engineering
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 261 S. graph. Darst. |
| ISBN: | 1853123358 1562522590 |
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| 245 | 1 | 0 | |a Boundary elements in nonlinear fracture mechanics |c V. M. A. Leitão |
| 264 | 1 | |a Southampton u.a. |b Computational Mechanics Publ. |c 1994 | |
| 300 | |a 261 S. |b graph. Darst. | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Boundary element methods | |
| 650 | 4 | |a Elastoplasticity |x Mathematical models | |
| 650 | 4 | |a Fracture mechanics |x Mathematical models | |
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| adam_text |
Titel: Boundary elements in nonlinear fracture mechanics
Autor: Leitão, V. M.
Jahr: 1994
Contents
1 Introduction 1
1.1 Fracture Mechanics. 1
1.2 Problems Addressed by Fracture Mechanics. 2
1.2.1 Stress Fields at the Crack Tip . 2
1.2.2 Fatigue Crack Growth. 3
1.3 Numerical Fracture Mechanics . 4
1.3.1 The Finite Element Method. 4
1.3.2 The Boundary Element Method. 4
1.4 Aim of this Work. 6
1.4.1 Applications of the Formulations Developed. 7
1.5 Description of this Work. 8
2 Basic Solid Mechanics 11
2.1 Elasticity.11
2.1.1 Strain-Displacement Relationships. 12
2.1.2 Compatibility Equations. 12
2.1.3 Equilibrium Conditions . 12
2.1.4 Constitutive Relationships. 13
2.1.5 Plane Elasticity. 14
2.1.6 Governing Differential Equations. 14
2.2 Elastoplasticity. 15
2.2.1 Brief Account of Contributions to the Theory of Plasticity . 16
2.2.2 Plastic Behaviour due to Uniaxial Loading . 17
2.2.3 Multiaxial Loading. 22
2.3 Prandtl-Reuss Equations. 24
2.3.1 Prandtl-Reuss Equations in Terms of Equivalent Quantities 25
2.3.2 Prandtl-Reuss Equations in Terms of Total Strains. 26
3 Basic Fracture Mechanics 29
3.1 Overview. 29
3.2 Linear Elastic Fracture Mechanics (LEFM). 31
3.2.1 Modes of Fracture. 31
3.2.2 Near-Tip Fields Characterization. 32
3.2.3 The Stress Intensity Factor, K. 33
3.2.4 Griffith's Criterion for Crack Growth. 34
3.2.5 Small Scale Yielding. 35
3.2.6 Irwin's Plastic Zone Correction. 36
3.2.7 Evaluation of Stress Intensity Factors. 37
3.3 The /-integral . 40
3.4 Elasto-Plastic Fracture Mechanics (EPFM). 42
3.4.1 The CTOD Approach. 43
3.4.2 The Dugdaie Model. 45
3.4.3 J-type Integrals . 46
3.4.4 Plastic Near-tip Fields Characterization. 46
3.5 Fatigue Crack Growth. 47
3.5.1 Crack Closure. . 48
4 An Elastoplastic Boundary Element Formulation 49
4.1 Boundary Element Methods in SoEd Mechanics. 50
4.2 The Governing Equations. 51
4.3 Boundary Integral Formulation. 55
4.3.1 Displacement Boundary Equation . 58
4.3.2 Boundary Integral Representation of the Stresses . 59
4.3.3 Alternative Approaches. 61
4.3.4 Selection of the Approach. 63
4.4 Numerical Aspects. 65
4.4.1 Boundary Discretization. 66
4.4.2 Domain Discretization. 69
4.4.3 Discretized Boundary Equations. 73
4.5 Treatment of the Integrals. 73
4.6 Formation of the System Matrices. 77
4.7 Solution Techniques for Nonlinear Problems. 81
4.7.1 Explicit Iterative Procedures. 81
4.7.2 Implicit Procedures. . 84
4.8 Benchmark Problems. 86
4.8.1 Perforated Aluminium Strip. 86
4.8.2 Thick Cylinder. 93
4.8.3 Notched Plate. §7
4.8.4 Discussion of the Benchmark Results . ,. . 100
4.9 Conclusions. 100
5 Application to Crack Problems; /-type Integrals 103
5.1 Introduction.104
5.2 Some J-type Integrals. . 105
5.2.1 The J BitegraL [119} . 106
5.2.2 The J* Integral, [12] .107
5.2.3 The T* Integral, [6] .107
5.2.4 The J Integral, [71] .108
5.2.5 The Jf Integral, [3] .109
5.3 Implementation of Contour Integrals in a BEM Elastoplastic
Formulation.109
5.4 Numerical Integration.110
5.5 Numerical Comparison of the Various Integrals.Ill
5.5.1 Discussion.117
5.6 Conclusions.118
6 The Elastoplastic Dual Boundary Element Method (EPDBEM) 119
6.1 Introduction.120
6.2 The Elastoplastic DBEM .122
6.2.1 Traction Boundary Integral Equation .122
6.3 Treatment of the Integrals.125
6.3.1 Modelling Strategy.128
6.3.2 Incremental and Iterative Strategies-Update.129
6.4 Numerical Applications .130
6.4.1 Centre-cracked Plate.130
6.4.2 Slant Edge-cracked Plate.133
6.5 Conclusions.135
7 Application of the EPDBEM to Crack Contact Problems 137
7.1 Introduction.138
7.2 Background.139
7.3 Contact Mechanics. . 140
7.3.1 Modes of Contact. 140
7.3.2 Contact Status and Modelling.141
7.3.3 Elastoplastic Contact Problem.142
7.3.4 Systems Updating.144
7.3.5 Incremental and Iterative Strategies.145
7.4 Evaluation of /-type EPFM Parameters.146
7.5 Numerical Applications.146
7.5.1 Edge-cracked Plate'.146
7.5.2 Straight Crack from a Hole.152
7.5.3 Kinked Crack from a Hole.156
7.5.4 Discussion.156
7.6 Conclusions.161
8 Effect of Residual Stresses on Fatigue Crack Growth 163
8.1 Introduction. 164
8.2 Fatigue Crack Growth.166
8.2.1 AK and R in the Presence of Residual Stresses.167
8.3 The Weight Function Technique.167
8.3.1 Stress Intensity Factors for the Remote Load.169
8.3.2 Stress Intensity Factors for Loading on the Crack Faces . . 169
8.3.3 Numerical Weight Functions .170
8.3.4 Interpolation of the Fields.171
8.4 Numerical Application (LEFM/WF).171
8.4.1 Prestressing Technique. . 172
8.4.2 Cold-expansion .185
8.4.3 Comparative Analysis of the Results . 195
8.5 Conclusions. 199
9 Elastoplastic Simulation of Crack Growth in the Presence of
Residual Stress Fields 201
9.1 Introduction.202
9.2 Modelling of Stable Crack Growth.203
9.2.1 Algorithm.206
9.3 Numerical Application (EPFM//).208
9.3.1 Crack Growth of Initially Uncracked Specimens.208
9.3.2 Crack Growth of Initially Cracked Specimens.216
9.4 Conclusions.231
10 Conclusions and Future Work 233
Bibliography 241
Appendix A 257
A Irwin's and Dugdale's Models 257
A.l Irwin's Equivalent Crack Model.257
A.2 Dugdale's Strip Yield Model.258
A.3 Results.259
Appendix B 263
B 263
B.l Prediction of Crack Growth Rates.263
B.2 Experimental Crack Growth Rates.263 |
| any_adam_object | 1 |
| author | Leitão, V. M. |
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| id | DE-604.BV010171562 |
| illustrated | Illustrated |
| indexdate | 2025-01-30T09:00:57Z |
| institution | BVB |
| isbn | 1853123358 1562522590 |
| language | English |
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| physical | 261 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Computational Mechanics Publ. |
| record_format | marc |
| series | Topics in engineering |
| series2 | Topics in engineering |
| spelling | Leitão, V. M. Verfasser aut Boundary elements in nonlinear fracture mechanics V. M. A. Leitão Southampton u.a. Computational Mechanics Publ. 1994 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topics in engineering 21 Mathematisches Modell Boundary element methods Elastoplasticity Mathematical models Fracture mechanics Mathematical models Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Elastoplastische Bruchmechanik (DE-588)4220750-2 gnd rswk-swf Elastoplastische Bruchmechanik (DE-588)4220750-2 s Randwertproblem (DE-588)4048395-2 s DE-604 Randelemente-Methode (DE-588)4076508-8 s Topics in engineering 21 (DE-604)BV001897978 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006755993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leitão, V. M. Boundary elements in nonlinear fracture mechanics Topics in engineering Mathematisches Modell Boundary element methods Elastoplasticity Mathematical models Fracture mechanics Mathematical models Randwertproblem (DE-588)4048395-2 gnd Randelemente-Methode (DE-588)4076508-8 gnd Elastoplastische Bruchmechanik (DE-588)4220750-2 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4076508-8 (DE-588)4220750-2 |
| title | Boundary elements in nonlinear fracture mechanics |
| title_auth | Boundary elements in nonlinear fracture mechanics |
| title_exact_search | Boundary elements in nonlinear fracture mechanics |
| title_full | Boundary elements in nonlinear fracture mechanics V. M. A. Leitão |
| title_fullStr | Boundary elements in nonlinear fracture mechanics V. M. A. Leitão |
| title_full_unstemmed | Boundary elements in nonlinear fracture mechanics V. M. A. Leitão |
| title_short | Boundary elements in nonlinear fracture mechanics |
| title_sort | boundary elements in nonlinear fracture mechanics |
| topic | Mathematisches Modell Boundary element methods Elastoplasticity Mathematical models Fracture mechanics Mathematical models Randwertproblem (DE-588)4048395-2 gnd Randelemente-Methode (DE-588)4076508-8 gnd Elastoplastische Bruchmechanik (DE-588)4220750-2 gnd |
| topic_facet | Mathematisches Modell Boundary element methods Elastoplasticity Mathematical models Fracture mechanics Mathematical models Randwertproblem Randelemente-Methode Elastoplastische Bruchmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006755993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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