Introduction to practical peridynamics: computational solid mechanics without stress and strain
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2016
|
| Schriftenreihe: | Frontier research in computation and mechanics of materials and biology
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 397 - 404 |
| Beschreibung: | XV, 410 S. graph. Darst. |
| ISBN: | 9789814699549 |
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| 245 | 1 | 0 | |a Introduction to practical peridynamics |b computational solid mechanics without stress and strain |c Walter Herbert Gerstle |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2016 | |
| 300 | |a XV, 410 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 397 - 404 | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Mechanics, Applied |x Mathematics | |
| 650 | 4 | |a Materials |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804174913637974016 |
|---|---|
| adam_text | Titel: Introduction to practical peridynamics
Autor: Gerstle, Walter Herbert
Jahr: 2016
Contents
Dedication..........................................................................................................................v
Preface.............................................................................................................................vii
Chapter 1............................................................................................................................1
Deformable Solids.............................................................................................................1
1.1 Difficulties with differential equations....................................................................2
1.2 Classical solid mechanics......................................................................................10
1.3 Where classical solid mechanics fails....................................................................12
1.4 Introduction to the peridynamic model..................................................................14
1.5 What is a solid material ?....................................................................................17
1.6 Geometric modeling of solids...............................................................................19
1.7 Digital aspects of geometric modeling..................................................................23
1.8 Scope of book........................................................................................................23
1.9 Exercises...............................................................................................................26
Chapter 2..........................................................................................................................29
Beginnings of the Theory of Elasticity.............................................................................29
2.1 Brief history of solid mechanics............................................................................30
2.2 Navier s treatise.....................................................................................................36
2.3 Discussion of Navier s paper.................................................................................55
2.4 Cauchy s treatise...................................................................................................64
2.5 Summary...............................................................................................................69
2.6 Exercises...............................................................................................................70
Chapter 3..........................................................................................................................72
Continuum Mechanics.....................................................................................................72
3.1 Newton, vectors, calculus, and continuity.............................................................76
3.2 Vectors and tensors...............................................................................................79
3.3 Kinematics.............................................................................................................85
3.4 Physical laws of mechanics and thermodynamics.................................................95
3.5 Traction and stress.................................................................................................98
3.6 Constitutive relations...........................................................................................105
xi
xii Contents
3.7 Solving the continuum equations........................................................................108
3.8 Summary.............................................................................................................Ill
3.9 Exercises.............................................................................................................112
Chapter 4........................................................................................................................114
Fracture Mechanics........................................................................................................114
4.1 Historical overview of fracture mechanics..........................................................116
4.2 Linear elastic fracture mechanics........................................................................120
4.3 Griffith energy criterion......................................................................................124
4.4 Mixed-mode fracture propagation criteria...........................................................128
4.5 Fatigue crack propagation...................................................................................130
4.6 Nonlinear fracture mechanics..............................................................................130
4.7 Computational fracture mechanics......................................................................133
4.8 Conclusions regarding fracture mechanics..........................................................137
4.9 Exercises.............................................................................................................138
Chapter 5........................................................................................................................146
Bond-Based Continuum Peridynamics..........................................................................146
5.1 Introduction to the bond-based peridynamic theory............................................147
5.2 Kinematics of the bond-based peridynamic theory.............................................148
5.3 Kinetics of the bond-based peridynamic theory..................................................149
5.4 Restrictions on the pairwise force function, /.....................................................151
5.5 Isotropic ordinary bond-based peridynamic model.............................................154
5.6 Elastic bond-based peridynamic models.............................................................155
5.7 Relationship between peridynamic traction and stress........................................161
5.8 Microelasticity under homogeneous deformation...............................................162
5.9 Classical elastic moduli.......................................................................................165
5.10 Boundary conditions..........................................................................................166
5.11 Fracture.............................................................................................................167
5.12 Generality of the bond-based peridynamic model.............................................168
5.13 Bond-based micropolar peridynamic model......................................................169
5.14 Summary...........................................................................................................170
5.15 Exercises...........................................................................................................171
Chapter 6........................................................................................................................174
Particle Lattice Model for Solids...................................................................................174
6.1 Real numbers and continuous functions..............................................................175
6.2 Foundations of solid modeling............................................................................176
6.3 Solid modeling in Euclidean space......................................................................183
6.4 Solid bodies modeled as particle lattices.............................................................185
6.5 Lattice topology...................................................................................................190
6.6 Computational lattice model for a structure........................................................193
6.7 Modeling issues...................................................................................................196
6.8 Summary.............................................................................................................197
Contents xiii
6.9 Exercises.............................................................................................................198
Chapter 7........................................................................................................................202
Elastic Bond-Based Peridynamic Lattice Model............................................................202
7.1 Linear elastic bond-based lattice models.............................................................203
7.2 Linear elastic regular lattice model.....................................................................205
7.2.1 One-dimensional strand............................................................................205
7.2.2 Two-dimensional planar lattice................................................................207
7.2.3 3D face centered cubic lattice..................................................................211
7.3 Linear elastic micropolar lattice model...............................................................213
7.4 Conclusions regarding bond-based lattice models...............................................220
7.5 Exercises.............................................................................................................222
Chapter 8........................................................................................................................225
State-Based Peridynamic Lattice Model (SPLM)..........................................................225
8.1 Generalizing Navier s theory..............................................................................226
8.2 Reasons for state-based peridynamic theory.......................................................229
8.3 Bond-based peridynamic states...........................................................................231
8.4 Vector states and tensors.....................................................................................235
8.5 State fields...........................................................................................................240
8.6 State based peridynamic theory...........................................................................240
8.7 Deformation state and state-based constitutive models.......................................241
8.8 Adaptation of classical material models..............................................................245
8.9 Summary.............................................................................................................246
8.10 Exercises...........................................................................................................247
Chapter 9........................................................................................................................250
Elastic SPLM.................................................................................................................250
9.1 SPLM stretch and SPLM force............................................................................253
9.2 Relationship between SPLM stretch and strain...................................................256
9.3 Relationship between SPLM force and stress......................................................259
9.4 Linear elastic constitutive relation.......................................................................262
9.5 Boundary particles...............................................................................................266
9.6 Uniaxial case.......................................................................................................267
9.7 Plane stress case..................................................................................................269
9.8 Plane strain case..................................................................................................272
9.9 Summary.............................................................................................................272
9.10 Exercises...........................................................................................................274
Chapter 10......................................................................................................................277
Plasticity........................................................................................................................277
10.1 History of theory of plasticity............................................................................278
10.2 Continuum plasticity.........................................................................................279
10.2.1 Yield condition.......................................................................................284
10.2.2 Plastic flow mle.....................................................................................286
xiv Contents
10.2.3 Evolution of the yield surface................................................................288
10.3 Adaptation of classical material models to continuum state-based peridynamic
model...................................................................................................................289
10.4 SPLM mobile plasticity models........................................................................291
10.4.1 First force state plasticity model............................................................293
10.4.2 Second force state plasticity model........................................................295
10.5 Summary...........................................................................................................296
10.6 Exercises...........................................................................................................298
Chapter 11......................................................................................................................300
Damage..........................................................................................................................300
11.1 History of damage mechanics...........................................................................302
11.2 Continuum damage mechanics theory...............................................................304
11.3 Damage localization..........................................................................................306
11.4 Damage model for micropolar peridynamic lattice...........................................311
11.5 Isotropic SPLM damage mechanics..................................................................317
11.6 Relationship to fracture mechanics....................................................................322
11.7 Damage due to excessive plastic deformation...................................................323
11.8 Summary...........................................................................................................323
11.9 Exercises...........................................................................................................324
Chapter 12......................................................................................................................327
Particle Dynamics..........................................................................................................327
12.1 Basic algorithm for explicit particle dynamics..................................................328
12.2 Critical time step for a single degree of freedom system...................................329
12.3 Critical time step in terms of speed of sound.....................................................334
12.4 Damping............................................................................................................337
12.4.1 Internal damping....................................................................................337
12.4.2 External damping...................................................................................339
12.4.3 Artificial damping for dynamic relaxation.............................................339
12.5 Summary...........................................................................................................340
12.6 Exercises...........................................................................................................341
Chapter 13......................................................................................................................343
Computational Implementation......................................................................................343
13.1 Domain decomposition algorithm.....................................................................345
13.2 Design and implementation of pdQ...................................................................350
13.3 Interprocessor communication..........................................................................351
13.4 Neighbor lists....................................................................................................354
13.5 Shuffle: moving particles from cell to cell........................................................356
13.6 Domain boundary conditions............................................................................358
13.7 Pre- and post-processing....................................................................................359
13.8 Computational performance..............................................................................360
13.9 Summary...........................................................................................................361
Contents xv
13.10 Exercises.........................................................................................................362
Chapter 14......................................................................................................................364
Simulation of Reinforced Concrete................................................................................364
14.1 SPLM model for reinforced concrete structures................................................365
14.1.1 Plain concrete.........................................................................................366
14.1.2 Reinforcing bars.....................................................................................368
14.1.3 Bond between concrete and reinforcement............................................368
14.1.4 Interaction between concrete and loading plates....................................369
14.2 Particle-level study of SPLM............................................................................370
14.2.1 One-dimensional lattice..........................................................................370
14.2.2 Two-dimensional lattice.........................................................................373
14.2.3 Three-dimensional lattice.......................................................................376
14.3 Standard concrete cylinder under axial loading.................................................377
14.3.1 One-dimensional lattice..........................................................................378
14.3.2 Two-dimensional lattice.........................................................................381
14.3.3 Three-dimensional lattice.......................................................................382
14.3.4 Brazilian split cylinder...........................................................................384
14.4 Simulation of reinforced concrete beams..........................................................386
14.5 Discussion.........................................................................................................393
14.6 Exercises...........................................................................................................395
Bibliography..................................................................................................................397
Index..............................................................................................................................405
|
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| language | English |
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| spelling | Gerstle, Walter Herbert 1956- Verfasser (DE-588)1081961007 aut Introduction to practical peridynamics computational solid mechanics without stress and strain Walter Herbert Gerstle New Jersey [u.a.] World Scientific 2016 XV, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frontier research in computation and mechanics of materials and biology 1 Literaturverz. S. 397 - 404 Mathematik Mathematisches Modell Mechanics, Applied Mathematics Materials Mathematical models Solids Mathematical models Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Computerphysik (DE-588)4273564-6 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Computerphysik (DE-588)4273564-6 s DE-604 Frontier research in computation and mechanics of materials and biology 1 (DE-604)BV044235336 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028142007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gerstle, Walter Herbert 1956- Introduction to practical peridynamics computational solid mechanics without stress and strain Frontier research in computation and mechanics of materials and biology Mathematik Mathematisches Modell Mechanics, Applied Mathematics Materials Mathematical models Solids Mathematical models Festkörpermechanik (DE-588)4129367-8 gnd Computerphysik (DE-588)4273564-6 gnd |
| subject_GND | (DE-588)4129367-8 (DE-588)4273564-6 |
| title | Introduction to practical peridynamics computational solid mechanics without stress and strain |
| title_auth | Introduction to practical peridynamics computational solid mechanics without stress and strain |
| title_exact_search | Introduction to practical peridynamics computational solid mechanics without stress and strain |
| title_full | Introduction to practical peridynamics computational solid mechanics without stress and strain Walter Herbert Gerstle |
| title_fullStr | Introduction to practical peridynamics computational solid mechanics without stress and strain Walter Herbert Gerstle |
| title_full_unstemmed | Introduction to practical peridynamics computational solid mechanics without stress and strain Walter Herbert Gerstle |
| title_short | Introduction to practical peridynamics |
| title_sort | introduction to practical peridynamics computational solid mechanics without stress and strain |
| title_sub | computational solid mechanics without stress and strain |
| topic | Mathematik Mathematisches Modell Mechanics, Applied Mathematics Materials Mathematical models Solids Mathematical models Festkörpermechanik (DE-588)4129367-8 gnd Computerphysik (DE-588)4273564-6 gnd |
| topic_facet | Mathematik Mathematisches Modell Mechanics, Applied Mathematics Materials Mathematical models Solids Mathematical models Festkörpermechanik Computerphysik |
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