Computational contact mechanics: with 12 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 518 S. Ill., graph. Darst. |
| ISBN: | 9783540326083 3540326081 |
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| 245 | 1 | 0 | |a Computational contact mechanics |b with 12 tables |c Peter Wriggers |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
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Record in the Search Index
| _version_ | 1804140629748350976 |
|---|---|
| adam_text | Titel: Computational contact mechanics
Autor: Wriggers, Peter
Jahr: 2006
Contents
1 Introduction 1
2 Introduction to Contact Mechanics 11
2.1 Contact in a Mass Spring System 11
2.1.1 General formulation 11
2.1.2 Lagrange multiplier method 15
2.1.3 Penalty method 17
2.2 Finite Element Analysis of the Contact of Two Bars 18
2.3 Thermo-mechanical Contact 21
2.4 Impact 25
3 Continuum Solid Mechanics and Weak Forms 31
3.1 Kinematics 31
3.1.1 Motion and deformation gradient 31
3.1.2 Strain measures 34
3.1.3 Transformation of vectors and tensors 36
3.1.4 Time derivatives 36
3.2 Balance Laws 38
3.2.1 Balance of mass 38
3.2.2 Local balance of momentum and moments of momentum 38
3.2.3 First law of thermodynamics 39
3.2.4 Transformation to the initial configuration, different
stress tensors 39
3.3 Weak Form of Balance of Momentum, Variational Principles .. 41
3.3.1 Weak form of balance of momentum in the initial
configuration 41
3.3.2 Spatial form of the weak formulation 42
3.3.3 Minimum of total potential energy 43
3.4 Constitutive Equations 44
3.4.1 Hyperelastic response function 44
3.4.2 Incremental constitutive tensor 46
VIII Contents
3.5 Linearizations
3.5.1 Linearization of kinematical quantities
3.5.2 Linearization of constitutive equations
3.5.3 Linearization of the weak form
3.5.4 Linearization of a deformation dependent load . . .
4 Contact Kinematics
4.1 Normal Contact of Three-dimensional Bodies
4.2 Tangential Contact of Three-dimensional Bodies
4.2.1 Stick condition
4.2.2 Slip condition
4.3 Variation of the Normal and Tangential Gap
4.3.1 Variation of normal gap
4.3.2 Variation of tangential gap
5 Constitutive Equations for Contact Interfaces
5.1 Normal Contact
5.1.1 Constraint formulation
5.1.2 Constitutive equations for normal contact
5.2 Tangential Contact
5.2.1 Stick as a constraint
5.2.2 Coulomb law
5.2.3 Regularization of the Coulomb law
5.2.4 Elasto-plastic analogy for friction
5.2.5 Friction laws for metal forming
5.2.6 Friction laws for rubber and polymers
5.2.7 EViction laws for concrete structures on soil
5.2.8 Friction laws from computational homogenization
procedures
5.3 Lubrication
5.4 Adhesion
5.5 Decohesion
5.6 Wear
5.7 Fractal Contact Interfaces
6 Contact Boundary Value Problem and Weak Form .. .
6.1 Frictionless Contact in Linear Elasticity
6.2 Frictionless Contact in Finite Deformations Problems .. .
6.3 Treatment of Contact Constraints
6.3.1 Lagrange multiplier method
6.3.2 Penalty method
6.3.3 Direct constraint elimination
6.3.4 Constitutive equation in the interface
6.3.5 Nitsche method
6.3.6 Perturbed Lagrange formulation
40
51
52
53
55
57
58
62
62
63
66
G6
67
69
G9
70
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77
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88
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98
100
102
103
106
109
109
113
115
117
118
120
121
122
124
Contents IX
6.3.7 Barrier method 124
6.3.8 Augmented Lagrange methods 126
6.3.9 Cross-constraint method 128
6.4 Comparison of Different Methods 131
6.4.1 Normal Contact 131
6.4.2 Frictional Contact 136
6.5 Linearization of the Contact Contributions 140
6.5.1 Normal contact 141
6.5.2 Tangential contact 144
6.5.3 Special case of stick 147
6.6 Rolling Contact 147
6.6.1 Special reference frames for rolling contact 148
6.6.2 Strain measures 150
6.6.3 Weak Form 151
6.6.4 Constitutive equation 152
6.6.5 Contact kinematics 153
7 Discretization of the Continuum 157
7.1 Isoparametric Concept 158
7.1.1 Isoparametric interpolation functions 161
7.1.2 One-dimensional shape functions 161
7.1.3 Two-dimensional shape functions 163
7.1.4 Three-dimensional shape functions 165
7.2 Discretization of the Weak Forms 167
7.2.1 FE formulation of the weak form with regard to the
initial configuration 168
7.2.2 Linearization of the weak form in the initial configuration 172
7.2.3 FE formulation of the weak form in the current
configuration 178
7.2.4 Linearization of the weak form in the current
configuration 180
8 Discretization, Small Deformation Contact 183
8.1 General Approach for Contact Discretization 184
8.1.1 Lagrange multiplier method 184
8.1.2 Penalty method 187
8.2 Node-to-Node Contact Element 188
8.2.1 Frictionless contact 188
8.2.2 Contact with friction 192
8.3 Isoparametric Discretization of the Contact Contribution 194
8.3.1 Examples for isoparametric contact elements 199
8.4 Discretization for Non-matching Meshes 205
8.4.1 Discretization with contact segments 206
8.4.2 Mortar method 211
8.4.3 Nitsche method 217
X Contents
9 Discretization, Large Deformation Contact 225
9.1 Two-dimensional Node-to-Segment Contact Discretization ... .22
9.2 Alternative Discretization for the Two-dimensional
NTS-Contact 235
9.3 Three-dimensional Contact Discretization 241
9.3.1 Node-to-surface contact element 242
9.4 Three-Node Master Segment for Frictionless Contact 246
9.4.1 Matrices for Node-To-Edge (NTE) elements 249
9.4.2 Matrices for Node-To-Node (NTV) elements 251
9.5 Mortar Discretization for Large Deformations 253
9.5.1 Introduction 253
9.5.2 Mortar discretization for finite deformations 254
9.5.3 Linear approximation for the frictionless case 256
9.5.4 Quadratic approximation for the frictionless case 262
9.5.5 Numerical examples for frictionless contact 265
9.5.6 Quadratic Approximation for the Frictional Case 270
9.5.7 Numerical examples for frictional contact 273
9.6 Smooth Contact Discretization 279
9.6.1 Hermite interpolation for frictionless contact 280
9.6.2 Bezier interpolation for frictionless contact 286
9.6.3 Bezier interpolation for frictional contact 291
9.6.4 Three-dimensional contact discretization 299
9.7 Numerical Examples 303
9.7.1 The sheet/plate rolling simulation 303
9.7.2 Simulation of a sliding and rolling wheel 305
10 Solution Algorithms 309
10.1 Contact Search 311
10.1.1 Spatial search, phase (I) 314
10.1.2 Contact detection, phase (II) 316
10.2 Solution Methods for Unconstrained Nonlinear Problems 321
10.2.1 Algorithms for time-independent problems 321
10.2.2 Algorithms for time-dependent problems 323
10.3 Global Solution Algorithms for Contact 328
10.3.1 Basic notation 329
10.3.2 Dual formulation
10.3.3 Penalty method 335
10.3.4 Lagrange multiplier method 336
10.3.5 Augmented Lagrange method, Uzawa algorithm 338
10.3.6 Partitioning method 349
10.3.7 SQP method 344
10.3.8 Active set method for quadratic program 346
10 3.9 Linear complementary problem 347
10.3.10Contact algorithm of Dirichlet-Neumann type 348
10.3.11Contact algorithm based on projected gradients 349
Contents XI
10.3.12Algorithm for dynamic contact 352
10.4 Global Algorithms for Friction 355
10.5 Local Integration of Constitutive Equations in the Contact
Area 359
10.5.1 Evolution of adhesion 360
10.5.2 Friction laws 360
11 Thermo-mechanical Contact 365
11.1 Equations for the Continuum 366
11.1.1 Kinematical relations, multiplicative split 366
11.1.2 Thermoelastic constitutive law 367
11.2 Constitutive Equations for Thermo-mechanical Contact 368
11.2.1 Heat conductance through spots 370
11.2.2 Heat conductance through gas 371
11.2.3 Heat conductance by radiation 373
11.3 Initial Value Problem for Thermo-mechanical Contact 374
11.4 Weak Forms in Thermo-mechanical Analysis 376
11.5 Algorithmic Treatment 377
11.6 Discretization Techniques 378
11.6.1 Node-to-node contact element 379
11.6.2 Node-to-segment contact element 382
11.7 Examples 384
11.7.1 Heat transfer at finite deformations 385
11.7.2 Frictional heating at finite deformations 386
12 Beam Contact 391
12.1 Kinematics 391
12.1.1 Normal contact ...392
12.1.2 Tangential contact 395
12.2 Variation of the Gap in Normal and Tangential Directions 396
12.3 Contact Contribution to Weak Form 399
12.4 Finite Element Formulation 400
12.5 Contact Search for Beams 402
12.6 Examples 404
12.6.1 Three beams in frictionless contact 404
12.6.2 Two beams in contact with friction 406
13 Computation of Critical Points with Contact Constraints .. 411
13.1 Inequality Constraints for Contact 412
13.2 Calculation of Stability Points 413
13.3 Extended System with Contact Constraints 414
13.4 Examples 415
13.4.1 Block pressing on arch 416
13.4.2 Two arches 419
XII
Contents
14 Adaptive Finite Element Methods for Contact Problems 423
14.1 Contact problem and discretization 425
14.2 Residual Based Error Estimator for Frictionless Contact 42G
14.3 Error Indicator for Contact Based on Projection 430
14.4 Error Estimators based on Dual Principles 434
14.4.1 Displacement error control 434
14.4.2 Stress error control 430
14.5 Adaptive Mesh Refinement Strategy 437
14.6 Numerical Examples 441
14.G.1 Hertzian contact problem 441
14.6.2 Crossing tubes 443
14.6.3 Fractal interface 444
14.7 Error Indicator for Frictional Problems 448
14.7.1 Adaptive strategies 450
14.7.2 Transfer of history variables 452
14.7.3 Numerical examples 455
14.8 Adaptive methods for thermo-mechanical contact 461
14.8.1 Staggered solution scheme with independent spatial
grids 461
14.8.2 Error measures for the coupled problem 461
14.8.3 Adaptive method for the coupled problem 466
14.8.4 Example 467
A Gauss integration rules 473
A.l One-dimensional Integration 473
A.2 Two-dimensional Integration 474
B Convective Coordinates 477
C Parameter Identification for Friction Materials 483
References
Index c10
|
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| author | Wriggers, Peter 1951- |
| author_GND | (DE-588)135541875 |
| author_facet | Wriggers, Peter 1951- |
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| discipline | Maschinenbau / Maschinenwesen Physik Maschinenbau |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV024612451 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:01Z |
| institution | BVB |
| isbn | 9783540326083 3540326081 |
| language | English |
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| spelling | Wriggers, Peter 1951- Verfasser (DE-588)135541875 aut Computational contact mechanics with 12 tables Peter Wriggers 2. ed. Berlin [u.a.] Springer 2006 XII, 518 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kontakt Reibung (DE-588)4293741-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Kontakt Reibung (DE-588)4293741-3 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Kontaktmechanik (DE-588)4798356-5 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2768735&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018585056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wriggers, Peter 1951- Computational contact mechanics with 12 tables Kontakt Reibung (DE-588)4293741-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| subject_GND | (DE-588)4293741-3 (DE-588)4128130-5 (DE-588)4017233-8 (DE-588)4129367-8 (DE-588)4798356-5 |
| title | Computational contact mechanics with 12 tables |
| title_auth | Computational contact mechanics with 12 tables |
| title_exact_search | Computational contact mechanics with 12 tables |
| title_full | Computational contact mechanics with 12 tables Peter Wriggers |
| title_fullStr | Computational contact mechanics with 12 tables Peter Wriggers |
| title_full_unstemmed | Computational contact mechanics with 12 tables Peter Wriggers |
| title_short | Computational contact mechanics |
| title_sort | computational contact mechanics with 12 tables |
| title_sub | with 12 tables |
| topic | Kontakt Reibung (DE-588)4293741-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Kontaktmechanik (DE-588)4798356-5 gnd |
| topic_facet | Kontakt Reibung Numerisches Verfahren Finite-Elemente-Methode Festkörpermechanik Kontaktmechanik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2768735&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018585056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wriggerspeter computationalcontactmechanicswith12tables |