Computational contact and impact mechanics: fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 454 S. graph. Darst. |
| ISBN: | 3540429069 |
Staff View
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| 245 | 1 | 0 | |a Computational contact and impact mechanics |b fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables |c Tod A. Laursen |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 2002 | |
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE VII
1 INTRODUCTION 1
1.1 SCOPE OF THIS MONOGRAPH 2
1.2 USEFUL BACKGROUND FOR THIS PRESENTATION 3
1.3 OVERVIEW 4
2 FINITE ELEMENT FORMULATIONS IN NONLINEAR SOLID MECHANICS 7
2.1 INITIAL/BOUNDARY VALUE PROBLEMS IN THE KINEMATICALLY LIN-
EAR REGIME 8
2.1.1 STRONG FORM OF THE EBVP 9
2.1.2 WEAK FORM OF THE IBVP 15
2.2 THE IBVP IN THE FINITE STRAIN CASE 17
2.2.1 NOTATION AND PROBLEM FORMULATION 17
2.2.2 FINITE STRAIN KINEMATICS 18
2.2.3 STRESS DEFINITIONS APPROPRIATE FOR LARGE DEFORMATIONS 24
2.2.4 FRAME INDIFFERENCE 27
2.2.5 THE STRONG FORM IN FINITE STRAINS 31
2.2.6 THE WEAK FORM IN FINITE STRAINS 39
2.3 FINITE ELEMENT DISCRETIZATION 41
2.3.1 DISCRETIZED WEAK FORM; GENERATION OF DISCRETE NON-
LINEAR EQUATIONS 43
2.3.2 DISCRETE NONLINEAR EQUATIONS FOR THE KINEMATICALLY
LINEAR CASE 46
XII CONTENTS
2.4 SOLUTION STRATEGIES FOR SPATIALLY DISCRETE SYSTEMS 48
2.4.1 QUASISTATICS AND INCREMENTAL LOAD METHODS 48
2.4.2 DYNAMICS AND GLOBAL TIME STEPPING PROCEDURES . . 50
2.4.3 LOCAL (CONSTITUTIVE) TIME STEPPING PROCEDURES ... 54
2.4.4 NONLINEAR EQUATION SOLVING 56
2.4.5 CONSISTENT ALGORITHMIC LINEARIZATION OF MATERIAL RE-
SPONSE 61
3 THE KINEMATICALLY LINEAR CONTACT PROBLEM 69
3.1 STRONG FORMS IN LINEARIZED FRICTIONLESS CONTACT 70
3.1.1 THE SIGNORINI PROBLEM: CONTACT WITH A RIGID OBSTACLE 70
3.1.2 THE TWO BODY CONTACT PROBLEM 75
3.2 WEAK STATEMENTS OF THE CONTACT PROBLEM 79
3.2.1 VARIATIONAL INEQUALITIES 81
3.2.2 THE QUASISTATIC ELASTIC CASE: CONTACT AS A PROBLEM
OF CONSTRAINED OPTIMIZATION 83
3.3 METHODS OF CONSTRAINT ENFORCEMENT 85
3.3.1 CLASSICAL LAGRANGE MULTIPLIER METHODS 85
3.3.2 PENALTY METHODS 89,
3.3.3 AUGMENTED LAGRANGIAN METHODS 91
3.4 INCLUSION OF FRICTION INTO THE PROBLEM DESCRIPTION 94
3.4.1 FRICTION KINEMATICS AND TRACTION MEASURES 94
3.4.2 UNREGULARIZED COULOMB FRICTION LAWS 96
3.4.3 REGULARIZATION OF FRICTION 98
3.4.4 VARIATIONAL STATEMENTS INCLUDING FRICTION 101
3.4.5 NONLOCAL FRICTIONAL DESCRIPTIONS 106
4 CONTINUUM MECHANICS OF LARGE DEFORMATION CONTACT 109
4.1 TWO BODY CONTACT PROBLEM DEFINITION 110
4.1.1 LOCAL MOMENTUM BALANCES ILL
4.1.2 INITIAL AND BOUNDARY CONDITIONS 112
4.2 CONTACT CONSTRAINTS IN LARGE DEFORMATIONS 113
4.2.1 THE GAP FUNCTION AS DEFINED BY CLOSEST POINT PRO-
JECTION 113
4.2.2 FRICTIONAL KINEMATICS ON INTERFACES 116
4.2.3 FRAME INDIFFERENCE OF CONTACT RATE VARIABLES .... 121
4.2.4 COULOMB FRICTION IN LARGE SLIDING 129
4.3 SUMMARY: STRONG FORM OF THE LARGE DEFORMATION CONTACT
PROBLEM 134
4.4 VIRTUAL WORK EXPRESSIONS INCORPORATING CONTACT 137
4.4.1 CONTACT VIRTUAL WORK: THE CONTACT INTEGRAL .... 139
4.4.2 LINEARIZATION OF CONTACT VIRTUAL WORK 141
4.4.3 SUMMARY: WEAK FORM OF THE LARGE DEFORMATION CON-
TACT PROBLEM 144
CONTENTS XIII
FINITE ELEMENT IMPLEMENTATION OF CONTACT INTERACTION 145
5.1 FINITE DIMENSIONAL REPRESENTATION OF CONTACT INTERACTION . 147
5.1.1 CONTACT SURFACE DISCRETIZATION 147
5.1.2 NUMERICAL INTEGRATION OF THE CONTACT INTEGRAL .... 148
5.1.3 CONTACT DETECTION (SEARCHING) 152
5.2 TIME DISCRETIZATION 158
5.2.1 GLOBAL TIME INTEGRATION SCHEMES 158
5.2.2 TEMPORALLY DISCRETE FRICTIONAL LAWS FOR THE PENALTY
REGULARIZED CASE 159
5.3 CONTACT STIFFNESS AND RESIDUAL: PENALTY REGULARIZED CASE . 162
5.3.1 THREE DIMENSIONAL MATRIX EXPRESSIONS 162
5.3.2 TWO DIMENSIONAL MATRIX EXPRESSIONS 166
5.4 AUGMENTED LAGRANGIAN CONSTRAINT ENFORCEMENT ALGORITHMS 169
5.4.1 UZAWA S METHOD (METHOD OF MULTIPLIERS) 170
5.4.2 ALGORITHMIC SYMMETRIZATION USING AUGMENTED LA-
GRANGIANS 174
5.4.3 AUGMENTED LAGRANGIAN DISCRETE FORCE AND STIFFNESS
EXPRESSIONS 178
5.5 NUMERICAL EXAMPLES 180
5.5.1 GENERAL DEMONSTRATIONS OF THE COMPUTATIONAL FRAME-
WORK 180
5.5.2 DEMONSTRATIONS OF AUGMENTED LAGRANGIAN ALGORITH-
MIC PERFORMANCE 196
TRIBOLOGICAL COMPLEXITY IN INTERFACE CONSTITUTIVE MODELS 211
6.1 RATE AND STATE DEPENDENT FRICTION 212
6.1.1 MOTIVATION 213
6.1.2 ONE DIMENSIONAL MODEL DEVELOPMENT 215
6.1.3 MODEL INCORPORATION INTO CONVECTIVE SLIP ADVECTED
FRAME 220
6.1.4 LOCAL TIME STEPPING ALGORITHM 222
6.1.5 CONTACT FORCE VECTOR AND STIFFNESS MATRIX 226
6.1.6 NUMERICAL EXAMPLES 227
6.2 THERMOMECHANICALLY COUPLED FRICTION ON INTERFACES .... 238
6.2.1 MOTIVATION 239
6.2.2 THERMALLY COUPLED PROBLEM DEFINITION 241
6.2.3 A THERMODYNAMICALLY CONSISTENT FRICTION MODEL . . 244
6.2.4 VARIATIONAL PRINCIPLE AND FINITE ELEMENT IMPLEMEN-
TATION 255
6.2.5 NUMERICAL EXAMPLES 269
6.3 THERMODYNAMICAL ALGORITHMIC CONSISTENCY 279
6.3.1 CONSTITUTIVE FRAMEWORK FOR BULK CONTINUA 280
6.3.2 THERMOMECHANICAL INTERFACE MODEL FRAMEWORK . . . 283
6.3.3 A PRIORI STABILITY ESTIMATES FOR DYNAMIC FRICTIONAL
CONTACT 286
XIV CONTENTS
6.3.4 A NEW PARTITIONED SCHEME FOR THERMOMECHANICAL
CONTACT 289
6.3.5 ALGORITHMIC TREATMENT OF CONTACT CONDITIONS AC-
CORDING TO THE ADIABATIC SPLIT 291
7 ENERGY-MOMENTUM APPROACHES TO IMPACT MECHANICS 295
7.1 ENERGY STABILITY OF TRADITIONAL SCHEMES 297
7.1.1 A MODEL SYSTEM 297
7.1.2 THE CONCEPT OF ENERGY STABILITY 299
7.1.3 INFLUENCE OF CONTACT CONSTRAINTS ON SYSTEM ENERGY. 300
7.2 ENERGY-MOMENTUM METHODS FOR ELASTODYNAMICS 304
7.2.1 CONSERVATION LAWS . 305
7.2.2 CONSERVATIVE DISCRETIZATION SCHEMES 309
7.3 ENERGY-MOMENTUM ALGORITHMIC TREATMENT OF PRICTIONLESS
IMPACT 312
7.3.1 DISCRETE CONTACT CONSTRAINTS 313
7.3.2 SPATIAL DISCRETIZATION AND IMPLEMENTATION 316
7.3.3 NUMERICAL EXAMPLES 318
7.4 INTRODUCTION OF FRICTIONAL AND BULK DISSIPATION: ENERGY CON-
SISTENCY 325
7.4.1 COULOMB FRICTION MODEL FORMULATION 325
7.4.2 LOCAL SPLIT OF THE COULOMB MODEL 331
7.4.3 ALGORITHMIC FORMULATION 332
7.4.4 ENERGY CONSISTENT TREATMENT OF BULK INELASTICITY . . 338
7.4.5 NUMERICAL EXAMPLES WITH FRICTION AND INELASTICITY . 339
7.5 EM ALGORITHMS INVOLVING A DISCONTINUOUS VELOCITY UPDATE 347
7.5.1 TEMPORALLY DISCONTINUOUS VELOCITY UPDATE 348
7.5.2 REEXAMINATION OF CONSERVATION CONDITIONS 350
7.5.3 CONTACT CONSTRAINTS 355
7.5.4 SUMMARY OF THE ALGORITHM 357
7.5.5 NUMERICAL EXAMPLES 357
8 EMERGING PARADIGMS FOR CONTACT SURFACE DISCRETIZATION 369
8.1 CONTACT SMOOTHING 371
8.1.1 AN ALTERNATIVE VARIATIONAL FRAMEWORK 372
8.1.2 SMOOTHING STRATEGIES IN TWO DIMENSIONS 374
8.1.3 SMOOTHING STRATEGIES IN THREE DIMENSIONS 382
8.1.4 NUMERICAL EXAMPLES 390
8.2 MORTAR-FINITE ELEMENT METHODS FOR CONTACT DESCRIPTION . . 404
8.2.1 TIED CONTACT AND THE ROLE OF MORTAR FORMULATIONS
IN CONVERGENCE 404
8.2.2 A MORTAR-FINITE ELEMENT FORMULATION OF FRICTIONAL
CONTACT 416
8.2.3 NUMERICAL EXAMPLES OF MORTAR TREATMENT OF FRIC-
TIONAL CONTACT 425
CONTENTS XV
REFERENCES 435
INDEX 451
|
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| indexdate | 2024-07-09T18:57:01Z |
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| spelling | Laursen, Tod A. Verfasser aut Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables Tod A. Laursen Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 XV, 454 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kontakt <Reibung> - Nichtlineare Mechanik - Finite-Elemente-Methode Stoß - Nichtlineare Mechanik - Finite-Elemente-Methode Finite element method Nonlinear theories Stoß (DE-588)4124258-0 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Kontakt Reibung (DE-588)4293741-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Kontakt Reibung (DE-588)4293741-3 s Nichtlineare Mechanik (DE-588)4042095-4 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Stoß (DE-588)4124258-0 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009632735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laursen, Tod A. Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables Kontakt <Reibung> - Nichtlineare Mechanik - Finite-Elemente-Methode Stoß - Nichtlineare Mechanik - Finite-Elemente-Methode Finite element method Nonlinear theories Stoß (DE-588)4124258-0 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Kontakt Reibung (DE-588)4293741-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4124258-0 (DE-588)4042095-4 (DE-588)4293741-3 (DE-588)4017233-8 |
| title | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables |
| title_auth | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables |
| title_exact_search | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables |
| title_full | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables Tod A. Laursen |
| title_fullStr | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables Tod A. Laursen |
| title_full_unstemmed | Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables Tod A. Laursen |
| title_short | Computational contact and impact mechanics |
| title_sort | computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis with 6 tables |
| title_sub | fundamentals of modeling interfacial phenomena in nonlinear finite element analysis ; with 6 tables |
| topic | Kontakt <Reibung> - Nichtlineare Mechanik - Finite-Elemente-Methode Stoß - Nichtlineare Mechanik - Finite-Elemente-Methode Finite element method Nonlinear theories Stoß (DE-588)4124258-0 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Kontakt Reibung (DE-588)4293741-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Kontakt <Reibung> - Nichtlineare Mechanik - Finite-Elemente-Methode Stoß - Nichtlineare Mechanik - Finite-Elemente-Methode Finite element method Nonlinear theories Stoß Nichtlineare Mechanik Kontakt Reibung Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009632735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laursentoda computationalcontactandimpactmechanicsfundamentalsofmodelinginterfacialphenomenainnonlinearfiniteelementanalysiswith6tables |