Quasistatic contact problems in viscoelasticity and viscoplasticity:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathemat. Soc. [u.a.]
2002
|
| Series: | AMS, IP studies in advanced mathematics
30 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 442 S. graph. Darst. |
| ISBN: | 0821831925 |
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Record in the Search Index
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| adam_text | Titel: Quasistatic contact problems in viscoelasticity and viscoplasticity
Autor: Han, Weimin
Jahr: 2002
Contents
Preface xi
List of Symbols xv
I Nonlinear Variational Problems and Numerical Ap-
proximation 1
1 Preliminaries of Functional Analysis 3
1.1 Normed Spaces and Banach Spaces................. 3
1.2 Linear Operators and Linear Functional.............. 8
1.3 Hubert Spaces ............................ 13
1.4 Convex Functions........................... 17
1.5 Banach Fixed-point Theorem.................... 21
2 Function Spaces and Their Properties 25
2.1 The Spaces Cm(fi) and Lp(fi).................... 25
2.2 Sobolev Spaces............................ 29
2.3 Spaces of Vector-valued Functions ................. 37
3 Introduction to Finite Difference and Finite Element Approxi-
mations 43
3.1 Finite Difference Approximations.................. 43
3.2 Basis of the Finite Element Approximation............ 45
3.3 Finite Element Interpolation Error
Estimates............................... 53
3.4 Finite Element Analysis of Linear Elliptic Boundary Value Prob-
lems .................................. 54
4 Variational Inequalities 59
4.1 Elliptic Variational Inequalities................... 59
4.2 Approximation of Elliptic Variational
Inequalities.............................. 65
4.3 An Evolutionary Variational Inequality............... 68
4.4 Semi-discrete Approximations of the Evolutionary Variational In-
equality ................................ 76
4.5 Fully Discrete Approximations of the Evolutionary Variational
Inequality............................... 78
Bibliographical Notes 89
vii
viii CONTENTS
II Mathematical Modelling in Contact Mechanics 91
5 Preliminaries of Contact Mechanics of Continua 93
5.1 Kinematics of Continua....................... 93
5.2 Dynamics of Continua........................ 98
5.3 Physical Setting of Contact Problems ............... 102
5.4 Contact Boundary Conditions and Friction Laws......... 104
6 Constitutive Relations in Solid Mechanics 113
6.1 Physical Background and Experiments...............113
6.2 Constitutive Relations in Elasticity.................121
6.3 Constitutive Relations in Viscoelasticity..............125
6.4 Constitutive Relations in Viscoplasticity..............133
7 Background on Variational and Numerical Analysis in Contact
Mechanics 141
7.1 Function Spaces in Solid Mechanics.................141
7.2 Semi-discrete and Fully Discrete Approximations.........152
7.3 Convergence under Basic Solution Regularity...........156
7.4 Some Inequalities...........................162
8 Contact Problems in Elasticity 167
8.1 Frictionless Contact Problems....................167
8.2 Numerical Analysis of the Frictionless Contact Problems.....173
8.3 Quasistatic Frictional Contact Problems..............177
8.4 Numerical Analysis of Quasistatic Frictional Contact Problems . 181
8.5 Numerical Examples.........................184
Bibliographical Notes 189
III Contact Problems in Viscoelasticity 191
9 A Frictionless Contact Problem 193
9.1 Problem Statement..........................193
9.2 An Existence and Uniqueness Result................195
9.3 Numerical Approximations .....................197
9.4 Dual Formulation...........................202
10 Bilateral Contact with Slip Dependent Friction 207
10.1 Problem Statement..........................207
10.2 An Existence and Uniqueness Result................209
10.3 Semi-discrete Approximation....................214
10.4 Fully Discrete Approximations ...................218
10.5 Dual Formulation...........................222
CONTENTS ix
11 Prictional Contact with Normal Compliance 227
11.1 Problem Statement..........................227
11.2 An Abstract Problem and its
Well-posedness............................ 230
11.3 Semi-discrete Approximation.................... 234
11.4 Fully Discrete Approximation.................... 237
11.5 Applications to the Contact Problem................ 239
11.6 Continuous Dependence with Respect to Contact Conditions . . 243
11.7 Numerical Examples......................... 246
12 Frictional Contact with Normal Damped Response 255
12.1 Problem Statement.......................... 255
12.2 An Abstract Problem and its
Well-posedness............................ 257
12.3 Semi-discrete Approximation of the
Abstract Problem........................... 262
12.4 Fully Discrete Approximation of the Abstract Problem...... 264
12.5 Applications to the Contact Problem................ 267
12.6 Two Field Variational Formulations ................ 271
12.7 Numerical Examples......................... 273
13 Other Viscoelastic Contact Problems 285
13.1 Bilateral Contact with Nonlocal Coulomb Friction Law......285
13.2 Bilateral Contact with Friction and Wear.............289
13.3 Contact with Normal Compliance, Friction and Wear.......292
13.4 Contact with Dissipative Frictional Potential...........296
Bibliographical Notes 305
IV Contact Problems in Viscoplasticity 307
14 A Signorini Contact Problem 309
14.1 Problem Statement..........................309
14.2 Existence and Uniqueness Results..................311
14.3 Some Properties of the Solution...................316
15 Frictionless Contact with Dissipative Potential 321
15.1 Problem Statement and Variational Analysis ........... 321
15.2 Semi-discrete Approximation.................... 324
15.3 Fully Discrete Approximation.................... 327
15.4 The Signorini Contact Problem................... 330
15.5 A Frictionless Contact Problem with Normal Compliance .... 333
15.6 A Convergence Result........................ 335
15.7 Numerical Examples......................... 340
x CONTENTS
16 Frictionless Contact between Two Viscoplastic Bodies 347
16.1 Problem Statement..........................347
16.2 Unique Solvability and Properties of the Solution.........350
16.3 Semi-discrete Approximation....................352
16.4 Fully Discrete Approximation....................357
16.5 Numerical Examples.........................360
17 Bilateral Contact with Tresca s Friction Law 365
17.1 Problem Statement.......................... 365
17.2 Existence and Uniqueness Results.................. 368
17.3 Some Properties of the Solution................... 376
17.4 Semi-discrete Approximation.................... 379
17.5 Fully Discrete Approximation.................... 384
17.6 Convergence of the Fully Discrete Scheme............. 390
18 Other Viscoplastic Contact Problems 397
18.1 Contact with Simplified Coulomb s Friction Law.........397
18.2 Contact with Dissipative Frictional Potential...........399
18.3 Stress Formulation in Perfect Plasticity ..............404
18.4 A Frictionless Contact Problem for Materials with Internal State
Variable................................414
Bibliographical Notes J^21
Bibliography 423
Index 439
|
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| discipline | Physik Mathematik |
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| institution | BVB |
| isbn | 0821831925 |
| language | English |
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| spelling | Han, Weimin 1963- Verfasser (DE-588)121177971 aut Quasistatic contact problems in viscoelasticity and viscoplasticity Weimin Han and Mircea Sofonea Providence, RI American Mathemat. Soc. [u.a.] 2002 XVII, 442 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier AMS, IP studies in advanced mathematics 30 Mathematisches Modell Contact mechanics Mathematical models Viscoelasticity Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd rswk-swf Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Kontakt Reibung (DE-588)4293741-3 gnd rswk-swf Kontakt Reibung (DE-588)4293741-3 s Viskoelastizität (DE-588)4063621-5 s Viskoplastizität (DE-588)4136051-5 s DE-604 Sofonea, Mircea 1957- Sonstige (DE-588)1028214723 oth AMS, IP studies in advanced mathematics 30 (DE-604)BV011103148 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009909540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Han, Weimin 1963- Quasistatic contact problems in viscoelasticity and viscoplasticity AMS, IP studies in advanced mathematics Mathematisches Modell Contact mechanics Mathematical models Viscoelasticity Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd Viskoelastizität (DE-588)4063621-5 gnd Kontakt Reibung (DE-588)4293741-3 gnd |
| subject_GND | (DE-588)4136051-5 (DE-588)4063621-5 (DE-588)4293741-3 |
| title | Quasistatic contact problems in viscoelasticity and viscoplasticity |
| title_auth | Quasistatic contact problems in viscoelasticity and viscoplasticity |
| title_exact_search | Quasistatic contact problems in viscoelasticity and viscoplasticity |
| title_full | Quasistatic contact problems in viscoelasticity and viscoplasticity Weimin Han and Mircea Sofonea |
| title_fullStr | Quasistatic contact problems in viscoelasticity and viscoplasticity Weimin Han and Mircea Sofonea |
| title_full_unstemmed | Quasistatic contact problems in viscoelasticity and viscoplasticity Weimin Han and Mircea Sofonea |
| title_short | Quasistatic contact problems in viscoelasticity and viscoplasticity |
| title_sort | quasistatic contact problems in viscoelasticity and viscoplasticity |
| topic | Mathematisches Modell Contact mechanics Mathematical models Viscoelasticity Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd Viskoelastizität (DE-588)4063621-5 gnd Kontakt Reibung (DE-588)4293741-3 gnd |
| topic_facet | Mathematisches Modell Contact mechanics Mathematical models Viscoelasticity Viscoplasticity Viskoplastizität Viskoelastizität Kontakt Reibung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009909540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011103148 |
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