Viscoelastic structures: mechanics of growth and aging
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
San Diego [u.a.]
Acad. Press
1998
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XV, 596 S. graph. Darst. |
ISBN: | 0122222806 |
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adam_text | IMAGE 1
VISCOELASTIC STRUCTURES
MECHANICS OF GROWTH AND AGING
ALEKSEY D. DROZDOV INSTITUTE FOR INDUSTRIAL MATHEMATICS BEN-GURION
UNIVERSITY OF THE NEGEV BE ERSHEBA, ISRAEL
ACADEMIC PRESS SAN DIEGO LONDON BOSTON NEW YORK SYDNEY TOKYO TORONTO
IMAGE 2
KINEMATICS OF CONTINUA
1 . 1 BASIC DEFINITIONS AND FORMULAS 1.1.1 DESCRIPTION OF MOTION 1.1.2
TANGENT VECTORS 1.1.3 THE NABLA OPERATOR 1.1.4 DEFORMATION GRADIENT
1.1.5 DEFORMATION TENSORS AND STRAIN TENSORS 1.1.6 STRETCH TENSORS
1.1.7 RELATIVE DEFORMATION TENSORS 1.1.8 RIGID MOTION 1.1.9 GENERALIZED
STRAIN TENSORS 1.1.10 VOLUME DEFORMATION 1.1.11 DEFORMATION OF THE
SURFACE ELEMENT 1.1.12 OBJECTIVE TENSORS 1.1.13 VELOCITY VECTOR AND ITS
GRADIENT 1.1.14 COROTATIONAL DERIVATIVES 1.1.15 THE RIVLIN-ERICKSEN
TENSORS BIBLIOGRAPHY
CONSTITUTIVE MODELS IN LINEAR VISCOELASTICITY 2.1 DIFFERENTIAL
CONSTITUTIVE MODELS 2.1.1 DIFFERENTIAL CONSTITUTIVE MODELS 2.1.2
FRACTIONAL DIFFERENTIAL MODELS
2.2 INTEGRAL CONSTITUTIVE MODELS 2.2.1 BOLTZMANN S SUPERPOSITION
PRINCIPLE 2.2.2 CONNECTIONS BETWEEN CREEP AND RELAXATION MEASURES 2.2.3
A MODEL OF ADAPTIVE LINKS
2.2.4 SPECTRAL PRESENTATION OF THE FUNCTION X(T , *) 2.2.5
THREE-DIMENSIONAL LOADING 2.3 CREEP AND RELAXATION KERNELS 2.3.1 CREEP
AND RELAXATION KERNELS FOR NONAGING MEDIA
2.3.2 CREEP AND RELAXATION KERNELS FOR AGING MEDIA 2.3.3 PROPERTIES OF
CREEP AND RELAXATION MEASURES
1
1
1
3
5
6
7
10 11 12 13
14 15 16 18 20
22
23
25
25 26 28 34
35 39 41 44
48
54
54
59 66
IMAGE 3
X LL
CONTENTS
2.4 THERMODYNAMIC POTENTIALS AND VARIATIONAL PRINCIPLES IN LINEAR
VISCOELASTICITY 71
2.4.1 THERMODYNAMIC POTENTIALS OF AGING VISCOELASTIC MEDIA 72 2.4.2
VARIATIONAL PRINCIPLES IN VISCOELASTICITY 73
2.4.3 GIBBS PRINCIPLE AND THE SECOND LAW OF THERMODYNAMICS 77 2.4.4
THERMODYNAMIC INEQUALITIES IN LINEAR VISCOELASTICITY 19
2.5 A MODEL OF ADAPTIVE LINKS FOR AGING VISCOELASTIC MEDIA 80
2.5.1 A MODEL OF ADAPTIVE LINKS 81
2.5.2 VALIDATION OF THE MODEL 89
2.5.3 PREDICTION OF STRESS-STRAIN CURVES FOR TIME-VARYING LOADS 93
BIBLIOGRAPHY 97
NONLINEAR CONSTITUTIVE MODELS WITH SMALL STRAINS 107
3.1 NONLINEAR DIFFERENTIAL MODELS 107
3.2 NONLINEAR INTEGRAL MODELS 117
3.2.1 UNIAXIAL LOADING 117
3.2.2 THREE-DIMENSIONAL LOADING 126
3.3 A MODEL FOR CROSSLINKED POLYMERS 130
3.3.1 A MODEL OF ADAPTIVE LINKS 131
3.3.2 DETERMINATION OF ADJUSTABLE PARAMETERS 136
3.3.3 CONSTITUTIVE EQUATIONS FOR THREE-DIMENSIONAL LOADING 140 3.3.4
CORRESPONDENCE PRINCIPLES IN NONLINEAR VISCOELASTICITY 143 3.4 A MODEL
FOR NON-CROSSLINKED POLYMERS 145
3.4.1 A MODEL OF ADAPTIVE LINKS 146
3.4.2 A GENERALIZED MODEL OF ADAPTIVE LINKS 149
3.4.3 VALIDATION OF THE MODEL 153
BIBLIOGRAPHY 161
NONLINEAR CONSTITUTIVE MODELS WITH FINITE STRAINS 171
4.1 DIFFERENTIAL CONSTITUTIVE MODELS 171
4.1.1 THE RIVLIN-ERICKSEN MODEL 172
4.1.2 THE KELVIN-VOIGT MODEL 173
4.1.3 THE MAXWELL MODEL 174
4.1.4 THE STANDARD VISCOELASTIC SOLID 176
4.2 FRACTIONAL DIFFERENTIAL MODELS , 177
4.2.1 FRACTIONAL DIFFERENTIAL OPERATORS WITH FINITE STRAINS 178
4.2.2 FRACTIONAL DIFFERENTIAL MODELS 180
4.2.3 UNIAXIAL EXTENSION OF AN INCOMPRESSIBLE BAR 182
4.2.4 RADIAL DEFORMATION OF A SPHERICAL SHELL 188
4.2.5 UNIAXIAL EXTENSION OF A COMPRESSIBLE BAR 195
4.2.6 SIMPLE SHEAR OF A COMPRESSIBLE MEDIUM 198
4.3 INTEGRAL CONSTITUTIVE MODELS 203
4.3.1 LINEAR CONSTITUTIVE EQUATIONS 203
4.3.2 CONSTITUTIVE EQUATIONS IN THE FORM OF TAYLOR SERIES 205
IMAGE 4
CONTENTS
**
4.3.3 BKZ-TYPE CONSTITUTIVE EQUATIONS 206
4.3.4 SEMILINEAR CONSTITUTIVE EQUATIONS 210
4.4 A MODEL OF ADAPTIVE LINKS 212
4.4.1 A MODEL OF ADAPTIVE LINKS 212
4.4.2 THE LAGRANGE VARIATIONAL PRINCIPLE 213
4.4.3 THERMODYNAMIC STABILITY OF A VISCOELASTIC MEDIUM 219
4.4.4 CONSTITUTIVE EQUATIONS FOR INCOMPRESSIBLE MEDIA 221
4.4.5 EXTENSION OF A VISCOELASTIC BAR 223
4.5 A CONSTITUTIVE MODEL IN FINITE VISCOELASTICITY 226
4.5.1 A MODEL OF ADAPTIVE LINKS 227
4.5.2 UNIAXIAL EXTENSION OF A VISCOELASTIC BAR 231
4.5.3 BIAXIAL EXTENSION OF A VISCOELASTIC SHEET 236
4.5.4 TORSION OF A VISCOELASTIC CYLINDER 248
BIBLIOGRAPHY 255
CONSTITUTIVE RELATIONS FOR THERMOVISCOELASTIC MEDIA 262
5.1 CONSTITUTIVE MODELS IN THERMOVISCOELASTICITY 262
5.1.1 THERMORHEOLOGICALLY SIMPLE MEDIA 262
5.1.2 THE PROPORTIONALITY HYPOTHESIS 270
5.1.3 THE MCCRUM MODEL 272
5.2 A MODEL OF ADAPTIVE LINKS IN THERMOVISCOELASTICITY 275
5.2.1 GOVERNING EQUATIONS 275
5.2.2 A REFINED MODEL OF ADAPTIVE LINKS 284
5.3 CONSTITUTIVE MODELS FOR THE NONISOTHERMAL BEHAVIOR 294
5.3.1 CONSTITUTIVE EQUATIONS FOR ISOTHERMAL LOADING 297
5.3.2 CONSTITUTIVE EQUATIONS FOR NONISOTHERMAL LOADING 302
5.3.3 THREE-DIMENSIONAL LOADING 306
5.3.4 THE STANDARD THERMOVISCOELASTIC SOLID 307
5.3.5 COOLING OF A CYLINDRICAL PRESSURE VESSEL 313
BIBLIOGRAPHY 328
ACCRETION OF AGING VISCOELASTIC MEDIA WITH FINITE STRAINS 337
6.1 CONTINUOUS ACCRETION OF AGING VISCOELASTIC MEDIA 337
6.1.1 A MODEL FOR CONTINUOUS ACCRETION 338
6.1.2 CONTINUOUS ACCRETION OF A VISCOELASTIC CYLINDER 347
6.1.3 CONTINUOUS ACCRETION OF AN ELASTOPLASTIC BAR 353
6.2 WINDING OF A CYLINDRICAL PRESSURE VESSEL 371
6.2.1 THE LAME PROBLEM FOR AN ACCRETED CYLINDER . 375
6.3 WINDING OF A COMPOSITE CYLINDER WITH ACCOUNT FOR RESIN FLOW 393
6.3.1 KINEMATICS OF DEFORMATION 394
6.3.2 GOVERNING EQUATIONS 398
6.3.3 ACCRETION ON A RIGID MANDREL 404
6.3.4 ACCRETION WITH SMALL STRAINS 406
IMAGE 5
CONTENTS
6.4 VOLUMETRIE GROWTH OF A VISCOELASTIC TISSUE 413
6.4.1 A BRIEF HISTORICAL SURVEY 414
6.4.2 CONSTITUTIVE EQUATIONS 417
6.4.3 COMPRESSION OF A GROWING BAR 423
6.4.4 THE LAME PROBLEM FOR A GROWING CYLINDER 430
BIBLIOGRAPHY 436
ACCRETION OF VISCOELASTIC MEDIA WITH SMALL STRAINS 446
7.1 ACCRETION OF A VISCOELASTIC CONIC PIPE 446
7.1.1 FORMULATION OF THE PROBLEM 446
7.1.2 KINEMATICS OF ACCRETION 447
7.1.3 CONSTITUTIVE EQUATIONS 450
7.1.4 GOVERNING EQUATIONS (MODEL 1) 451
7.1.5 GOVERNING EQUATIONS (MODEL 2) 455
7.1.6 NUMERICAL ANALYSIS 458
7.2 ACCRETION OF A VISCOELASTIC SPHERICAL DOME 464
7.2.1 FORMULATION OF THE PROBLEM 465
7.2.2 GOVERNING EQUATIONS 467
7.2.3 DETERMINATION OF PRELOAD 472
7.2.4 DISPLACEMENTS IN AN ACCRETED DOME 474
7.2.5 NUMERICAL ANALYSIS 475
7.3 DEBONDING OF ACCRETED VISCOELASTIC BEAMS 480
7.3.1 ACCRETION OF A TWO-LAYERED BEAM 480
7.3.2 ACCRETION OF AN ELASTIC BEAM ON A NONLINEAR WINKLER FOUNDATION 489
7.4 TORSION OF AN ACCRETED ELASTOPLASTIC CYLINDER 499
7.4.1 FORMULATION OF THE PROBLEM 499
7.4.2 STRESSES AND STRAINS IN A GROWING CYLINDER 501
7.4.3 ACCRETION OF AN ELASTIC CYLINDER 502
7.4.4 AN ELASTOPLASTIC CYLINDER WITH ONE PLASTIC REGION 505
7.4.5 AN ELASTOPLASTIC CYLINDER WITH TWO PLASTIC REGIONS 509
BIBLIOGRAPHY 510
OPTIMIZATION PROBLEMS FOR GROWING VISCOELASTIC MEDIA 511
8.1 AN OPTIMAL RATE OF ACCRETION FOR VISCOELASTIC SOLIDS 511
8.1.1 TORSION OF AN ACCRETED VISCOELASTIC CYLINDER WITH SMALL STRAINS
512
8.1.2 EXTENSION OF AN ACCRETED ELASTIC BAR WITH FINITE STRAINS 523 8.2
OPTIMAL ACCRETION OF AN ELASTIC COLUMN 532
8.2.1 FORMULATION OF THE PROBLEM AND GOVERNING EQUATIONS 532 8.2.2
OPTIMAL REGIME OF LOADING 536
8.2.3 OPTIMAL REGIME OF ACCRETION 538
8.3 PRELOAD OPTIMIZATION FOR A WOUND CYLINDRICAL PRESSURE VESSEL 542
8.3.1 FORMULATION OF THE PROBLEM AND GOVERNING EQUATIONS 542
IMAGE 6
CONTENTS
8.3.2 WINDING OF A NONAGING CYLINDRICAL PRESSURE VESSEL 548
8.3.3 WINDING OF AN AGING CYLINDRICAL PRESSURE VESSEL 550
8.4 OPTIMAL DESIGN OF GROWING BEAMS 554
8.4.1 FORMULATION OF THE PROBLEM AND GOVERNING EQUATIONS 555 8.4.2
OPTIMAL THICKNESS OF A NONAGING ELASTIC BEAM 558
8.4.3 OPTIMAL THICKNESS OF AN AGING ELASTIC BEAM 562
8.5 OPTIMAL SOLIDIFICATION OF A SPHERICAL PRESSURE VESSEL 569
8.5.1 FORMULATION OF THE PROBLEM 570
8.5.2 TEMPERATURE DISTRIBUTION 572
8.5.3 STRESSES AND DISPLACEMENTS 573
8.5.4 STRESSES IN A PRESSURE VESSEL AFTER COOLING 579
8.5.5 NUMERICAL ANALYSIS 582
BIBLIOGRAPHY 589
INDEX 593
|
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author | Drozdov, Aleksey D. |
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ctrlnum | (OCoLC)37379849 (DE-599)BVBBV011991795 |
dewey-full | 620.11232 620.1/06 |
dewey-hundreds | 600 - Technology (Applied sciences) |
dewey-ones | 620 - Engineering and allied operations |
dewey-raw | 620.11232 620.1/06 |
dewey-search | 620.11232 620.1/06 |
dewey-sort | 3620.11232 |
dewey-tens | 620 - Engineering and allied operations |
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id | DE-604.BV011991795 |
illustrated | Illustrated |
indexdate | 2024-07-09T18:19:49Z |
institution | BVB |
isbn | 0122222806 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008115087 |
oclc_num | 37379849 |
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physical | XV, 596 S. graph. Darst. |
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spelling | Drozdov, Aleksey D. Verfasser aut Viscoelastic structures mechanics of growth and aging Aleksey D. Drozdov San Diego [u.a.] Acad. Press 1998 XV, 596 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Kunststoffbauteil (DE-588)4033681-5 gnd rswk-swf Viskoelastisches Medium (DE-588)4426217-6 gnd rswk-swf Viskoelastisches Medium (DE-588)4426217-6 s DE-604 Kunststoffbauteil (DE-588)4033681-5 s Viskoelastizität (DE-588)4063621-5 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008115087&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 | Drozdov, Aleksey D. Viscoelastic structures mechanics of growth and aging Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Viskoelastizität (DE-588)4063621-5 gnd Kunststoffbauteil (DE-588)4033681-5 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
subject_GND | (DE-588)4063621-5 (DE-588)4033681-5 (DE-588)4426217-6 |
title | Viscoelastic structures mechanics of growth and aging |
title_auth | Viscoelastic structures mechanics of growth and aging |
title_exact_search | Viscoelastic structures mechanics of growth and aging |
title_full | Viscoelastic structures mechanics of growth and aging Aleksey D. Drozdov |
title_fullStr | Viscoelastic structures mechanics of growth and aging Aleksey D. Drozdov |
title_full_unstemmed | Viscoelastic structures mechanics of growth and aging Aleksey D. Drozdov |
title_short | Viscoelastic structures |
title_sort | viscoelastic structures mechanics of growth and aging |
title_sub | mechanics of growth and aging |
topic | Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Viskoelastizität (DE-588)4063621-5 gnd Kunststoffbauteil (DE-588)4033681-5 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
topic_facet | Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Viskoelastizität Kunststoffbauteil Viskoelastisches Medium |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008115087&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT drozdovalekseyd viscoelasticstructuresmechanicsofgrowthandaging |