Mechanics of viscoelastic solids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 472 S. graph. Darst. |
| ISBN: | 0471975125 |
Internformat
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| 245 | 1 | 0 | |a Mechanics of viscoelastic solids |c Aleksey D. Drozdov |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1998 | |
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| adam_text | IMAGE 1
MECHANICS OF VISCOELASTIC
SOLIDS
ALEKSEY D. DROZDOV INSTITUTE FOR INDUSTRIAL MATHEMATICS, BEERSHEBA,
ISRAEL
JOHN WILEY & SONS CHICHESTER * NEW YORK * WEINHEIM * BRISBANE * TORONTO
* SINGAPORE
IMAGE 2
CONTENTS
PREFACE XI
1 CONSTITUTIVE MODELS IN LINEAR VISCOELASTICITY 1
1.1 THE BOLTZMANN SUPERPOSITION PRINCIPLE 2
1.2 THE SHORT-TERM RESPONSE IN PHYSICALLY AGED POLYMERS 8
1.2.1 A MODEL OF ADAPTIVE LINKS 9
1.2.2 A BALANCE EQUATION FOR THE NUMBER OF LINKS 10
1.2.3 COMPARISON WITH EXPERIMENTS 16
1.2.4 TIME-VARYING LOADING 18
1.3 THE LONG-TERM RESPONSE IN PHYSICALLY AGED POLYMERS 23
1.3.1 A MODEL OF ADAPTIVE LINKS 25
1.3.2 A FREE VOLUME CONCEPT 29
1.3.3 CONSTITUTIVE EQUATIONS 41
1.3.4 COMPARISON WITH EXPERIMENTS 47
1.4 CONSTITUTIVE RELATIONS FOR THREE-DIMENSIONAL LOADING 56
1.5 THERMODYNAMIC POTENTIALS OF A TRANSIENT NETWORK 63
1.5.1 STRAIN ENERGY DENSITY 63
1.5.2 THERMODYNAMIC POTENTIALS AND CONSTI TUTIVE EQUATIONS 69
1.5.3 PROPERTIES OF RELAXATION FUNCTIONS . .. 73 1.6 VARIATIONAL
PRINCIPLES IN VISCOELASTICITY . . .. 83 1.6.1 VARIATIONAL PRINCIPLES AND
GOVERNING EQUATIONS 83
1.6.2 GIBBS PRINCIPLE AND THE SECOND LAW OF THERMODYNAMICS 88
1.6.3 DEBONDING OF A STRIP LINKED TO A RIGID FOUNDATION BY A
VISCOELASTIC ADHESIVE LAYER 90
IMAGE 3
VIII CONTENTS
1.7 PHASE TRANSITIONS IN VISCOELASTIC MEDIA 106 1.7.1 FORMULATION OF THE
PROBLEM 106
1.7.2 AN INTEGRAL OVER A VARYING DOMAIN . . .. 110 1.7.3 INTERFACIAL
EQUILIBRIUM EQUATIONS 114 1.7.4 LOCAL MELTING OF A VISCOELASTIC MEDIUM .
120
REFERENCES 125
2 CONSTITUTIVE MODELS IN NONLINEAR VISCOELASTICITY . . . . . .. 135
2.1 A TRANSIENT NETWORK WITH NONLINEAR LINKS . . 136 2.1.1 CONSTITUTIVE
EQUATIONS 140
2.1.2 COMPARISON WITH EXPERIMENTS 145
2.1.3 THREE-DIMENSIONAL LOADING 148
2.1.4 TORSION OF A CONICAL PIPE 149
2.1.5 THE CORRESPONDENCE PRINCIPLES 155
2.2 A NETWORK WITH AN EYRING-TYPE CLOCK 157
2.2.1 STRESS-STRAIN RELATIONS 159
2.2.2 THE GENERALIZED ARRHENIUS EQUATION . .. 161 2.2.3 COMPARISON WITH
EXPERIMENTS 163
2.3 A NETWORK WITH AN ENTROPY-DRIVEN CLOCK . .. 172 2.3.1 THERMODYNAMIC
POTENTIALS 174
2.3.2 A DISSIPATION-DRIVEN INTERNAL CLOCK . . .. 177 2.3.3 COMPARISON
WITH EXPERIMENTS 180
2.4 CONSTITUTIVE RELATIONS IN VISCOELASTOPLASTICITY 189
2.4.1 A MODEL OF ADAPTIVE LINKS 189
2.4.2 COMPARISON WITH EXPERIMENTS 196
REFERENCES 203
3 CONSTITUTIVE MODELS IN FINITE VISCOELASTICITY 209
3.1 OPERATOR LINEAR CONSTITUTIVE RELATIONS . . . . 2 10 3.1.1 KINETIC
EQUATIONS 210
3.1.2 STRAIN ENERGY DENSITY 211
3.1.3 THERMODYNAMIC POTENTIALS 217
3.1.4 COMPARISON WITH EXPERIMENTS 221
3.1.5 THE PRINCIPLE OF MINIMUM FREE ENERGY . . 225 3.1.6 THERMODYNAMIC
STABILITY 233
3.2 THE MOONEY-RIVLIN MODEL 237
3.2.1 DIFFERENTIAL CONSTITUTIVE EQUATIONS . .. 237 3.2.2 UNIAXIAL
EXTENSION 239
3.2.3 SIMPLE SHEAR 245
3.2.4 TORSION OF A CIRCULAR CYLINDER 248
3.3 STRAIN ENERGY DENSITY OF A NETWORK 254
3.3.1 UNIAXIAL EXTENSION 256
IMAGE 4
CONTENTS IX
3.3.2 BIAXIAL EXTENSION 259
3.4 CONSTITUTIVE EQUATIONS BASED ON THE FREE VOLUME CONCEPT 271
3.4.1 THE TIME-STRAIN SUPERPOSITION PRINCIPLE 273 3.4.2 A NEO-HOOKEAN
VISCOELASTIC MEDIUM . . .. 275 3.4.3 UNIAXIAL EXTENSION 276
3.4.4 SIMPLE SHEAR 284
3.4.5 RADIAL DEFORMATION OF A SPHERICAL SHELL 289 3.5 A NETWORK WITH AN
ENTROPY-DRIVEN CLOCK . .. 299 3.5.1 A CONCEPT OF TRANSIENT NETWORKS 300
3.5.2 THERMODYNAMIC POTENTIALS 313
3.5.3 SIMPLE SHEAR 317
REFERENCES 323
4 C O N S T I T U T I VE MODELS IN THERMOVISCOELASTICITY 329
4.1 THERMORHEOLOGICALLY SIMPLE MEDIA 330
4.1.1 TIME-TEMPERATURE SUPERPOSITION PRINCI PLE . 331
4.1.2 THERMAL SHIFT FACTOR . 332
4.1.3 NONISOTHERMAL LOADING 337
4.2 THERMORHEOLOGICALLY COMPLEX MEDIA 340
4.2.1 BASIC HYPOTHESES 340
4.2.2 A CONCEPT OF TRANSIENT NETWORKS (MODEL I) 343
4.2.3 A CONCEPT OF TRANSIENT NETWORKS (MODEL I) 351
4.2.4 NONISOTHERMAL LOADING 358
4.3 THE NONISOTHERMAL RESPONSE IN NONAGING POLYMERS 364
4.3.1 THREE-DIMENSIONAL LOADING 371
4.3.2 THE STANDARD THERMOVISCOELASTIC SOLID . 372 4.3.3 COOLING OF A
RECTILINEAR BAR 378
4.3.4 COOLING OF A CYLINDRICAL SHELL 382
4.4 LINEAR MEDIA SUBJECTED TO PHYSICAL AGING . .. 400 4.4.1 CONSTITUTIVE
EQUATIONS 401
4.4.2 COOLING OF A SPHERICAL PRESSURE VESSEL . 404 4.5 NONLINEAR MEDIA
SUBJECTED TO PHYSICAL AGING 414 4.5.1 STRAIN ENERGY DENSITY OF A NETWORK
(ISOTHERMAL LOADING) 415
4.5.2 STRAIN ENERGY DENSITY OF A NETWORK (NONISOTHERMAL LOADING) 417
4.5.3 THERMODYNAMIC POTENTIALS 419
4.5.4 CONSTITUTIVE RELATIONS (FINITE STRAINS) . 421 4.5.5 CONSTITUTIVE
RELATIONS (SMALL STRAINS) . 425
IMAGE 5
X CONTENTS
4.5.6 CONSTITUTIVE RELATIONS FOR PHYSICALLY AGED POLYMERS 427
4.5.7 THE AGING SHIFT FACTOR 434
4.5.8 UNIAXIAL EXTENSION 439
4.5.9 COOLING OF A PLATE 446
REFERENCES 459
I N D EX 465
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| spelling | Drozdov, Aleksey D. Verfasser aut Mechanics of viscoelastic solids Aleksey D. Drozdov Chichester [u.a.] Wiley 1998 XII, 472 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Festkörper (DE-588)4016918-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Viskoelastisches Medium (DE-588)4426217-6 gnd rswk-swf Festkörper (DE-588)4016918-2 s Viskoelastisches Medium (DE-588)4426217-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008142122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drozdov, Aleksey D. Mechanics of viscoelastic solids Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Festkörper (DE-588)4016918-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4114528-8 (DE-588)4426217-6 |
| title | Mechanics of viscoelastic solids |
| title_auth | Mechanics of viscoelastic solids |
| title_exact_search | Mechanics of viscoelastic solids |
| title_full | Mechanics of viscoelastic solids Aleksey D. Drozdov |
| title_fullStr | Mechanics of viscoelastic solids Aleksey D. Drozdov |
| title_full_unstemmed | Mechanics of viscoelastic solids Aleksey D. Drozdov |
| title_short | Mechanics of viscoelastic solids |
| title_sort | mechanics of viscoelastic solids |
| topic | Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Festkörper (DE-588)4016918-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd |
| topic_facet | Mathematisches Modell Polymers Viscosity Mathematical models Viscoelastic materials Mechanical properties Viscoelasticity Mathematical models Festkörper Viskoelastisches Medium |
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