Nonlinear effects in fluids and solids:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Plenum Press
1996
|
| Schriftenreihe: | Mathematical concepts and methods in science and engineering
45 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 358 S. graph. Darst. |
| ISBN: | 0306451794 |
Internformat
MARC
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| 245 | 1 | 0 | |a Nonlinear effects in fluids and solids |c ed. by Michael M. Carroll ... |
| 264 | 1 | |a New York [u.a.] |b Plenum Press |c 1996 | |
| 300 | |a XXI, 358 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical concepts and methods in science and engineering |v 45 | |
| 650 | 4 | |a Continuum mechanics | |
| 650 | 4 | |a Elasticity | |
| 650 | 4 | |a Nonlinear mechanics | |
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Datensatz im Suchindex
| _version_ | 1804125539611443200 |
|---|---|
| adam_text | Contents
1. On Structural Changes in Two Phase Materials 1
D. R. Axelrad
1. Introduction 1
2. Stochastic State Space and Operators in Z 3
3. Evolution of States during the Transient Period 5
4. Structural Changes of the Aluminum Resin Composite 8
References 11
2. Introduction to Nonlinear Elasticity 13
M. F. Beatty
1. Introduction 15
2. Kinematics of Finite Deformation 18
3. Cauchy Stress Principle and Equations of Motion 22
4. Mechanical Energy Principle and Hyperelasticity 24
5. Change of Frame and Material Frame Indifference 25
6. Material Symmetry Transformations 27
7. Isotropic Hyperelastic Materials 28
8. Blatz Ko Constitutive Equation 30
8.1. Some Results Related to the Blatz Ko Experiments 32
8.2. Poisson Function and Blatz Ko Volume Control Relation 35
8.3. Reduced Form of the General Blatz Ko Equation 37
9. Incompressible Materials 38
9.1. Constraint Reaction Stress 39
9.2. Isotropic Hyperelastic Materials 40
10. Rivlin Saunders Strain Energy Function 41
10.1. Mooney Rivlin and Neo Hookean Materials 42
10.2. Constitutive Equation for Biological Tissue 44
11. Inflation Response of a Balloon 45
11.1. Neo Hookean Balloon 47
11.2. Mooney—Rivlin and Biological Membranes 49
11.3. Inflation of a Blatz Ko Balloon 53
11.4. Concluding Remarks on the Balloon Inflation Example 57
12. Remarks on Other Kinds of Internal Constraints 59
xvii
xviii Contents
13. Boundary Value Problems and Nonuniqueness in Elastostatics 63
13.1. Simple Examples Describing Nonuniqueness 64
13.2. Rivlin s Cube 65
14. Universal Inverse Solutions 68
14.1. Ericksen s Problem 69
14.2. Elusive Conclusion of Ericksen s Problem 72
15. Nonuniversal Inverse Solutions: Example 76
16. Class of Universal Relations 79
17. Truesdell s Problem: Restrictions on Constitutive Equations 81
17.1. Empirical Inequalities 82
17.2. Other Inequalities 84
17.3. Antiplane Shear Problem 86
17.4. Concluding Remarks 92
18. Elastic Stability and Nonuniqueness 94
18.1. Remarks on Euler s Criterion 95
18.2. Other Stability Criteria 97
18.3. Energy Method, Uniqueness, and Euler s Criterion 98
19. Concluding Remarks 101
References 104
3. Propagating and Static Exponential Solutions in a Deformed
Mooney Rivlin Material 113
Ph. Boulanger and M. Hayes
1. Introduction 114
2. Mooney—Rivlin Materials 115
3. Small Deformations Superimposed on Large 115
4. Propagating and Static Exponential Solutions 116
5. Propagation Condition Secular Equation 117
6. Homogeneous Waves 118
7. Propagating Evanescent Solutions 119
8. Static Exponential Solutions 121
References 123
4. Circularly Polarized Waves of Finite Amplitude in
Elastic Dielectrics 125
M. M. Carroll and M. F. McCarthy
1. Introduction 125
2. Basic Equations 126
3. Simple Shearing and Polarization 127
4. Circularly Polarized Progressive Waves 129
5. Circularly Polarized Standing Waves 131
6. Approximations 134
References 136
Contents xix
5. Static Theory of Point Defects in Nematic Liquid Crystals 137
J. L. Ericksen
1. Introduction 137
2. Basic Theory 138
3. Dirichlet Problems 140
4. Stable Point Defects 141
Acknowledgments 147
References 147
6. Function Spaces and Fading Memory 149
G. Fichera
1. Introduction 149
2. Stability of the Solution of a Volterra Integral Equation 150
3. Cauchy Problem for the Laplace Equation 152
4. Concept of Fading Memory for an Elastic Solid 154
References 159
7. On Thermomechanical Formulation of Theories of
Continuous Media 161
A. E. Green and P. M. Naghdi
1. Introduction 162
1.1. Background on the Three Dimensional Thermomechanical Theory 162
1.2. Background on the Developments of Thermoelastic Theories of Shells
and Rods 163
2. General Thermomechanical Theory 166
3. Thermomechanical Theory of Shells and Plates 173
4. Thermomechanical Theory of Rods 180
Acknowledgment 185
References 185
Supplementary Reference 187
8. Steady Flow of Slightly Viscoelastic Fluids 189
W. E. Langlois
1. Introduction 190
2. Theorem Concerning the Flow of Slightly Viscoelastic Fluids 193
3. Some General Remarks on Flows with Axial Symmetry 198
4. Convergent Flow in a Right Circular Cone 206
References 224
Supplementary References 225
xx Contents
9. Some Anomalies in the Structure of Elastic Plastic Theory at
Finite Strain 227
E. H. Lee
1. Introduction 228
2. Elastic Plastic Coupling 231
3. Objectivity 239
4. Elastic Plastic Constitutive Relations 243
Acknowledgment 248
References 248
Supplementary Reference 249
10. Nonlinear Thermoelastic Constitutive Equations for
Transversely Isotropic and Orthotropic Materials 251
J. M. O Neill and A. J. M. Spencer
1. Introduction 252
2. Notation and General Theory 253
3. Constitutive Equations for Transversely Isotropic Materials 255
4. Transverse Isotropy—Simple Shearing Deformations 261
5. Constitutive Equations for Orthotropic Materials 262
6. Orthotropy—Simple Shearing Deformations 267
Acknowledgment 268
References 268
11. Energy Minimization for Membranes 271
A. C. Pipkin
1. Introduction 272
2. Inextensible Networks 273
3. Networks with Shearing Stiffness 278
4. Rubber Membranes 280
5. Stress 282
Acknowledgment 284
References 284
12. On Boundary Layer Like Structures in
Finite Thermoelasticity 287
K. R. Rajagopal
1. Introduction 287
2. Governing Equations 289
References 294
Contents xxi
13. On the Thickness Limitation for Euler Buckling 297
K. N. Sawyers
1. Introduction 297
2. Potential Energy 299
3. Neutral Equilibrium of Critical States 303
4. Further Developments for the General Material 306
5. Asymptotic Analysis for a Thin Plate 311
6. Results for a Neo Hookean Plate 314
7. Bifurcation Conditions for a Thick Plate 317
References 319
14. Irreducible Constitutive Expressions 321
G. F. Smith and G. Bao
1. Introduction 321
2. Decomposition Procedure 323
3. Generating Functions 325
4. Procedure for Generating Irreducible Expressions 328
References 337
15. Determination of the Strain Energy Density Function for
Compressible Isotropic Nonlinear Elastic Solids by
Torsion Normal Force Experiments 339
A. S. Wineman and G. B. McKenna
1. Introduction 340
2. Governing Equations 342
3. Change of Variables 344
4. Axial Force, Twisting Moment 346
5. Material Identification by Torsion Experiments 348
5.1. Specification of the Experiment and Measured Quantities 348
5.2. Representation for W 348
5.3. Calculation of M,N,V 349
5.4. Determination of Constants 351
6. Summary 352
References 352
Index 355
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| id | DE-604.BV011049850 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:10Z |
| institution | BVB |
| isbn | 0306451794 |
| language | English |
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| physical | XXI, 358 S. graph. Darst. |
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| publisher | Plenum Press |
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| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Nonlinear effects in fluids and solids ed. by Michael M. Carroll ... New York [u.a.] Plenum Press 1996 XXI, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 45 Continuum mechanics Elasticity Nonlinear mechanics Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Kontinuumsmechanik (DE-588)4032296-8 s Nichtlineares Phänomen (DE-588)4136065-5 s DE-604 Nichtlineare Elastizitätstheorie (DE-588)4171750-8 s Carroll, Michael M. Sonstige oth Mathematical concepts and methods in science and engineering 45 (DE-604)BV000001144 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nonlinear effects in fluids and solids Mathematical concepts and methods in science and engineering Continuum mechanics Elasticity Nonlinear mechanics Nichtlineares Phänomen (DE-588)4136065-5 gnd Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4136065-5 (DE-588)4171750-8 (DE-588)4032296-8 (DE-588)4143413-4 |
| title | Nonlinear effects in fluids and solids |
| title_auth | Nonlinear effects in fluids and solids |
| title_exact_search | Nonlinear effects in fluids and solids |
| title_full | Nonlinear effects in fluids and solids ed. by Michael M. Carroll ... |
| title_fullStr | Nonlinear effects in fluids and solids ed. by Michael M. Carroll ... |
| title_full_unstemmed | Nonlinear effects in fluids and solids ed. by Michael M. Carroll ... |
| title_short | Nonlinear effects in fluids and solids |
| title_sort | nonlinear effects in fluids and solids |
| topic | Continuum mechanics Elasticity Nonlinear mechanics Nichtlineares Phänomen (DE-588)4136065-5 gnd Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Elasticity Nonlinear mechanics Nichtlineares Phänomen Nichtlineare Elastizitätstheorie Kontinuumsmechanik Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007400278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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