The non-linear field theories of mechanics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Ausgabe: | 3. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015190022&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXIX, 602 S. Ill., graph. Darst. |
| ISBN: | 3540027793 |
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Datensatz im Suchindex
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|---|---|
| adam_text | C.TRUESDELL-W.NOLL THE NON-LINEAR FIELD THEORIES OF MECHANICS EDITED BY
STUART S. ANTMAN THIRD EDITION SPRINGER CONTENTS. PUBLISHER S NOTE V THE
GENESIS OF THE NON-LINEAR FIELD THEORIES OF MECHANICS WALTER NOLL VII
PREFACE TO THE THIRD EDITION STUART S. ANTMAN XIII PREFACE TO THE SECOND
EDITION XXIII THE NON-LINEAR FIELD THEORIES OF MECHANICS. BY C.
TRUESDELL, PROFESSOR OF RATIONAL MECHANICS, THE JOHNS HOPKINS
UNIVERSITY, BALTIMORE, MARYLAND (USA) AND W. NOLL, PROFESSOR OF
MATHEMATICS, CARNEGIE INSTITUTE OF TECHNOLOGY, PITTSBURGH, PENNSYL-
VANIA (USA). (WITH 28 FIGURES) 1 A. INTRODUCTION 1 1. PURPOSE OF THE
NON-LINEAR THEORIES 1 2. METHOD AND PROGRAM OF THE NON-LINEAR THEORIES 3
3. STRUCTURE THEORIES AND CONTINUUM THEORIES 5 4. GENERAL LINES OF PAST
RESEARCH ON THE FIELD THEORIES OF MECHANICS . . 8 5. THE NATURE OF THIS
TREATISE 11 6. TERMINOLOGY AND GENERAL SCHEME OF NOTATION 13 6 A.
APPENDIX. CYLINDRICAL AND SPHERICAL CO-ORDINATES 19 B. TENSOR FUNCTIONS
20 I. BASIC CONCEPTS 20 7. DEFINITIONS 20 8. INVARIANTS AND ISOTROPIC
TENSOR FUNCTIONS 22 9. GRADIENTS OF TENSOR FUNCTIONS 24 II.
REPRESENTATION THEOREMS 27 10. REPRESENTATION OF INVARIANTS OF ONE
SYMMETRIC TENSOR 27 11. REPRESENTATION OF SIMULTANEOUS INVARIANTS 29 12.
TENSOR FUNCTIONS OF ONE VARIABLE 32 13. TENSOR AND VECTOR FUNCTIONS OF
SEVERAL VARIABLES 34 C. THE GENERAL THEORY OF MATERIAL BEHAVIOR 36 14.
SCOPE AND PLAN OF THE CHAPTER 36 I. BASIC PRINCIPLES 37 15. BODIES AND
MOTIONS 37 16. FORCES AND STRESSES 39 17. CHANGES OF FRAME. INDIFFERENCE
41 18. EQUIVALENT PROCESSES 43 19. THE PRINCIPLE OF MATERIAL
FRAME-INDIFFERENCE 44 19 A. APPENDIX. HISTORY OF THE PRINCIPLE OF
MATERIAL FRAME-INDIFFERENCE 45 20. THE MAIN OPEN PROBLEM OF THE THEORY
OF MATERIAL BEHAVIOR . . . . 47 II. KINEMATICS 48 21. DEFORMATION 48
XXVI CONTENTS PAGE 22. LOCALIZATIONS. LOCAL CONFIGURATIONS. HISTORIES 51
23. STRETCH AND ROTATION 52 24. STRETCHING AND SPIN 53 25. POLYNOMIAL
EXPRESSIONS FOR THE RATES 55 III. THE GENERAL CONSTITUTIVE EQUATION 56
26. THE PRINCIPLE OF DETERMINISM. THE GENERAL CONSTITUTIVE EQUATION . .
56 27. MATERIAL ISOMORPHISMS. HOMOGENEITY 58 28. SIMPLE MATERIALS,
MATERIALS OF GRADE N, DIMENSIONAL INVARIANCE . . 60 29. REDUCED
CONSTITUTIVE EQUATIONS 66 30. INTERNAL CONSTRAINTS, INCOMPRESSIBILITY,
INEXTENSIBILITY 69 31. THE ISOTROPY GROUP 76 32. SIMPLE FLUIDS 79 33.
SIMPLE SOLIDS 81 33 BIS. SIMPLE SUBFLUIDS 86 34. MATERIAL CONNECTIONS,
INHOMOGENEITY, CURVILINEAR AEOLOTROPY, CON- TINUOUS DISLOCATIONS 88 IV.
SPECIAL CLASSES OF MATERIALS 92 35. MATERIALS OF THE DIFFERENTIAL TYPE
93 36. MATERIALS OF THE RATE TYPE 95 37. MATERIALS OF THE INTEGRAL TYPE
98 V. FADING MEMORY 101 38. THE PRINCIPLE OF FADING MEMORY 101 39.
STRESS RELAXATION 106 40. ASYMPTOTIC APPROXIMATIONS 108 41. POSITION OF
THE CLASSICAL THEORIES OF VISCOSITY AND VISCO-ELASTICITY . 113 D.
ELASTICITY 117 42. SCOPE AND PLAN OF THE CHAPTER 117 I. ELASTIC
MATERIALS 119 A) GENERAL CONSIDERATIONS 119 43. DEFINITION OF AN ELASTIC
MATERIAL 119 43 A. APPENDIX. THE PIOLA-KIRCHHOFF STRESS TENSORS 124 44.
FORMULATION OF BOUNDARY-VALUE PROBLEMS 125 45. THE ELASTICITIES OF AN
ELASTIC MATERIAL 131 46. STOPPELI S THEOREMS OF THE EXISTENCE,
UNIQUENESS, AND ANALYTICITY OF THE SOLUTION OF A CLASS OF TRACTION
BOUNDARY-VALUE PROBLEMS . . . 133 47. ISOTROPIC ELASTIC MATERIALS, I.
GENERAL PROPERTIES 139 48. ISOTROPIC ELASTIC MATERIALS, II. THE
PRINCIPAL STRESSES AND PRINCIPAL FORCES 142 49. INCOMPRESSIBLE ISOTROPIC
ELASTIC MATERIALS 147 50. ELASTIC FLUIDS AND SOLIDS. NATURAL STATES 148
51. RESTRICTIONS UPON THE RESPONSE FUNCTIONS, I. ISOTROPIC COMPRESSIBLE
MATERIALS 153 52. RESTRICTIONS UPON THE RESPONSE FUNCTIONS, II.
COMPRESSIBLE MATERIALS IN GENERAL 162 53. RESTRICTIONS UPON THE RESPONSE
FUNCTIONS, III. INCOMPRESSIBLE MATERIALS 171 B) EXACT SOLUTIONS OF
SPECIAL PROBLEMS OF EQUILIBRIUM 171 54. HOMOGENEOUS STRAIN OF
COMPRESSIBLE ELASTIC BODIES 171 55. INCOMPRESSIBLE ELASTIC MATERIALS, I.
HOMOGENEOUS STRAIN 179 56. INCOMPRESSIBLE ELASTIC MATERIALS, II.
PRELIMINARIES FOR THE NON- HOMOGENEOUS SOLUTIONS FOR ARBITRARY MATERIALS
183 57. INCOMPRESSIBLE ELASTIC MATERIALS, III. THE NON-HOMOGENEOUS
SOLUTIONS FOR ARBITRARY ISOTROPIC MATERIALS 186 CONTENTS XXVII PAGE 58.
INCOMPRESSIBLE ELASTIC MATERIALS, IV. NON-HOMOGENEOUS SOLUTIONS FOR
BODIES WITH CERTAIN KINDS OF AEOLOTROPY AND INHOMOGENEITY . . . . 197
59. SEMI-INVERSE METHODS: REDUCTION OF CERTAIN STATIC DEFORMATIONS THAT
DEPEND UPON MATERIAL PROPERTIES 199 60. PLANE PROBLEMS 204 C) EXACT
SOLUTIONS OF SPECIAL PROBLEMS OF MOTION 208 61. QUASI-EQUILIBRATED
MOTIONS OF INCOMPRESSIBLE BODIES 208 62. RADIAL OSCILLATIONS OF
ISOTROPIC CYLINDERS AND SPHERES 214 D) SYSTEMATIC METHODS OF
APPROXIMATION 219 63. SIGNORINI S EXPANSION 219 64. SIGNORINI S THEOREMS
OF COMPATIBILITY AND UNIQUENESS OF THE EQUI- LIBRIUM SOLUTION 223 65.
RIVLIN AND TOPAKOGLU S INTERPRETATION 227 66. SECOND-ORDER EFFECTS IN
COMPRESSIBLE ISOTROPIC MATERIALS 229 67. SECOND-ORDER EFFECTS IN
INCOMPRESSIBLE ISOTROPIC MATERIALS . . . . 241 68. INFINITESIMAL STRAIN
SUPERIMPOSED UPON A GIVEN STRAIN. I. GENERAL EQUATIONS 246 68 BIS.
INFINITESIMAL STRAIN SUPERIMPOSED UPON A GIVEN STRAIN. II. IN-
FINITESIMAL STABILITY 252 69. INFINITESIMAL STRAIN SUPERIMPOSED UPON A
GIVEN STRAIN, III. GENERAL THEORY FOR ISOTROPIC MATERIALS 260 70.
INFINITESIMAL STRAIN SUPERIMPOSED UPON A GIVEN STRAIN, IV. SOLUTIONS OF
SPECIAL PROBLEMS 263 E) WAVE PROPAGATION 267 71. GENERAL THEORY OF
ACCELERATION WAVES 267 72. WAVES OF HIGHER ORDER 272 73. GENERAL THEORY
OF PLANE INFINITESIMAL PROGRESSIVE WAVES 273 74. WAVES IN ISOTROPIC
COMPRESSIBLE MATERIALS. I. GENERAL PROPERTIES . . 278 75. WAVES IN
ISOTROPIC COMPRESSIBLE MATERIALS. II. THE CASE OF HYDROSTATIC PRESSURE
284 76. WAVES IN ISOTROPIC COMPRESSIBLE MATERIALS. III. DETERMINATION OF
THE STRESS RELATION FROM WAVE SPEEDS 285 77. WAVES IN ISOTROPIC
COMPRESSIBLE MATERIALS. IV. SECOND-ORDER EFFECTS . 288 78. WAVES IN
INCOMPRESSIBLE MATERIALS 291 II. HYPERELASTIC MATERIALS 294 A) GENERAL
CONSIDERATIONS 294 79. THERMODYNAMIC PRELIMINARIES 294 80. PERFECT
MATERIALS . 296 81. THERMAL EQUILIBRIUM OF SIMPLE MATERIALS 298 82.
DEFINITION OF A HYPERELASTIC MATERIAL 301 82 A. APPENDIX. HISTORY OF THE
THEORY OF HYPERELASTIC MATERIALS IN FINITE STRAIN 304 83. WORK THEOREMS
304 84. THE STRAIN-ENERGY FUNCTION 307 85. THE ISOTROPY GROUP OF THE
STRAIN-ENERGY FUNCTION. ISOTROPIC HYPER- ELASTIC MATERIALS, HYPERELASTIC
FLUIDS AND SOLIDS 310 85 BIS. HYPERELASTIC SUBFLUIDS 314 86. EXPLICIT
FORMS OF THE STRESS RELATION FOR ISOTROPIC HYPERELASTIC MA- TERIALS 317
B) GENERAL THEOREMS 319 87. CONSEQUENCES OF RESTRICTIONS UPON THE
STRAIN-ENERGY FUNCTION . . . 319 88. BETTI S THEOREM. VARIATIONAL
PROBLEMS 324 XXVIII CONTENTS PAGE 89. STABILITY 328 90. WAVE PROPAGATION
332 C) SOLUTIONS OF SPECIAL PROBLEMS 336 91. ERICKSEN S ANALYSIS OF THE
DEFORMATIONS POSSIBLE IN EVERY ISOTROPIC HYPERELASTIC BODY 336 92.
SPECIAL PROPERTIES OF SOME EXACT SOLUTIONS FOR ISOTROPIC MATERIALS . 342
93. SECOND-ORDER EFFECTS IN ISOTROPIC MATERIALS 344 D) SPECIAL OR
APPROXIMATE THEORIES OF HYPERELASTICITY 347 94. THE NATURE OF SPECIAL OR
APPROXIMATE THEORIES 347 95. THE MOONEY-RIVLIN THEORY FOR RUBBER 349
III. VARIOUS GENERALIZATIONS OF ELASTICITY AND HYPERELASTICITY 355 96.
THERMO-ELASTICITY 355 96 BIS. COLEMAN S GENERAL THERMODYNAMICS OF SIMPLE
MATERIALS . . . . 363 96 TER. COLEMAN AND GURTIN S GENERAL THEORY OF
WAVE PROPAGATION IN SIMPLE MATERIALS 382 97. ELECTROMECHANICAL THEORIES
385 98. POLAR ELASTIC MATERIALS 389 IV. HYPO-ELASTIC MATERIALS 401 99.
DEFINITION OF A HYPO-ELASTIC MATERIAL 401 100. RELATION TO ELASTICITY
406 101. WORK THEOREMS 411 102. ACCELERATION WAVES 413 103. SOLUTIONS OF
SPECIAL PROBLEMS 415 E. FLUIDITY 426 104. SCOPE AND PLAN OF THE CHAPTER
426 I. SIMPLE FLUIDS 427 A) GENERAL CLASSES OF FLOWS 427 105. THE
CONCEPT OF A SIMPLE FLUID 427 106. LINEAL FLOWS, VISCOMETRIC FLOWS 429
107. CURVILINEAL FLOWS 432 108. STEADY VISCOMETRIC FLOWS 435 109.
MOTIONS WITH CONSTANT STRETCH HISTORY 438 110. DYNAMICAL PRELIMINARIES
FOR THE EXACT SOLUTIONS OF SPECIAL FLOW PROBLEMS 440 B) SPECIAL FLOW
PROBLEMS 441 111. PROBLEMS FOR LINEAL FLOWS. SIMPLE SHEARING, CHANNEL
FLOW, LINEAL OSCILLATIONS 441 112. HELICAL FLOWS, I. GENERAL EQUATIONS
445 113. HELICAL FLOWS, II. SPECIAL CASES: FLOWS IN CIRCULAR PIPES 448
114. NORMAL-STRESS END EFFECTS 452 115. STEADY TORSIONAL FLOWS 458 116.
POSITION OF THE GENERAL AND NAVIER-STOKES THEORIES OF VISCOMETRY . 465
117. STEADY FLOW THROUGH TUBES 468 118. STEADY EXTENSION 472 118 BIS.
SPECIAL FLOW PROBLEMS FOR SUBFLUIDS 473 C) SPECIAL SIMPLE FLUIDS 475
119. THE OLDER THEORIES OF NON-LINEAR VISCOSITY 475 119 A. APPENDIX.
TRUESDELL S THEORY OF THE STOKESIAN FLUID 485 120. ASYMPTOTIC
APPROXIMATIONS, I. STEADY VISCOMETRIC FLOWS . . . . . 488 121.
ASYMPTOTIC APPROXIMATIONS, II. GENERAL FLOWS 490 122. SECONDARY FLOWS IN
TUBES 497 123. FLUIDS OF SECOND GRADE 504 CONTENTS XXIX PAGE II. OTHER
FLUIDS 513 124. KORTEWEG S THEORY OF CAPILLARITY 513 125. TRUESDELL S
THEORY OF THE MAXWELLIAN FLUID 515 126. ANISOTROPIC SOLIDS CAPABLE OF
FLOW 520 127. THE ANISOTROPIC FLUIDS OF ERICKSEN, I. GENERAL THEORY 523
128. THE ANISOTROPIC FLUIDS OF ERICKSEN, II. STATICS 528 129. THE
ANISOTROPIC FLUIDS OF ERICKSEN, III. SPECIAL FLOWS 530 130. THEORIES OF
DIFFUSION 537 GENERAL REFERENCES 542 LIST OF WORKS CITED 542 ADDENDUM
578 SACHVERZEICHNIS (DEUTSCH-ENGLISCH) 580 SUBJECT-INDEX
(ENGLISH-GERMAN) 591
|
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| ctrlnum | (OCoLC)248850739 (DE-599)BVBBV021974875 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
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| dewey-search | 531 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV021974875 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:46:07Z |
| institution | BVB |
| isbn | 3540027793 |
| language | English |
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| physical | XXIX, 602 S. Ill., graph. Darst. |
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| publisher | Springer |
| record_format | marc |
| spellingShingle | Truesdell, Clifford 1919-2000 Noll, Walter 1907-1987 The non-linear field theories of mechanics Kontinuumsmechanik - Nichtlineare Mechanik Continuum mechanics Nonlinear mechanics Nichtlineare Feldtheorie (DE-588)4171752-1 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Mechanik (DE-588)4038168-7 gnd Feldtheorie (DE-588)4016698-3 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| subject_GND | (DE-588)4171752-1 (DE-588)4032296-8 (DE-588)4038168-7 (DE-588)4016698-3 (DE-588)4042095-4 |
| title | The non-linear field theories of mechanics |
| title_auth | The non-linear field theories of mechanics |
| title_exact_search | The non-linear field theories of mechanics |
| title_full | The non-linear field theories of mechanics C. Truesdell ; W. Noll |
| title_fullStr | The non-linear field theories of mechanics C. Truesdell ; W. Noll |
| title_full_unstemmed | The non-linear field theories of mechanics C. Truesdell ; W. Noll |
| title_short | The non-linear field theories of mechanics |
| title_sort | the non linear field theories of mechanics |
| topic | Kontinuumsmechanik - Nichtlineare Mechanik Continuum mechanics Nonlinear mechanics Nichtlineare Feldtheorie (DE-588)4171752-1 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Mechanik (DE-588)4038168-7 gnd Feldtheorie (DE-588)4016698-3 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| topic_facet | Kontinuumsmechanik - Nichtlineare Mechanik Continuum mechanics Nonlinear mechanics Nichtlineare Feldtheorie Kontinuumsmechanik Mechanik Feldtheorie Nichtlineare Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015190022&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT truesdellclifford thenonlinearfieldtheoriesofmechanics AT nollwalter thenonlinearfieldtheoriesofmechanics |