The non-linear field theories of mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1992
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 542 - 579 |
| Physical Description: | X, 591 S. Ill., graph. Darst. |
| ISBN: | 3540550984 0387550984 |
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| 245 | 1 | 0 | |a The non-linear field theories of mechanics |c Clifford Truesdell ; W. Noll |
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Record in the Search Index
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| adam_text | Titel: The non-linear field theories of mechanics
Autor: Truesdell, Clifford
Jahr: 1992
Contents.
Page
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
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 stibfluids..................... 86
34. Material connections, mhomogeneity, 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
VTII Contents.
Page
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............................... -j
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. Stoppelli 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 ma-
terials ........................... 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
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 speres........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 Topakogltj 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
Contents. IX
Page
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
85bis. 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
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
96ter. 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
X Contents.
Page
116. Position of the general and Navier-Stokes theories of viscometry . . 465
117. Steady flow through tubes.................. 468
118. Steady extension...................... 472
ll8bis. 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
II. Other fluids............................ 513
124. Korteweg s theory of capillarity............... 513
125. Truesdell s theory of the Maxwellian fluid......... 515
126. Anisotropic solids capable ot 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
Subject-Index (English-German)........................ 580
|
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| author | Truesdell, Clifford 1919-2000 Noll, Walter 1907-1987 |
| author_GND | (DE-588)121263983 (DE-588)140785949 |
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| 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 | 2. ed. |
| format | Book |
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| id | DE-604.BV004814117 |
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| indexdate | 2024-07-09T16:18:04Z |
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| isbn | 3540550984 0387550984 |
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| publishDate | 1992 |
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| spelling | Truesdell, Clifford 1919-2000 Verfasser (DE-588)121263983 aut The non-linear field theories of mechanics Clifford Truesdell ; W. Noll 2. ed. Berlin u.a. Springer 1992 X, 591 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 542 - 579 Continuum mechanics Nonlinear mechanics Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Nichtlineare Feldtheorie (DE-588)4171752-1 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s Nichtlineare Mechanik (DE-588)4042095-4 s DE-604 Nichtlineare Feldtheorie (DE-588)4171752-1 s Mechanik (DE-588)4038168-7 s 1\p DE-604 Feldtheorie (DE-588)4016698-3 s 2\p DE-604 Noll, Walter 1907-1987 Verfasser (DE-588)140785949 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002962964&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Truesdell, Clifford 1919-2000 Noll, Walter 1907-1987 The non-linear field theories of mechanics Continuum mechanics Nonlinear mechanics Nichtlineare Mechanik (DE-588)4042095-4 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Feldtheorie (DE-588)4016698-3 gnd Mechanik (DE-588)4038168-7 gnd Nichtlineare Feldtheorie (DE-588)4171752-1 gnd |
| subject_GND | (DE-588)4042095-4 (DE-588)4032296-8 (DE-588)4016698-3 (DE-588)4038168-7 (DE-588)4171752-1 |
| 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 Clifford Truesdell ; W. Noll |
| title_fullStr | The non-linear field theories of mechanics Clifford Truesdell ; W. Noll |
| title_full_unstemmed | The non-linear field theories of mechanics Clifford Truesdell ; W. Noll |
| title_short | The non-linear field theories of mechanics |
| title_sort | the non linear field theories of mechanics |
| topic | Continuum mechanics Nonlinear mechanics Nichtlineare Mechanik (DE-588)4042095-4 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Feldtheorie (DE-588)4016698-3 gnd Mechanik (DE-588)4038168-7 gnd Nichtlineare Feldtheorie (DE-588)4171752-1 gnd |
| topic_facet | Continuum mechanics Nonlinear mechanics Nichtlineare Mechanik Kontinuumsmechanik Feldtheorie Mechanik Nichtlineare Feldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002962964&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT truesdellclifford thenonlinearfieldtheoriesofmechanics AT nollwalter thenonlinearfieldtheoriesofmechanics |