Elements of continuum mechanics and thermodynamics
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
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| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Wegner, Joanne L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elements of continuum mechanics and thermodynamics |c Joanne L. Wegner ; James B. Haddow |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a X, 278 S |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | |a Continuum mechanics / Textbooks | |
| 650 | 0 | |a Thermodynamics / Textbooks | |
| 650 | 4 | |a Continuum mechanics |v Textbooks | |
| 650 | 4 | |a Thermodynamics |v Textbooks | |
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Haddow, James B. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0702 PHY 210f 2009 B 1822 |
|---|---|
| DE-BY-TUM_katkey | 1698892 |
| DE-BY-TUM_location | 07 |
| DE-BY-TUM_media_number | 040071306299 |
| _version_ | 1820896956518498304 |
| adam_text | Contents
Preface
Page
ix
1.
Cartesian Tensor Analysis
.................................................................... 1
1.1
Introduction
1
1.2
Rectangular Cartesian Coordinate Systems
3
1.3
Suffix and Symbolic Notation
4
1.4
Orthogonal Transformations
6
1.5
Concept of a Second-Order Tensor
11
1.6
Tensor Algebra
19
1.7
Invariants of Second-Order Tensors
20
1.8
Cayley-Hamilton Theorem
24
1.9
Higher-Order Tensors
25
1.10
Determinants
28
1.11
Polar Decomposition Theorem
32
1.12
Tensor Fields
38
1.13
Integral Theorems
44
EXERCISES
46
Sl. GGESTED READING
48
2.
Kinematics and Continuity Equation
................................................ 50
2.1
Description of Motion
50
2.2
Spatial and Referential Descriptions
53
2.3
Material Surface
54
2.4
Jacobian of Transformation and Deformation Gradient
F
56
2.5
Reynolds Transport Theorem
59
2.6
Continuity Equation
63
v¡
Contents
2.7
Velocity Gradient
64
2.8
Rate of Deformation and Spin Tensors
65
2.9
Polar Decomposition of
F
70
2.10
Further Decomposition of
F
74
2.11
Strain
75
2.12
Infinitesimal Strain
78
exercises
81
3.
Stress
...................................................................................................... 84
3.1
Contact Forces and Body Forces
84
3.2
Cauchy or True Stress
87
3.3
Spatial Form of Equations of Motion
90
3.4
Principal Stresses and Maximum Shearing Stress
91
3.5
Pure Shear Stress and Decomposition of the Stress Tensor
94
3.6
Octahedral Shearing Stress
95
3.7
Nominal Stress Tensor
98
3.8
Second Piola-Kirchhoff Stress Tensor
100
3.9
Other Stress Tensors
101
EXERCISES
102
REFERENCES
104
4.
Work, Energy, and Entropy Considerations
.................................. 105
4.1
Stress Power
105
4.2
Principle of Virtual Work
110
4.3
Energy Equation and Entropy Inequality
114
exercises
119
references
120
5.
Material Models and Constitutive Equations
................................ 121
5.1
Introduction
121
5.2
Rigid Bodies
121
5.3
Ideal Inviscid Fluid
123
5.4
Incompressible Inviscid Fluid
124
5.5
Newtonian Viscous Fluid
125
5.6
Classical Elasticity
126
5.7
Linear Thermoelasticity
130
5.8
Determinism, Local Action, and Material
Frame Indifference
138
Contents
vii
EXERCISES
147
REFERENCES
149
6.
Finite Deformation of an Elastic Solid ...........................................
150
6.1
Introduction
150
6.2
Cauchy Elasticity
150
6.3
Hyperelasticity
155
6.4
Incompressible Hyperelastic Solid
160
6.5
Alternative Formulation
162
EXERCISES
166
REFERENCES
167
7.
Some Problems of Finite Elastic Deformation
.............................. 168
7.1
Introduction
168
7.2
Strain Energy Functions and Stress-Strain Relations
169
7.3
Simple Shear of a Rectangular Block
170
7.4
Simple Tension
172
7.5
Extension and Torsion of an Incompressible
Cylindrical Bar
175
7.6
Spherically Symmetric Expansion of a
Thick-Walled Shell
180
7.7
Eversion
of a Cylindrical Tube
185
7.8
Pure Bending of an Hyperelastic Plate
189
7.9
Combined Telescopic and
Torsionai
Shear
195
exercises
200
references
201
8.
Finite Deformation Thermoelasticity
............................................. 202
8.1
Principle of Local State and Thermodynamic Potentials
202
8.2
Basic Relations for Finite Deformation Thermoelasticity
202
8.3
Ideal Rubber-Like Materials
209
8.4
Isentropic Simple Tension of Ideal Rubber
214
8.5
Isentropic Simple Tension of Compressible Rubber
215
exercises
218
REFERENCES
219
9.
Dissipative Media
.............................................................................. 220
9.1
Newtonian Viscous Fluids
220
viii Contents
9.2
A Non-Newtonian Viscous Fluid
223
9.3
Linear Viscoelastic Medium
224
9.4
Viscoelastic Dissipation
237
9.5
Some Thermodynamic Considerations in
Linear Thermoelasticity
240
9.6
Simple Shear Problem
244
EXERCISES
246
REFERENCES
248
APPENDIX
1:
Orthogonal Curvilinear Coordinate Systems
.............. 249
Al.l Introduction
249
Al.
2
Curvilinear Coordinates
249
A1.3 Orthogonality
252
A
1.4
Cylindrical and Spherical Polar Coordinate Systems
253
A
1.5
The V Operator
256
Al.
6
The V2 Operator
261
APPENDIX
2:
Physical Components of the Deformation Gradient
Tensor
............................................................................... 263
APPENDIX
3:
Legendre Transformation
.............................................. 266
APPENDIX* Linear Vector Spaces
..................................................... 269
Index
272
|
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| id | DE-604.BV035347634 |
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| indexdate | 2024-12-23T21:27:09Z |
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| language | English |
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| spellingShingle | Wegner, Joanne L. Haddow, James B. Elements of continuum mechanics and thermodynamics Continuum mechanics / Textbooks Thermodynamics / Textbooks Continuum mechanics Textbooks Thermodynamics Textbooks Kontinuumsmechanik (DE-588)4032296-8 gnd Thermodynamisches System (DE-588)4185141-9 gnd |
| subject_GND | (DE-588)4032296-8 (DE-588)4185141-9 |
| title | Elements of continuum mechanics and thermodynamics |
| title_auth | Elements of continuum mechanics and thermodynamics |
| title_exact_search | Elements of continuum mechanics and thermodynamics |
| title_full | Elements of continuum mechanics and thermodynamics Joanne L. Wegner ; James B. Haddow |
| title_fullStr | Elements of continuum mechanics and thermodynamics Joanne L. Wegner ; James B. Haddow |
| title_full_unstemmed | Elements of continuum mechanics and thermodynamics Joanne L. Wegner ; James B. Haddow |
| title_short | Elements of continuum mechanics and thermodynamics |
| title_sort | elements of continuum mechanics and thermodynamics |
| topic | Continuum mechanics / Textbooks Thermodynamics / Textbooks Continuum mechanics Textbooks Thermodynamics Textbooks Kontinuumsmechanik (DE-588)4032296-8 gnd Thermodynamisches System (DE-588)4185141-9 gnd |
| topic_facet | Continuum mechanics / Textbooks Thermodynamics / Textbooks Continuum mechanics Textbooks Thermodynamics Textbooks Kontinuumsmechanik Thermodynamisches System |
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