Introduction to continuum mechanics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 237 S. graph. Darst. |
| ISBN: | 9780521875622 |
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MARC
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| 245 | 1 | 0 | |a Introduction to continuum mechanics |c Sudhakar Nair |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XII, 237 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | |a Continuum mechanics | |
| 650 | 4 | |a Continuum mechanics | |
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017371935 | ||
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| _version_ | 1804138903248044032 |
|---|---|
| adam_text | Contents
Preface
page
xi
1
Introduction
........................................1
1.1
Concept of a Continuum
1
1.2
Sequence of Topics
2
2
Cartesian Tensors
....................................4
2.1
Index Notation and Summation Convention
4
2.2 Kronecker
Delta and Permutation Symbol
6
2.2.1
Example: Skew Symmetry
7
2.2.2
Example: Products
8
2.3
Coordinate System
8
2.4
Coordinate Transformations
9
2.5
Vectors
12
2.6
Tensors
14
2.6.1
Examples of Tensors
14
2.6.2
Quotient Rule
17
2.6.3
Inner Products: Notation
18
2.7
Quadratic Forms and Eigenvalue Problems
18
2.7.1
Example: Eigenvalue Problem
20
2.7.2
Diagonalization and Polar Decomposition
21
2.7.3
Example: Polar Decomposition
23
3
General Tensors
.....................................27
3.1
Vectors and Tensors
31
3.2
Physical Components
33
3.3
Tensor Calculus
33
3.4
Curvature Tensors
35
3.5
Applications
36
3.5.1
Example: Incompressible Flow
36
3.5.2
Example: Equilibrium of Stresses
37
VI
Contents
4 Integral Theorems...................................42
4.1
Gauss
Theorem 42
4.2
Stokes
Theorem 44
Deformation.......................................49
5.1 Lagrangian
and Eulerian Descriptions
49
5.2 Deformation
Gradients
51
5.2.1 Deformation Gradient
Vectors
52
5.2.2
Curvilinear
Systems 54
5.3
Strain
Tensors 55
5.3.1
Decomposition of Displacement Gradients
56
5.3.2
Stretch
57
5.3.3
Extension
58
5.3.4
Infinitesimal Strains and Rotations
58
5.3.5
Deformation Ellipsoids
60
5.3.6
Polar Decomposition of the Deformation Gradient
63
5.3.7
Stretch and Rotation
64
5.3.8
Example: Polar Decomposition
65
5.3.9
Example: Square Root of a Matrix
67
5.4
Logarithmic Strain
68
5.5
Change of Volume
68
5.6
Change of Area
69
5.7
Compatibility Equations
70
5.8
Spatial Rotation and Two-Point Tensors
71
5.9
Curvilinear Coordinates
72
Motion
...........................................76
6.1
Material Derivative
76
6.1.1
Some Terminology
77
6.1.2
Example: Path Line. Stream Line, and Streak Line
79
6.2
Length. Volume, and Area Elements
80
6.2.1
Length
81
6.2.2
Volume
81
6.2.3
Area
82
6.3
Material Derivatives of Integrals
82
6.3.1
Line Integrals
82
6.3.2
Area Integrals
83
6.3.3
Volume Integrals
83
6.4
Deformation Rate, Spin, and Vorticity
83
6.5
Strain Rate
86
6.6
Rotation Rate of Principal Axis
87
Contents
vii
7 Fundamental
Laws of Mechanics
..........................90
7.1
Mass
90
7.2
Conservation and Balance Laws
91
7.2.1
Conservation of Mass
91
7.2.2
Balance of Linear Momentum
91
7.2.3
Balance of Angular Momentum
92
7.2.4
Balance of Energy
92
7.2.5
Entropy Production
92
7.3
Axiom of Material Frame Indifference
92
7.4
Objective Measures of Rotation
94
7.5
Integrity Basis
95
8
Stress Tensor
.......................................98
8.1
External Forces and Moments
98
8.2
Internal Forces and Moments
98
8.3
Cauchy Stress and Couple Stress Tensors
100
8.3.1
Transformation of the Stress Tensor
101
8.3.2
Principal Stresses
101
8.3.3
Shear Stress
102
8.3.4
Hydrostatic Pressure and Deviatoric Stresses
103
8.3.5
Objective Stress Rates
104
8.4
Local Conservation and Balance Laws
106
8.4.1
Conservation of Mass
106
8.4.2
Balance of Linear Momentum
107
8.4.3
Balance of Moment of Momentum (Angular Momentum)
107
8.5
Material Description of the Equations of Motion
108
8.5.1
First Piola-Kirchhoff Stress Tensor
109
8.5.2
Second Piola-Kirchhoff Stress Tensor
110
9
Energy and Entropy Constraints
.........................114
9.1
Classical Thermodynamics
114
9.2
Balance of Energy
115
9.3
Clausius-Duhem Inequality
116
9.3.1
Fourier s Law of Heat Conduction
118
9.3.2
Newton s Law of Viscosity
119
9.3.3
Onsager s Principle
119
9.3.4
Strain Energy Density
119
9.3.5
Ideal Gas
120
9.4
Internal Energy
121
9.4.1
Legendre or Contact Transformation
121
9.4.2
Surface Energy
123
9.5
Method of Jacobians in Thermodynamics
123
vüi Contents
10
Constitutive
Relations
................................129
10.1
Invariance
Principles
130
10.1.1
Principles of
Exclusion
130
10.1.2
Principle of Coordinate
Invariance
131
10.1.3
Principle of Spatial
Invariance
131
10.1.4
Principle of Material
Invariance
132
10.1.5
Principle of Dimensional
Invariance
132
10.1.6
Principle of Consistency
132
10.2
Simple Materials
132
10.3
Elastic Materials
134
10.3.1
Elastic Materials of Cauchy
134
10.3.2
Elastic Materials of Green
135
10.4
Stokes Fluids
137
10.5
Invariant Surface Integrals
138
10.6
Singularities
140
11
Hyperelastic Materials
................................142
11.1
Finite Elasticity
142
11.1.1
Homogeneous Deformation
143
11.1.2
Simple Extension
144
11.1.3
Hydrostatic Pressure
145
11.1.4
Simple Shear
145
11.1.5
Torsion of a Circular Cylinder
146
11.2
Approximate Strain Energy Functions
148
11.2.1
Hookean Materials
149
11.2.2
Small-Strain Approximation
149
11.2.3
Plane Stress and Plane Strain
150
11.3
Integrated Elasticity
150
11.3.1
Example: Incremental Loading
151
11.4
A Variational Principle for Static Elasticity
152
11.5 Isotropie
Thermoelasticity
154
11.5.1
Specific Heats and Latent Heats
155
11.5.2
Strain Cooling
156
11.5.3
Adiabatic and Isothermal Elastic Modulus
156
11.5.4
Example: Rubber Elasticity
157
11.6
Linear
Anisotropie
Materials
159
11.7
Invariant Integrals
160
12
Fluid Dynamics
....................................164
12.1
Basic Equations
164
12.2
Approximate Constitutive Relations
165
12.3
Newtonian Fluids
165
12.4
Inviscid Fluids
167
Contents
12.5
Shearing Flow
12.6
Pipe Flow
12.7
Rotating Flow
12.8
Navier-Stokes Equations
12.9
Incompressible Flow
12.10
Compressible Flow
12.11
Inviscid Flow
12.11.1
Speed of Sound
12.11.2
Method of Characteristics
12.12
Bernoulli Equation
12.13
Invariant Integrals
IX
167
169
172
175
175
176
176
177
178
179
180
13
Viscoelasticity
.....................................184
13.1 Kelvin-Voigt
Solid
184
13.2
Maxwell Fluid
185
13.3
Standard Linear Solid
187
13.4
Superposition Principle
189
13.5
Constitutive Laws in the Operator Form
190
13.6
Three-Dimensional Linear Constitutive Relations
190
13.7
Anisotropy
191
13.8
Biot s Theory
192
13.8.1
Minimum Entropy Production Rate
194
13.9
Creep in Metals
194
13.10
Nonlinear Theories of Viscoelasticity
195
13.11
K-BKZ Model for Viscoelastic Fluids
196
14
Plasticity
.........................................200
14.1
Idealized Theories
200
14.1.1
Rigid Perfectly Plastic Material
200
14.1.2
Elastic Perfectly Plastic Material
201
14.1.3
Elastic Linearly Hardening Material
201
14.2
Three-Dimensional Theories
203
14.3
Postyield Behavior
206
14.3.1
Levy-Mises Flow Rule
206
14.3.2
Prandtl-Reuss Flow Rule
207
14.4
General Yield Condition and Plastic Work
208
14.4.1
Plane Stress and Plane Strain
209
14.4.2
Rigid Plasticity and Slip-Line Field
209
14.4.3
Example: Symmetric External Cracks
212
14.5
Drucker s Definition of Stability
213
14.6
Iliushin s Postulate
215
14.7
Work-Hardening Rules
216
14.7.1
Perfectly Plastic Material
216
14.7.2 Isotropie
Hardening
216
Contents
14.7.3
Kinematic Hardening
217
14.7.4
Hencky s Deformation Theory
219
14.8
Endochronic Theory of Valanis
219
14.9
Plasticity and Damage
221
14.10
Minimum Dissipation Rate Principle
224
Author Index
229
Subject Index
231
|
| any_adam_object | 1 |
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| id | DE-604.BV035451914 |
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| indexdate | 2024-07-09T21:35:35Z |
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| isbn | 9780521875622 |
| language | English |
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| physical | XII, 237 S. graph. Darst. |
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| spelling | Nair, Sudhakar 1944- Verfasser (DE-588)139330801 aut Introduction to continuum mechanics Sudhakar Nair 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XII, 237 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017371935&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nair, Sudhakar 1944- Introduction to continuum mechanics Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Introduction to continuum mechanics |
| title_auth | Introduction to continuum mechanics |
| title_exact_search | Introduction to continuum mechanics |
| title_full | Introduction to continuum mechanics Sudhakar Nair |
| title_fullStr | Introduction to continuum mechanics Sudhakar Nair |
| title_full_unstemmed | Introduction to continuum mechanics Sudhakar Nair |
| title_short | Introduction to continuum mechanics |
| title_sort | introduction to continuum mechanics |
| topic | Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017371935&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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