Homogenization of coupled phenomena in heterogenous media:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
London
ISTE [u.a.]
2009
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 476 S. Ill., graph. Darst. |
| ISBN: | 9781848211612 |
Internformat
MARC
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| 020 | |a 9781848211612 |9 978-1-84821-161-2 | ||
| 035 | |a (OCoLC)320432467 | ||
| 035 | |a (DE-599)BSZ308101170 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 082 | 0 | |a 620.1/1015118 | |
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 100 | 1 | |a Auriault, Jean-Louis |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Homogénéisation de phénomènes couples en milieux hétérogènes |
| 245 | 1 | 0 | |a Homogenization of coupled phenomena in heterogenous media |c Jean-Louis Auriault, Claude Boutin, Christian Geindreau |
| 264 | 1 | |a London |b ISTE [u.a.] |c 2009 | |
| 300 | |a 476 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Inhomogeneous materials |x Mathematical models | |
| 650 | 4 | |a Coupled problems (Complex systems) | |
| 650 | 4 | |a Homogenization (Differential equations) | |
| 650 | 0 | 7 | |a Inhomogener Festkörper |0 (DE-588)4225741-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Technische Mathematik |0 (DE-588)4827059-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homogenisierung |g Mathematik |0 (DE-588)4403079-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Homogenisierung |g Mathematik |0 (DE-588)4403079-4 |D s |
| 689 | 0 | 1 | |a Inhomogener Festkörper |0 (DE-588)4225741-4 |D s |
| 689 | 0 | 2 | |a Technische Mathematik |0 (DE-588)4827059-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Boutin, Claude |e Verfasser |4 aut | |
| 700 | 1 | |a Geindreau, Christian |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018650574 | ||
Datensatz im Suchindex
| _version_ | 1804140732041134080 |
|---|---|
| adam_text | Contents
Main
notations
.................................... 17
Introduction
..................................... 21
Part one. Upscaling Methods
....................... 27
Chapter
1.
An Introduction to Upscaling Methods
.............. 29
1.1.
Introduction
................................. 29
1.2.
Heat transfer in a periodic bilaminate composite
............ 30
1.2.1.
Transfer parallel to the layers
.................... 31
1.2.2.
Transfer perpendicular to the layers
................ 33
1.2.3.
Comments
............................... 35
1.2.4.
Characteristic macroscopic length
................. 35
1.3.
Bounds on the effective coefficients
................... 36
1.3.1.
Theorem of virtual powers
...................... 36
1.3.2.
Minima in the complementary power and
potential
power
.... 38
1.3.3.
Hill principle
............................. 39
1.3.4. Voigt
and Reuss bounds
....................... 40
1.3.4.1.
Upper bound:
Voigt...................... 40
1.3.4.2.
Lower bound: Reuss
..................... 42
1.3.5.
Comments
............................... 44
1.3.6.
Hashin and Shtrikman s bounds
................... 45
1.3.7.
Higher-order bounds
......................... 46
1.4.
Self-consistent method
........................... 46
1.4.1.
Boundary-value problem
....................... 47
1.4.2.
Self-consistent hypothesis
...................... 48
1.4.3.
Self-consistent method with simple inclusions
.......... 49
6
Homogenization of Coupled Phenomena
1.4.3.1.
Determination of
ßa
for a homogenous spherical inclusion
49
1.4.3.2.
Self-consistent estimate
.................... 51
1.4.3.3.
Implicit morphological constraints
............. 52
1.4.4.
Comments
............................... 53
Chapter
2.
Heterogenous Medium: Is an Equivalent
Macroscopic Description Possible?
........................ 55
2.1.
Introduction
................................. 55
2.2.
Comments on techniques for micro-macro upscaling
.......... 56
2.2.1.
Homogenization techniques for separated length scales
..... 57
2.2.2.
The ideal homogenization method
................. 59
2.3.
Statistical modeling
............................ 60
2.4.
Method of multiple scale expansions
................... 61
2.4.1.
Formulation of multiple scale problems
.............. 61
2.4.1.1.
Homogenizability conditions
................ 61
2.4.1.2.
Double spatial variable
.................... 62
2.4.1.3.
Stationarity, asymptotic expansions
............. 64
2.4.2.
Methodology
............................. 65
2.4.3.
Parallels between macroscopic models for materials with
periodic and random structures
................... 68
2.4.3.1.
Periodic materials
....................... 68
2.4.3.2.
Random materials with a REV
................ 68
2.4.4.
Hill macro-homogenity and separation of scales
......... 69
2.5.
Comments on multiple scale methods and statistical methods
..... 69
2.5.1.
On the periodicity, the stationarity and the concept of the REV
. 69
2.5.2.
On the absence of, or need for macroscopic prerequisites
.... 70
2.5.3.
On the homogenizability and consistency of the macroscopic
description
............................... 71
2.5.4.
On the treatment of problems with several small parameters
... 72
Chapter
3.
Homogenization by Multiple Scale
Asymptotic Expansions
............................... 75
3.1.
Introduction
................................. 75
3.2.
Separation of scales: intuitive approach and experimental visualization
75
3.2.1.
Intuitive approach to the separation of scales
........... 75
3.2.2.
Experimental visualization of fields with two length scales
... 78
3.2.2.1.
Investigation of a flexible net
................ 78
3.2.2.2.
Photoelastic investigation of a perforated plate
....... 81
3.3.
One-dimensional example
......................... 84
3.3.1.
Elasto-statics
............................. 85
Contents 7
3.3.1.1.
Equivalent macroscopic
description
............. 86
3.3.1.2.
Comments
........................... 89
3.3.2.
Elasto-dynamics
........................... 91
3.3.2.1.
Macroscopic dynamics:
Vi =
Ο(ε2)
............ 92
3.3.2.2.
Steady state:
Vi =
Ο(ε3)
.................. 95
3.3.2.3.
Non-homogenizable description:
Vi =
Ο(ε)
....... 95
3.3.3.
Comments on the different possible choices for spatial
variables
................................ 97
3.4.
Expressing problems within the formalism of multiple scales
..... 100
3.4.1.
How do we select the correct mathematical formulation based
on the problem at hand?
....................... 100
3.4.2.
Need to evaluate the actual scale ratio
єг
............. 101
3.4.3.
Evaluation of the actual scale ratio
εΓ
............... 102
3.4.3.1.
Homogenous treatment of simple compression
...... 103
3.4.3.2.
Point force in an elastic object
................ 104
3.4.3.3.
Propagation of a harmonic plane wave in elastic
composites
........................... 104
3.4.3.4.
Diffusion wave in heterogenous media
........... 105
3.4.3.5.
Conclusions to be drawn from the examples
........ 106
Part two. Heat and Mass Transfer
................... 107
Chapter
4.
Heat Transfer in Composite Materials
............... 109
4.1.
Introduction
................................. 109
4.2.
Heat transfer with perfect contact between constituents
........ 109
4.2.1.
Formulation of the problem
..................... 110
4.2.2.
Thermal conductivities of the same order of magnitude
..... 113
4.2.2.1.
Homogenization
........................ 113
4.2.2.2.
Macroscopic model
...................... 117
4.2.2.3.
Example: bilaminate composite
............... 119
4.2.3.
Weakly conducting phase in a connected matrix: memory
effects
................................. 121
4.2.3.1.
Homogenization
........................ 122
4.2.3.2.
Macroscopic model
...................... 124
4.2.3.3.
Example: bilaminate composite
............... 125
4.2.4.
Composites with highly conductive inclusions embedded in
a matrix
................................ 126
4.2.4.1.
Homogenization
........................ 127
4.2.4.2.
Macroscopic model
...................... 129
4.3.
Heat transfer with contact resistance between constituents
...... 130
4.3.1.
Model I
-
Very weak contact resistance
.............. 132
8
Homogenization of Coupled Phenomena
4.3.2.
Model II
-
Moderate contact resistance
.............. 133
4.3.3.
Model
ΙΠ
-
High contact resistance
................. 135
4.3.4.
Model IV
-
Model with two coupled temperature fields
..... 138
4.3.5.
Model V
-
Model with two decoupled temperature fields
.... 140
4.3.6.
Example: bilaminate composite
................... 141
4.3.7.
Choice of model
........................... 142
Chapter
5.
Diffusion/Advection in Porous Media
............... 143
5.1.
Introduction
................................. 143
5.2.
Diffusion-convection on the pore scale and estimates
......... 143
5.3.
Diffusion dominates at the macroscopic scale
.............. 146
5.3.1.
Homogenization
........................... 146
5.3.1.1.
Boundary value problem for c*^
.............. 146
5.3.1.2.
Boundary value problem for c*^
.............. 147
5.3.1.3.
Boundary value problem for c*^
.............. 148
5.3.2.
Macroscopic diffusion model
.................... 148
5.4.
Comparable diffusion and advection on the macroscopic scale
.... 149
5.4.1.
Homogenization
........................... 149
5.4.1.1.
Boundary value problems fore* 0) and c*^
........ 149
5.4.1.2.
Boundary value problem for c*^
.............. 149
5.4.2.
Macroscopic diffusion-advection model
.............. 150
5.5.
Advection dominant at the macroscopic scale
.............. 151
5.5.1.
Homogenization
........................... 151
5.5.1.1.
Boundary value problem for c*^
.............. 151
5.5.1.2.
Boundary value problem for c*^
.............. 151
5.5.1.3.
Boundary value problem for c*^
.............. 153
5.5.2.
Dispersion model
........................... 154
5.6.
Very strong advection
........................... 154
5.7.
Example: Porous medium consisting of a periodic lattice of narrow
parallel slits
................................. 155
5.7.1.
Analysis of the flow
......................... 156
5.7.2.
Determination of the dispersion coefficient
............ 157
5.8.
Conclusion
................................. 159
Chapter
6.
Numerical and Analytical Estimates for the Effective Diffusion
Coefficient
....................................... 161
6.1.
Introduction
................................. 161
6.2.
Effective thermal conductivity for some periodic media
........ 162
6.2.1.
Media with spherical inclusions, connected or
non-connected
............................ 162
Contents 9
6.2.1.1.
Microstructures
........................ 162
6.2.1.2.
Solution
to the boundary value problem over the period
. 163
6.2.1.3.
Effective thermal conductivity
................ 163
6.2.2.
Fibrous media consisting of parallel fibers
............. 168
6.2.2.1.
Microstructures
........................ 168
6.2.2.2.
Solution to the boundary value problem over the period
. 169
6.2.2.3.
Effective thermal conductivity
................ 170
6.3.
Study of various self-consistent schemes
................ 175
6.3.1.
Self-consistent scheme for bi-composite inclusions
........ 175
6.3.1.1.
Granular or cellular media
.................. 175
6.3.1.2.
Fibrous media
......................... 178
6.3.1.3.
General remarks on bi-composite models
.......... 179
6.3.2.
Self-consistent scheme with multi-composite substructures
... 181
6.3.2.1.
n-composite substructure
................... 181
6.3.2.2.
Treatment of a contact resistance
.............. 183
6.3.3.
Combined self-consistent schemes
................. 184
6.3.3.1.
Mixed self-consistent schemes
................ 185
6.3.3.2.
Multiple self-consistent schemes
.............. 185
6.4.
Comparison with experimental results for the thermal conductivity
of cellular concrete
............................. 188
6.4.1.
Dry cellular concrete
......................... 189
6.4.2.
Damp cellular concrete
........................ 190
Part three. Newtonian Fluid Flow Through Rigid Porous
Media
......................................... 195
Chapter
7.
Incompressible Newtonian Fluid Flow Through a Rigid Porous
Medium
........................................ 197
7.1.
Introduction
................................. 197
7.2.
Steady-state flow of an incompressible Newtonian fluid in a porous
medium: Darcy s law
........................... 199
7.2.1.
Darcy s law
.............................. 201
7.2.2.
Comments on macroscopic behavior
................ 203
7.2.2.1.
Physical meaning of the macroscopic quantities
...... 203
7.2.2.2.
Structure of the macroscopic law
.............. 204
7.2.2.3.
Study of the underlying problem
.............. 205
7.2.2.4.
Properties of K*
........................ 205
7.2.2.5.
Energetic consistency
..................... 206
7.2.3.
Non-homogenizable situations
................... 206
7.2.3.1.
Case where QL
=
Ο(ε-1)
.................. 207
10
Homogenization of Coupled Phenomena
7.2.3.2.
Case where QL
=
Ο(ε 3)
.................. 208
7.3.
Dynamics of an incompressible fluid in a rigid porous medium
.... 209
7.3.1.
Local description and estimates
................... 209
7.3.2.
Macroscopic behavior: generalized Darcy s law
......... 211
7.3.3.
Discussion of the macroscopic description
............. 213
7.3.3.1.
Physical meaning of macroscopic quantities
........ 213
7.3.3.2.
Energetic consistency
..................... 213
7.3.3.3.
The tensors H* and
Λ*
are symmetric
........... 215
7.3.3.4.
Low-frequency behavior
................... 215
7.3.3.5.
Additional mass effect
.................... 215
7.3.3.6.
Transient excitation: Dynamics with memory effects
. . . 216
7.3.3.7.
Quasi-periodicity
....................... 216
7.3.4.
Circular cylindrical pores
...................... 216
7.4.
Appearance of
inerţial
non-linearities
.................. 220
7.4.1.
Macroscopic model
.......................... 221
7.4.2.
Macroscopically
isotropie
and homogenous medium
....... 224
7.4.3.
Conclusion
.............................. 226
7.5.
Summary
.................................. 226
Chapter
8.
Compressible Newtonian Fluid Flow Though a Rigid Porous
Medium
........................................ 229
8.1.
Introduction
................................. 229
8.2.
Slow isothermal flow of a highly compressible fluid
.......... 229
8.2.1.
Estimates
............................... 230
8.2.2.
Steady-state flow
........................... 231
8.2.3.
Transient conservation of mass
................... 235
8.3.
Wall slip: Klinkenberg s law
....................... 238
8.3.1.
Pore scale description and estimates
................ 238
8.3.2.
Klinkenberg s law
.......................... 240
8.3.3.
Small Knudsen numbers
....................... 241
8.3.4.
Properties of the
Klinkenberg
tensor Hk
.............. 243
8.3.4.1.
Hk is positive
......................... 243
8.3.4.2.
Symmetries
.......................... 244
8.4.
Acoustics in a rigid porous medium saturated with a gas
....... 245
8.4.1.
Harmonic perturbation of a gas in a porous medium
....... 246
8.4.2.
Analysis of local physics
....................... 247
8.4.3.
Non-dimensionalization and renormalization
........... 249
8.4.4.
Homogenization
........................... 251
8.4.4.1.
Pressure and temperature
................... 251
8.4.4.2.
Velocity field
.......................... 252
Contents 11
8.4.4.3.
Macroscopic conservation
of mass
............. 252
8.4.5.
Biot-Allard model
.......................... 253
Chapter
9.
Numerical Estimation of the Permeability of Some Periodic
Porous Media
..................................... 257
9.1.
Introduction
................................. 257
9.2.
Permeability tensor: recap of results from periodic homogenization
. 259
9.3.
Steady state permeability of fibrous media
............... 259
9.3.1.
Microstructures
............................ 259
9.3.2.
Transverse permeability
....................... 260
9.3.2.1.
Mesh, velocity fields and microscopic pressure fields
. . . 261
9.3.2.2.
Transverse permeability )CT
................. 262
9.3.3.
Longitudinal permeability
...................... 264
9.3.3.1.
Mesh, velocity fields
..................... 264
9.3.3.2.
Longitudinal permeability fC^
................ 264
9.4.
Steady state and dynamic permeability of granular media
....... 267
9.4.1.
Microstructures
............................ 267
9.4.2.
Methodology
............................. 267
9.4.3.
Steady state permeability
...................... 269
9.4.4.
Dynamic permeability
........................ 269
9.4.4.1.
Effect of frequency
...................... 269
9.4.4.2.
Low-frequency approximation
................ 270
9.4.4.3.
High-frequency approximation
............... 272
Chapter
10.
Self-consistent Estimates and Bounds for Permeability
.... 275
10.1.
Introduction
................................. 275
10.1.1.
Notation and glossary
........................ 277
10.2.
Intrinsic (or steady state) permeability of granular and fibrous media
278
10.2.1.
Summary of results obtained through periodic
homogenization
............................ 279
10.2.1.1.
Global and local descriptions
-
energetic consistency
... 280
10.2.1.2.
Connections between the micro- and macroscopic
descriptions
.......................... 281
10.2.2.
Self-consistent estimate of the permeability of granular media
. 281
10.2.2.1.
Formulation of the self-consistent problem
......... 281
10.2.2.2.
General expression for the fields in the inclusion
..... 283
10.2.2.3.
Boundary conditions
..................... 285
10.2.3.
Solution and self-consistent estimates
............... 288
10.2.3.1.
Pressure approach:
τσρ
field
................. 288
10.2.3.2.
Velocity approach: wv field
................. 289
12
Homogenization of Coupled Phenomena
10.2.3.3.
Comparison of estimates
................... 289
10.2.4.
From spherical substructure to granular materials
......... 291
10.2.4.1.
Cubic lattices of spheres
................... 291
10.2.4.2.
Bounds on the permeability of ordered or disordered
granular media
......................... 292
10.2.4.3.
Empirical laws
......................... 296
10.2.5.
Intrinsic permeability of fibrous media
............... 297
10.2.5.1.
Periodic arrangements of identical cylinders
........ 298
10.2.5.2.
Permeability bounds for ideal ordered and disordered
fibrous media
......................... 298
10.3.
Dynamic permeability
........................... 299
10.3.1.
Summary of homogenization results
................ 300
10.3.1.1.
Global and local description
-
Energetic consistency
. . . 300
10.3.1.2.
Frequency characteristics of dynamic permeability
.... 302
10.3.2.
Self-consistent estimates of dynamic permeability
........ 304
10.3.3.
Formulation of the problem in the inclusion
............ 304
10.3.3.1.
Expressions for the fields
................... 305
10.3.3.2.
Boundary conditions
..................... 306
10.3.4.
Solution and self-consistent estimates
............... 307
10.3.4.1.
Ρ
estimate: rop field
...................... 308
10.3.4.2.
V estimate: rov field
..................... 309
10.3.4.3.
Commentary and comparisons with numerical results for
periodic lattices
........................ 310
10.3.4.4.
Bounds on the dynamic permeability of granular media
. 314
10.3.4.5.
Bounds on the real and imaginary parts of
Κ(ω)
...... 315
10.3.4.6.
Bounds on the real and imaginary parts of
Η(ω)
...... 316
10.3.4.7.
Low-frequency bounds
.................... 317
10.3.4.8.
High-frequency bounds for tortuosity
............ 318
10.4. Klinkenberg
correction to intrinsic permeability
............ 318
10.4.1.
Local and global descriptions obtained through homogenization
318
10.4.2.
Self-consistent estimates of
Klinkenberg
permeability
...... 319
10.5.
Thermal permeability
-
compressibility of a gas in a porous medium
322
10.5.1.
Dynamic compressibility obtained by homogenization
..... 322
10.5.2.
Self-consistent estimate of the thermal permeability of
granular media
............................ 323
10.5.3.
Properties of thermal permeability
................. 324
10.5.4.
Significance of connectivity of phases
............... 326
10.5.5.
Critical thermal and viscous frequencies
.............. 327
10.6.
Analogy between the trapping constant and permeability
....... 328
10.6.1.
Trapping constant
........................... 328
Contents 13
10.6.1.1.
Comparison between the trapping constant and
intrinsic permeability
..................... 330
10.6.1.2.
Self-consistent estimate of the trapping constant for
granular media
......................... 331
10.6.2.
Diffusion-trapping in the transient regime
............. 332
10.6.3.
Steady-state diffusion-trapping regime in media with a finite
absorptivity
.............................. 333
10.7.
Conclusion
................................. 334
Part four. Saturated Deformable Porous Media
......... 337
Chapter
11.
Quasi-statics of Saturated Deformable Porous Media
..... 339
11.1.
Empty porous matrix
............................ 340
11.1.1.
Local description
........................... 340
11.1.2.
Equivalent macroscopic behavior
.................. 342
11.1.2.1.
Boundary-value problem for u*(0)
............. 342
11.1.2.2.
Boundary-value problem for u*(1)
............. 343
11.1.2.3.
Boundary-value problem for u* 2^
............. 344
11.1.3.
Investigation of the equivalent macroscopic behavior
....... 345
11.1.3.1.
Physical meaning of quantities involved in macroscopic
description
........................... 345
11.1.3.2.
Properties of the effective elastic tensor
........... 346
11.1.3.3.
Energetic consistency
..................... 348
11.1.4.
Calculation of the effective coefficients
.............. 348
11.2.
Deformable saturated porous medium
.................. 349
11.2.1.
Local description and estimates
................... 350
11.2.2.
Diphasic macroscopic behavior: Biot model
............ 352
11.2.2.1.
Boundary-value problem for u*(°)
............. 352
11.2.2.2.
Boundary-value problem forp*(°> and v*W
........ 352
11.2.2.3.
Boundary-value problem for u*(1)
............. 353
11.2.2.4.
First compatibility equation
................. 354
11.2.2.5.
Second compatibility equation
................ 355
11.2.2.6.
Macroscopic description
................... 355
11.2.3.
Properties of the macroscopic diphasic description
........ 355
11.2.3.1.
Properties of macroscopic quantities and effective
coefficients
........................... 355
11.2.3.2.
The coupling between
(11.31)
and
(11.32)
is
symmetric,
α
= 7....................... 356
11.2.3.3.
The tensor
α*
is symmetric
................. 356
11.2.3.4.
The coefficient
0*
is positive,
β*
> 0............ 357
11.2.3.5.
Specific cases
......................... 357
14
Homogenization of Coupled Phenomena
11.2.3.6.
Homogenious matrix material
................ 357
11.2.3.7.
Homogenous and
isotropie
matrix material and
macroscopically
isotropie
matrix
.............. 358
11.2.3.8.
Diphasic consolidation equations: Biot model
....... 359
11.2.3.9.
Effective stress
......................... 361
11.2.3.10.
Compressible interstitial fluid
................ 361
11.2.4.
Monophasic elastic macroscopic behavior: Gassman model
. . . 362
11.2.5.
Monophasic viscoelastic macroscopic behavior
.......... 363
11.2.6.
Relationships between the three macroscopic models
...... 365
Chapter
12.
Dynamics of Saturated
Deformatile
Porous Media
....... 367
12.1.
Introduction
................................. 367
12.2.
Local description and estimates
...................... 368
12.3.
Diphasic macroscopic behavior: Biot model
.............. 370
12.4.
Study of diphasic macroscopic behavior
................. 374
12.4.1.
Equations for the diphasic dynamics of a saturated deformable
porous medium
............................ 374
12.4.2.
Rheology and dynamics
....................... 375
12.4.3.
Additional mass
............................ 376
12.4.4.
Transient motion
........................... 376
12.4.5.
Small pulsation
ω
........................... 376
12.4.6.
Dispersive waves
........................... 376
12.5.
Macroscopic monophasic elastic behavior: Gassman model
...... 377
12.6.
Monophasic viscoelastic macroscopic behavior
............. 378
12.7.
Choice of macroscopic behavior associated with a given material and
disturbance
................................. 380
12.7.1.
Effects of viscosity
.......................... 382
12.7.1.1.
Transition from diphasic behavior to elastic behavior
... 382
12.7.1.2.
Transition from viscoelastic behavior to elastic behavior
. 383
12.7.2.
Effector rigidity of the porous skeleton
.............. 384
12.7.3.
Effect of frequency
.......................... 384
12.7.3.1.
Low-dispersion Pi and
S
waves
............... 384
12.7.3.2.
Dispersive P2 wave
...................... 385
12.7.4.
Effect of pore size
.......................... 385
12.7.5.
Application example: bituminous concretes
............ 385
Chapter
13.
Estimates and Bounds for Effective Poroelastic Coefficients
. 389
13.1.
Introduction
................................. 389
13.2.
Recap of the results of periodic homogenization
............ 389
13.3.
Periodic granular medium
......................... 391
Contents 15
13.3.1.
Microstructure
and
material
..................... 391
13.3.2.
Effective elastic tensor
с
....................... 392
13.3.2.1.
Methodology
......................... 392
13.3.2.2.
Compressibility and shear moduli
.............. 394
13.3.2.3.
Degree of anisotropy
..................... 396
13.3.2.4.
Young s modulus and Poisson s ratio
............ 396
13.3.3.
Biot tensor
............................... 398
13.4.
Influence of
microstructure:
bounds and self-consistent estimates
. . 398
13.4.1. Voigt
and Reuss bounds
....................... 399
13.4.2.
Hashin and Shtrikman bounds
.................... 399
13.4.3.
Self-consistent estimates
....................... 400
13.4.4.
Comparison: numerical results, bounds and self-consistent
estimates
................................ 401
13.5.
Comparison with experimental data
................... 403
Chapter
14.
Wave Propagation in
Isotropie
Saturated Poroelastic Media
. 407
14.1.
Introduction
................................. 407
14.2.
Basics
.................................... 408
14.2.1.
Notation
................................ 408
14.2.2.
Comments on the parameters
.................... 410
14.2.2.1.
Elastic coefficients
...................... 410
14.2.2.2.
Dynamic permeability
.................... 410
14.2.3.
Degrees of freedom and dimensionless parameters
........ 411
14.3.
Three modes of propagation in a saturated porous medium
...... 412
14.3.1.
Wave equations
............................ 413
14.3.2.
Elementary wave fields: plane waves
................ 416
14.3.2.1.
Homogeneous plane waves
.................. 416
14.3.2.2.
Inhomogenous plane waves
................. 417
14.3.3.
Physical characteristics of the modes
................ 419
14.3.3.1.
Low frequencies:
ƒ
<C fc
.................. 419
14.3.3.2.
High frequencies:
ƒ »
fc
.................. 421
14.3.3.3.
Full spectrum
......................... 423
14.4.
Transmission at an elastic-poroelastic interface
............. 423
14.4.1.
Expression for the conditions at the interface
........... 426
14.4.2.
Transmission of compression waves
................ 428
14.5.
Rayleigh waves
............................... 430
14.6.
Green s functions
.............................. 432
14.6.1.
Source terms
............................. 432
14.6.2.
Determination of the fundamental solutions
............ 433
14.6.3.
Fundamental solutions in plane geometry
............. 437
16
Homogenization of Coupled Phenomena
14.6.4.
Symmetry of the Green s matrix, and reciprocity theorem
.... 438
14.6.5.
Properties of radiated fields
..................... 439
14.6.5.1.
Far-field
-
near-field
-
quasi-static regime
......... 441
14.6.5.2.
Decomposition into elementary waves
........... 442
14.6.6.
Energy and moment sources: explosion and injection
...... 442
14.7.
Integral representation
........................... 445
14.8.
Dislocations in porous media
....................... 448
Bibliography
..................................... 453
Index
.......................................... 473
Both naturally-occurring and man-made materials are often
heterogenous materials formed of various constituents with
different properties and behaviors
-
such as aggregates or
composite materials. Studies of material characteristics are
usually carried out on sample volumes of materials that contain a
large number of heterogenities. Describing these media using
appropriate mathematical models to describe each constituent
turns out to be an intractable problem. Instead they are generally
investigated using an equivalent macroscopic description
-
relative to the microscopic
heterogenity
scale
-
which describes
the overall behavior of the media.
Fundamental questions then arise
-
is such an equivalent
macroscopic description possible? What is the domain of validity
of this macroscopic description? The homogenization technique
described in this book provides complete and rigorous answers
to these questions.
The book aims to summarize the homogenization technique and
its contribution to engineering sciences. Aimed at researchers,
graduate students and engineers, it provides a unified and
concise presentation.
Jean-Louis Auriault is Professor of Continuum Mechanics at
Joseph Fourier University, Grenoble, France.
Claude Boutin is Professor at
École Nationale des Travaux
publics de l Etat, Lyon, France.
Christian Geindreau
is Professor of Mechanics at Joseph
Fourier University, Grenoble, France.
|
| any_adam_object | 1 |
| author | Auriault, Jean-Louis Boutin, Claude Geindreau, Christian |
| author_facet | Auriault, Jean-Louis Boutin, Claude Geindreau, Christian |
| author_role | aut aut aut |
| author_sort | Auriault, Jean-Louis |
| author_variant | j l a jla c b cb c g cg |
| building | Verbundindex |
| bvnumber | BV035791242 |
| callnumber-first | T - Technology |
| callnumber-label | TA418 |
| callnumber-raw | TA418.9.I53 |
| callnumber-search | TA418.9.I53 |
| callnumber-sort | TA 3418.9 I53 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)320432467 (DE-599)BSZ308101170 |
| dewey-full | 620.1/1015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1/1015118 |
| dewey-search | 620.1/1015118 |
| dewey-sort | 3620.1 71015118 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035791242 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:39Z |
| institution | BVB |
| isbn | 9781848211612 |
| language | English French |
| lccn | 2009016650 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018650574 |
| oclc_num | 320432467 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 476 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | ISTE [u.a.] |
| record_format | marc |
| spelling | Auriault, Jean-Louis Verfasser aut Homogénéisation de phénomènes couples en milieux hétérogènes Homogenization of coupled phenomena in heterogenous media Jean-Louis Auriault, Claude Boutin, Christian Geindreau London ISTE [u.a.] 2009 476 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Inhomogeneous materials Mathematical models Coupled problems (Complex systems) Homogenization (Differential equations) Inhomogener Festkörper (DE-588)4225741-4 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Homogenisierung Mathematik (DE-588)4403079-4 s Inhomogener Festkörper (DE-588)4225741-4 s Technische Mathematik (DE-588)4827059-3 s DE-604 Boutin, Claude Verfasser aut Geindreau, Christian Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Auriault, Jean-Louis Boutin, Claude Geindreau, Christian Homogenization of coupled phenomena in heterogenous media Mathematisches Modell Inhomogeneous materials Mathematical models Coupled problems (Complex systems) Homogenization (Differential equations) Inhomogener Festkörper (DE-588)4225741-4 gnd Technische Mathematik (DE-588)4827059-3 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd |
| subject_GND | (DE-588)4225741-4 (DE-588)4827059-3 (DE-588)4403079-4 |
| title | Homogenization of coupled phenomena in heterogenous media |
| title_alt | Homogénéisation de phénomènes couples en milieux hétérogènes |
| title_auth | Homogenization of coupled phenomena in heterogenous media |
| title_exact_search | Homogenization of coupled phenomena in heterogenous media |
| title_full | Homogenization of coupled phenomena in heterogenous media Jean-Louis Auriault, Claude Boutin, Christian Geindreau |
| title_fullStr | Homogenization of coupled phenomena in heterogenous media Jean-Louis Auriault, Claude Boutin, Christian Geindreau |
| title_full_unstemmed | Homogenization of coupled phenomena in heterogenous media Jean-Louis Auriault, Claude Boutin, Christian Geindreau |
| title_short | Homogenization of coupled phenomena in heterogenous media |
| title_sort | homogenization of coupled phenomena in heterogenous media |
| topic | Mathematisches Modell Inhomogeneous materials Mathematical models Coupled problems (Complex systems) Homogenization (Differential equations) Inhomogener Festkörper (DE-588)4225741-4 gnd Technische Mathematik (DE-588)4827059-3 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd |
| topic_facet | Mathematisches Modell Inhomogeneous materials Mathematical models Coupled problems (Complex systems) Homogenization (Differential equations) Inhomogener Festkörper Technische Mathematik Homogenisierung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650574&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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