Flow, deformation and fracture: lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2014
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 255 S. Ill., graph. Darst. |
| ISBN: | 9780521887526 9780521715386 |
Staff View
MARC
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| 245 | 1 | 0 | |a Flow, deformation and fracture |b lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |c Grigory Isaakovich Barenblatt |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2014 | |
| 300 | |a XIX, 255 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Fluid mechanics / Textbooks | |
| 650 | 4 | |a Deformations (Mechanics) / Textbooks | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
џ
Foreword page
xi
Preface
xiii
Introduction
1
Idealized continuous media: the basic concepts
10
1.1
The idealized model of a continuous medium
10
1.2
Properties of a continuum and its motion. Density, flux and
velocity. Law of mass balance
18
1.3
Law of momentum balance. Stress tensor
24
Dimensional analysis and physical similitude
29
2.1
Examples
29
2.2
Dimensional analysis
37
2.3
Physical similitude
40
2.4
Examples. Classical parameters of similitude
43
The ideal incompressible fluid approximation: general concepts
and relations
48
3.1
The fundamental idealization (model).
Euler
equations
48
3.2
Decomposition of the velocity field in the vicinity of an
arbitrary point. The vorticity. The strain-rate tensor
51
3.3
Irrotational motions. Lagrange s theorem. Potential flows
53
3.4
Lagrange-Cauchy integral. Bernoulli integral
56
3.5
Plane potential motions of an ideal incompressible fluid
58
The ideal incompressible fluid approximation: analysis
and applications
63
4.1
Physical meaning of the velocity potential. The Lavrentiev
problem of a directed explosion
63
4.2
Lift force on a wing
66
viii Contents
5
The linear elastic solid approximation. Basic equations
and boundary value problems in the linear theory
of elasticity
79
5.1
The fundamental idealization
79
5.2
Basic equations and boundary conditions of the linear
theory of elasticity
86
5.3
Plane problem in the theory of elasticity
89
5.4
Analytical solutions of some special problems in
plane elasticity
95
6
The linear elastic solid approximation. Applications:
brittle and quasi-brittle fracture; strength of structures
101
6.1
The problem of structural integrity
101
6.2
Defects and cracks
102
6.3
Cohesion crack model
109
6.4
What is fracture from the mathematical viewpoint?
113
6.5
Time effects; lifetime of a structure; fatigue
119
7
The Newtonian viscous fluid approximation. General
comments and basic relations
124
7.1
The fundamental idealization. The Navier-Stokes equations
124
7.2
Angular momentum conservation law
128
7.3
Boundary value and initial value problems for the Newtonian
viscous incompressible fluid approximation. Smoothness of
the solutions
129
7.4
The viscous dissipation of mechanical energy into heat
135
8
The Newtonian viscous fluid approximation. Applications:
the boundary layer
137
8.1
The drag on a moving wing.
Friedrichs
example
137
8.2
Model of the boundary layer at a thin weakly inclined wing
of infinite span
140
8.3
The boundary layer on a flat plate
143
9
Advanced similarity methods: complete and incomplete
similarity
150
9.1
Examples
150
9.2
Complete and incomplete similarity
153
9.3
Self-similar solutions of the first and second kind
157
9.4
incomplete similarity in fatigue experiments
(Paris law)
158
9.5
A note concerning scaling laws in nanomechanics
161
Contents
ix
10
The ideal gas approximation. Sound waves; shock waves
164
10.1
Soundwaves
164
10.2
Energy equation. The basic equations of the ideal gas model
167
10.3
Simple waves. The formation of shock waves
168
10.4
An intense explosion at a plane interface: the external
intermediate asymptotics
171
10.5
An intense explosion at a plane interface: the internal
intermediate asymptotics
173
11
Turbulence:
generalities; scaling laws for shear flows
182
11.1
Kolmogorov s example
185
11.2
The Reynolds equation, Reynolds stress
187
11.3
Turbulent shear flow
189
11.4
Scaling laws for turbulent flows at very large
Reynolds numbers. Flow in pipes
190
11.5
Turbulent flow in pipes at very large Reynolds numbers:
advanced similarity analysis
195
11.6
Reynolds-number dependence of the drag in pipes
following from the power law
201
11.7
Further comparison of the Reynolds-number-dependent
scaling law and the universal logarithmic law
204
11.8
Modification of the Izakson-Millikan-von
Mises
analysis
of the flow in the intermediate region
208
11.9
Further comparison of scaling laws with experimental data
211
11.10
Scaling laws for turbulent boundary layers
219
12
Turbulence: mathematical models of turbulent shear flows
and of the local structure of turbulent flows at very large
Reynolds numbers
225
12.1
Basic equations for wall-bounded turbulent shear flows.
Wai] region
225
12.2
Kolmogorov-Prandtl semi-empirical model for the wall
region of a shear flow
227
12.3
A model for drag reduction by polymeric additives
230
12.4
The local structure of turbulent flows at very large
Reynolds numbers
234
Bibliography and References
243
Index
253
Over
40
years of teaching experience are distilled into this text. The guiding principle is the
wide use of the concept of intermediate asymptotics, which enables the natural introduction of
the modeling of real bodies by
continua.
Beginning with a detailed explanation of the continuum approximation for the mathematical
modeling of the motion and equilibrium of real bodies, the author continues with a general
survey of the necessary methods and tools for analyzing models. Next, specific idealized
approximations are presented, including ideal incompressible fluids, elastic bodies and
Newtonian viscous fluids. The author not only presents general concepts, but also devotes
chapters to examining significant problems, including turbulence, wave propagation, defects
and cracks, fatigue and fracture. Each of these applications reveals essential information about
the particular approximation.
The author s tried and tested approach reveals insights that
wili
be valued by every teacher
and student of mechanics.
Those not fortunate enough to have been able to attend the course now have the opportunity
to see what has made it so special. The present book is a masterful exposition of fluid and
solid mechanics, informed by the ideas of scaling and intermediate asymptotics, a methodology
and point of view of which Professor Barenbiatt is one of the originators
...
This is indeed a
remarkable book.
Alexandre J.
Chorin,
Foreword
G.
I. Barenbiatt is Emeritus G.I. Taylor Professor of Fluid Mechanics at the University of
Cambridge, Emeritus Professor at the University of California, Berkeley, and Principal Scientist
in the Institute of Oceanology of the Russian Academy of Sciences, Moscow.
CAMBRIDGE TEXTS IN APPLIED MATHEMATICS
EDITORIAL BOARD
Professor
M. J.
Ablowitz, Department of Applied Mathematics, University of
Colorado, Boulder, USA
Professor S. Davis,
Schooi
of Engineering Sciences
&
Applied Mathematics,
Northwestern University, USA
Professor
E. J. H i
neh,
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, UK
Professor A. I
seri
es,
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, UK
Dr
J.
Oc
kendőn,
Mathematical Institute, University of Oxford, UK
Professor P. J. Olver, School of Mathematics, University of Minnesota, USA
The aim of this series is to provide a focus for publishing textbooks in applied
mathematics at the advanced undergraduate and beginning graduate level. It is
planned that the books will be devoted to covering certain mathematical techniques
and theories and exploring their applications.
|
| any_adam_object | 1 |
| author | Barenblatt, Grigorij I. 1927-2018 |
| author_GND | (DE-588)128640677 |
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| author_role | aut |
| author_sort | Barenblatt, Grigorij I. 1927-2018 |
| author_variant | g i b gi gib |
| building | Verbundindex |
| bvnumber | BV041969396 |
| classification_rvk | SK 950 UF 1500 UF 4000 |
| ctrlnum | (OCoLC)886688522 (DE-599)BVBBV041969396 |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV041969396 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:09:30Z |
| institution | BVB |
| isbn | 9780521887526 9780521715386 |
| language | English |
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| spelling | Barenblatt, Grigorij I. 1927-2018 Verfasser (DE-588)128640677 aut Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists Grigory Isaakovich Barenblatt 1. publ. Cambridge Cambridge Univ. Press 2014 XIX, 255 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fluid mechanics / Textbooks Deformations (Mechanics) / Textbooks Fracture mechanics / Textbooks Deformations (Mechanics) fast Fluid mechanics fast Fracture mechanics fast Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Festkörpermechanik (DE-588)4129367-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027412061&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027412061&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Barenblatt, Grigorij I. 1927-2018 Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists Fluid mechanics / Textbooks Deformations (Mechanics) / Textbooks Fracture mechanics / Textbooks Deformations (Mechanics) fast Fluid mechanics fast Fracture mechanics fast Festkörpermechanik (DE-588)4129367-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4129367-8 (DE-588)4077970-1 |
| title | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |
| title_auth | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |
| title_exact_search | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |
| title_full | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists Grigory Isaakovich Barenblatt |
| title_fullStr | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists Grigory Isaakovich Barenblatt |
| title_full_unstemmed | Flow, deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists Grigory Isaakovich Barenblatt |
| title_short | Flow, deformation and fracture |
| title_sort | flow deformation and fracture lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |
| title_sub | lectures on fluid mechanics and the mechanics of deformable solids for mathematicians and physicists |
| topic | Fluid mechanics / Textbooks Deformations (Mechanics) / Textbooks Fracture mechanics / Textbooks Deformations (Mechanics) fast Fluid mechanics fast Fracture mechanics fast Festkörpermechanik (DE-588)4129367-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Fluid mechanics / Textbooks Deformations (Mechanics) / Textbooks Fracture mechanics / Textbooks Deformations (Mechanics) Fluid mechanics Fracture mechanics Festkörpermechanik Strömungsmechanik |
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