Numerical simulation of waves and fronts in inhomogeneous solids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2008
|
| Schriftenreihe: | World Scientific series on nonlinear science
A ; 62 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 209-219) and index |
| Beschreibung: | xi, 223 p. ill. |
| ISBN: | 9789812832672 981283267X |
Internformat
MARC
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| 020 | |a 981283267X |c hardcover : alk. paper |9 981-283267-X | ||
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| 100 | 1 | |a Berezovski, Arkadi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical simulation of waves and fronts in inhomogeneous solids |c Arkadi Berezovski, Jüri Engelbrecht, Gérard A Maugin |
| 264 | 1 | |a Singapore |b World Scientific |c 2008 | |
| 300 | |a xi, 223 p. |b ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a World Scientific series on nonlinear science : A |v 62 | |
| 500 | |a Includes bibliographical references (p. 209-219) and index | ||
| 650 | 4 | |a Elastic solids | |
| 650 | 4 | |a Inhomogeneous materials | |
| 650 | 4 | |a Wave-motion, Theory of | |
| 700 | 1 | |a Engelbrecht, Jüri |d 1939- |e Sonstige |0 (DE-588)172063027 |4 oth | |
| 700 | 1 | |a Maugin, Gérard A. |e Sonstige |4 oth | |
| 830 | 0 | |a World Scientific series on nonlinear science |v A ; 62 |w (DE-604)BV009051753 |9 62 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018632926 | ||
Datensatz im Suchindex
| _version_ | 1804140704137478144 |
|---|---|
| adam_text | Titel: Numerical simulation of waves and fronts in inhomogeneous solids
Autor: Berezovski, Arkadi
Jahr: 2008
Contents
Preface v
1. Introduction 1
1.1 Waves and fronts....................... 1
1.2 True and quasi-inhomogeneities............... 2
1.3 Driving force and the corresponding dissipation...... 2
1.4 Example of a straight brittle crack............. 3
1.5 Example of a phase-transition front............. 4
1.6 Numerical simulations of moving discontinuities...... 5
1.7 Outline of the book...................... 7
2. Material Inhomogeneities in Thermomechanics 9
2.1 Kinematics.......................... 9
2.2 Integral balance laws..................... 11
2.3 Localization and jump relations............... 12
2.3.1 Local balance laws.................. 12
2.3.2 Jump relations.................... 13
2.3.3 Constitutive relations................ 14
2.4 True and quasi-material inhomogeneities.......... 14
2.4.1 Balance of pseudomomentum............ 15
2.5 Brittle fracture........................ 18
2.5.1 Straight brittle crack................ 20
2.6 Phase-transition fronts.................... 23
2.6.1 Jump relations.................... 23
2.6.2 Driving force..................... 24
viii Numerical Simulation of Waves and Fronts in Inhomogeneous Solids
2.7 On the exploitation of Eshelby s stress in isothermal and
adiabatic conditions..................... 26
2.7.1 Driving force at singular surface in adiabatic con-
ditions ........................ 28
2.7.2 Another approach to the driving force....... 29
2.8 Concluding remarks..................... 30
3. Local Phase Equilibrium and Jump Relations at Moving
Discontinuities 31
3.1 Intrinsic stability of simple systems............. 32
3.2 Local phase equilibrium................... 34
3.2.1 Classical equilibrium conditions.......... 34
3.2.2 Local equilibrium jump relations.......... 36
3.3 Non-equilibrium states.................... 38
3.4 Local equilibrium jump relations at discontinuity..... 39
3.5 Excess quantities at a moving discontinuity........ 41
3.6 Velocity of moving discontinuity .............. 43
3.7 Concluding remarks..................... 44
4. Linear Thermoelasticity 45
4.1 Local balance laws...................... 45
4.2 Balance of pseudomomentum................ 47
4.3 Jump relations........................ 47
4.4 Wave-propagation algorithm: an example of finite volume
methods............................ 48
4.4.1 One-dimensional elasticity............. 48
4.4.2 Averaged quantities................. 50
4.4.3 Numerical fluxes................... 51
4.4.4 Second order corrections.............. 52
4.4.5 Conservative wave propagation algorithm..... 52
4.5 Local equilibrium approximation.............. 53
4.5.1 Excess quantities and numerical fluxes ...... 53
4.5.2 Riemann problem.................. 55
4.5.3 Excess quantities at the boundaries between cells 56
4.6 Concluding remarks..................... 57
5. Wave Propagation in Inhomogeneous Solids 59
5.1 Governing equations..................... 60
Contents ix
5.2 One-dimensional waves in periodic media......... 60
5.3 One-dimensional weakly nonlinear waves in periodic media 62
5.4 One-dimensional linear waves in laminates......... 65
5.5 Nonlinear elastic wave in laminates under impact loading 68
5.5.1 Problem formulation................ 70
5.5.2 Comparison with experimental data........ 71
5.5.3 Discussion of results................. 77
5.6 Waves in functionally graded materials........... 80
5.7 Concluding remarks..................... 83
6. Macroscopic Dynamics of Phase-Transition Fronts 85
6.1 Isothermal impact-induced front propagation....... 87
6.1.1 Uniaxial motion of a slab.............. 88
6.1.2 Excess quantities in the bulk............ 90
6.1.3 Excess quantities at the phase boundary..... 91
6.1.4 Initiation criterion for the stress-induced phase
transformation.................... 93
6.1.5 Velocity of the phase boundary........... 97
6.2 Numerical simulations.................... 100
6.2.1 Algorithm description................ 100
6.2.2 Comparison with experimental data........ 100
6.3 Interaction of a plane wave with phase boundary..... 102
6.3.1 Pseudoelastic behavior............... 104
6.4 One-dimensional adiabatic fronts in a bar......... 109
6.4.1 Formulation of the problem............. 109
6.4.2 Adiabatic approximation.............. 112
6.4.3 Initiation criterion for the stress-induced phase
transformation in adiabatic case.......... 112
6.4.4 Velocity of the phase boundary........... 115
6.4.5 Temperature field.................. 117
6.5 Numerical simulations.................... 118
6.5.1 Pulse loading..................... 119
6.5.2 Temperature distribution.............. 120
6.5.3 Kinetic behavior................... 122
6.6 Concluding remarks..................... 125
7. Two-Dimensional Elastic Waves in Inhomogeneous Media 127
7.1 Governing equations..................... 128
x Numerical Simulation of Waves and Fronts in Inhomogeneous Solids
7.1.1 Averaged quantities................. 128
7.1.2 Conservation law .................. 129
7.2 Fluctuation splitting..................... 130
7.3 First-order Godunov scheme................. 133
7.4 Transverse propagation ................... 135
7.4.1 Vertical transverse propagation .......... 135
7.4.2 Horizontal transverse propagation......... 137
7.4.3 Boundary conditions ................ 139
7.5 Numerical tests........................ 139
7.6 Concluding remarks..................... 145
8. Two-Dimensional Waves in Functionally Graded Materials 147
8.1 Impact loading of a plate .................. 147
8.2 Material properties...................... 149
8.3 Numerical simulations.................... 151
8.4 Centreline stress distribution................ 153
8.5 Wave interaction with functionally graded inclusion ... 155
8.6 Concluding remarks..................... 157
9. Phase Transitions Fronts in Two Dimensions 161
9.1 Material velocity at the phase boundary.......... 161
9.2 Numerical procedure..................... 163
9.3 Interaction of a non-plane wave with phase boundary . . . 164
9.4 Wave interaction with martensitic inclusion........ 166
9.5 Concluding remarks..................... 168
10. Dynamics of a Straight Brittle Crack 171
10.1 Formulation of the problem................. 172
10.2 Stationary crack under impact load............. 173
10.3 Jump relations at the crack front.............. 175
10.4 Velocity of the crack in mode I............... 176
10.4.1 Zero excess stress.................. 178
10.4.2 Non-zero excess stress................ 179
10.5 Concluding remarks..................... 182
11. Summing Up 185
Appendix A Thermodynamic interaction between two dis-
crete systems in non-equilibrium 189
Contents xi
A.I Equilibrium/non-equilibrium contacts........... 190
A.I.I Contact quantities.................. 190
A.1.2 Partial contact quantities.............. 193
A.2 Interacting non-equilibrium systems............ 195
A.2.1 Replacement quantities............... 195
A.2.2 Composite systems................. 197
A.3 Compound deficiency..................... 200
A.3.1 The inequalities................... 200
A.3.2 Energy and entropy................. 201
A.3.3 Example: An endoreversible system........ 203
A.3.4 Excess quantities .................. 205
A.4 Concluding remarks..................... 206
Bibliography 209
Index 221
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:12Z |
| institution | BVB |
| isbn | 9789812832672 981283267X |
| language | English |
| lccn | 2008015670 |
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| physical | xi, 223 p. ill. |
| publishDate | 2008 |
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| publisher | World Scientific |
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| series | World Scientific series on nonlinear science |
| series2 | World Scientific series on nonlinear science : A |
| spelling | Berezovski, Arkadi Verfasser aut Numerical simulation of waves and fronts in inhomogeneous solids Arkadi Berezovski, Jüri Engelbrecht, Gérard A Maugin Singapore World Scientific 2008 xi, 223 p. ill. txt rdacontent n rdamedia nc rdacarrier World Scientific series on nonlinear science : A 62 Includes bibliographical references (p. 209-219) and index Elastic solids Inhomogeneous materials Wave-motion, Theory of Engelbrecht, Jüri 1939- Sonstige (DE-588)172063027 oth Maugin, Gérard A. Sonstige oth World Scientific series on nonlinear science A ; 62 (DE-604)BV009051753 62 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018632926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berezovski, Arkadi Numerical simulation of waves and fronts in inhomogeneous solids World Scientific series on nonlinear science Elastic solids Inhomogeneous materials Wave-motion, Theory of |
| title | Numerical simulation of waves and fronts in inhomogeneous solids |
| title_auth | Numerical simulation of waves and fronts in inhomogeneous solids |
| title_exact_search | Numerical simulation of waves and fronts in inhomogeneous solids |
| title_full | Numerical simulation of waves and fronts in inhomogeneous solids Arkadi Berezovski, Jüri Engelbrecht, Gérard A Maugin |
| title_fullStr | Numerical simulation of waves and fronts in inhomogeneous solids Arkadi Berezovski, Jüri Engelbrecht, Gérard A Maugin |
| title_full_unstemmed | Numerical simulation of waves and fronts in inhomogeneous solids Arkadi Berezovski, Jüri Engelbrecht, Gérard A Maugin |
| title_short | Numerical simulation of waves and fronts in inhomogeneous solids |
| title_sort | numerical simulation of waves and fronts in inhomogeneous solids |
| topic | Elastic solids Inhomogeneous materials Wave-motion, Theory of |
| topic_facet | Elastic solids Inhomogeneous materials Wave-motion, Theory of |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018632926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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