Mathematical theory of elasticity of quasicrystals and its applications
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2011
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| 245 | 1 | 0 | |a Mathematical theory of elasticity of quasicrystals and its applications |c Tianyou Fan |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2011 | |
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Datensatz im Suchindex
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CONTENTS
PREFACE CHAPTER 1 CRYSTALS 1
1.1 PERIODICITY OF CRYSTAL STRUCTURE, CRYSTAL CELL 1
1.2 THREE-DIMENSIONAL LATTICE TYPES 1
1.3 SYMMETRY AND POINT GROUPS 3
1.4 RECIPROCAL LATTICE 5
1.5 APPENDIX OF CHAPTER 1: SOME BASIC CONCEPTS 6
REFERENCES 10
CHAPTER 2 FRAMEWORK OF THE CLASSICAL THEORY OF ELASTICITY 13
2.1 REVIEW ON SOME BASIC CONCEPTS 13
2.2 BASIC ASSUMPTIONS OF THEORY OF ELASTICITY 16
2.3 DISPLACEMENT AND DEFORMATION 17
2.4 STRESS ANALYSIS AND EQUATIONS OF MOTION 18
2.5 GENERALIZED HOOKE S LAW 19
2.6 ELASTODYNAMICS, WAVE MOTION 23
2.7 SUMMARY 23
REFERENCES 24
CHAPTER 3 QUASICRYSTAL AND ITS PROPERTIES 25
3.1 DISCOVERY OF QUASICRYSTAL 25
3.2 STRUCTURE AND SYMMETRY OF QUASICRYSTALS 27
3.3 A BRIEF INTRODUCTION ON PHYSICAL PROPERTIES OF QUASICRYSTALS 29 3.4
ONE-, TWO- AND THREE-DIMENSIONAL QUASICRYSTALS 30
3.5 TWO-DIMENSIONAL QUASICRYSTALS AND PLANAR QUASICRYSTALS 30
REFERENCES 30
CHAPTER 4 THE PHYSICAL BASIS OF ELASTICITY OF QUASICRYSTALS 35
4.1 PHYSICAL BASIS OF ELASTICITY OF QUASICRYSTALS 35
4.2 DEFORMATION TENSORS 36
4.3 STRESS TENSORS AND THE EQUATIONS OF MOTION 38
4.4 FREE ENERGY AND ELASTIC CONSTANTS 40
4.5 GENERALIZED HOOKE S LAW 42
4.6 BOUNDARY CONDITIONS AND INITIAL CONDITIONS 42
4.7 A BRIEF INTRODUCTION ON RELEVANT MATERIAL CONSTANTS OF QUASICRYSTALS
43 4.8 SUMMARY AND MATHEMATICAL SOLVABILITY OF BOUNDARY VALUE OR
INITIAL-
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1003791263
DIGITALISIERT DURCH
IMAGE 2
VIA CONTENTS
BOUNDARY VALUE PROBLEM 44
4.9 APPENDIX OF CHAPTER 4: DESCRIPTION ON PHYSICAL BASIS OF ELASTICITY
OF QUASICRYSTALS BASED ON THE LANDAU DENSITY WAVE THEORY 46 REFERENCES
50
CHAPTER 5 ELASTICITY THEORY OF ONE-DIMENSIONAL QUASICRYSTALS AND
SIMPLIFICATION 53
5.1 ELASTICITY OF HEXAGONAL QUASICRYSTALS 54
5.2 DECOMPOSITION OF THE PROBLEM INTO PLANE AND ANTI-PLANE PROBLEMS 56
5.3 ELASTICITY OF MONOCLINIC QUASICRYSTALS 58
5.4 ELASTICITY OF ORTHORHOMBIC QUASICRYSTALS 61
5.5 TETRAGONAL QUASICRYSTALS 62
5.6 THE SPACE ELASTICITY OF HEXAGONAL QUASICRYSTALS 63
5.7 OTHER RESULTS OF ELASTICITY OF ONE-DIMENSIONAL QUASICRYSTALS 65
REFERENCES 65
CHAPTER 6 ELASTICITY OF TWO-DIMENSIONAL QUASICRYSTALS AND SIMPLIFICATION
67
6.1 BASIC EQUATIONS OF PLANE ELASTICITY OF TWO-DIMENSIONAL
QUASICRYSTALS: POINT GROUPS 5M AND 10MM IN FIVE- AND TEN-FOLD SYMMETRIES
71 6.2 SIMPLIFICATION OF THE BASIC EQUATION SET: DISPLACEMENT POTENTIAL
FUNCTION METHOD 76
6.3 SIMPLIFICATION OF THE BASIC EQUATIONS SET: STRESS POTENTIAL FUNCTION
METHOD 79
6.4 PLANE ELASTICITY OF POINT GROUP 5, 5 PENTAGONAL AND POINT GROUP 10,
10 DECAGONAL QUASICRYSTALS 81
6.5 PLANE ELASTICITY OF POINT GROUP 12MM OF DODECAGONAL QUASICRYSTALS 85
6.6 PLANE ELASTICITY OF POINT GROUP 8MM OF OCTAGONAL QUASICRYSTALS,
DISPLACEMENT POTENTIAL 89
6.7 STRESS POTENTIAL OF POINT GROUP 5,5 PENTAGONAL AND POINT GROUP 10,
10 DECAGONAL QUASICRYSTALS 94
6.8 STRESS POTENTIAL OF POINT GROUP 8MM OCTAGONAL QUASICRYSTALS 95 6.9
ENGINEERING AND MATHEMATICAL ELASTICITY OF QUASICRYSTALS 98 REFERENCES *
101
CHAPTER 7 APPLICATION I: SOME DISLOCATION AND INTERFACE PROBLEMS AND
SOLUTIONS IN ONE- AND TWO-DIMENSIONAL QUASICRYSTALS - 103 7.1
DISLOCATIONS IN ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS 104 7.2
DISLOCATIONS IN QUASICRYSTALS WITH POINT GROUPS 5M AND 10MM
SYMMETRIES 106
7.3 DISLOCATIONS IN QUASICRYSTALS WITH POINT GROUPS 5,5 FIVE-FOLD AND
10,
IMAGE 3
CONTENTS IX
10 TEN-FOLD SYMMETRIES 112
7.4 DISLOCATIONS IN QUASICRYSTALS WITH EIGHT-FOLD SYMMETRY 117
7.5 DISLOCATIONS IN DODECAGONAL QUASICRYSTALS 120
7.6 INTERFACE BETWEEN QUASICRYSTAL AND CRYSTAL 120
7.7 CONCLUSION AND DISCUSSION 124
REFERENCES 124
CHAPTER 8 APPLICATION II: SOLUTIONS OF NOTCH AND CRACK PROBLEMS OF
ONE-AND TWO-DIMENSIONAL QUASICRYSTALS 127
8.1 CRACK PROBLEM AND SOLUTION OF ONE-DIMENSIONAL QUASICRYSTALS 128 8.2
CRACK PROBLEM IN FINITE-SIZED ONE-DIMENSIONAL QUASICRYSTALS 134 8.3
GRIFFITH CRACK PROBLEMS IN POINT GROUPS 5M AND 10MM QUASICRYSTALS BASED
ON DISPLACEMENT POTENTIAL FUNCTION METHOD 139
8.4 STRESS POTENTIAL FUNCTION FORMULATION AND COMPLEX VARIABLE FUNCTION
METHOD FOR SOLVING NOTCH AND CRACK PROBLEMS OF QUASICRYSTALS OF POINT
GROUPS 5, 5 AND 10, 10 145
8.5 SOLUTIONS OF CRACK/NOTCH PROBLEMS OF TWO-DIMENSIONAL OCTAGONAL
QUASICRYSTALS 152
8.6 OTHER SOLUTIONS OF CRACK PROBLEMS IN ONE-AND TWO-DIMENSIONAL
QUASICRYSTALS 153
8.7 APPENDIX OF CHAPTER 8: DERIVATION OF SOLUTION OF SECTION 8.1 154
REFERENCES 156
CHAPTER 9 THEORY OF ELASTICITY OF THREE-DIMENSIONAL QUASICRYSTALS AND
ITS APPLICATIONS 159
9.1 BASIC EQUATIONS OF ELASTICITY OF ICOSAHEDRAL QUASICRYSTALS 160 9.2
ANTI-PLANE ELASTICITY OF ICOSAHEDRAL QUASICRYSTALS AND PROBLEM OF
INTERFACE BETWEEN QUASICRYSTAL AND CRYSTAL 164
9.3 PHONON-PHASON DECOUPLED PLANE ELASTICITY OF ICOSAHEDRAL
QUASICRYSTALS 168
9.4 PHONON-PHASON COUPLED PLANE ELASTICITY OF ICOSAHEDRAL QUASICRYSTALS-
DISPLACEMENT POTENTIAL FORMULATION 169
9.5 PHONON-PHASON COUPLED PLANE ELASTICITY OF ICOSAHEDRAL QUASICRYSTALS-
STRESS POTENTIAL FORMULATION 172
9.6 A STRAIGHT DISLOCATION IN AN ICOSAHEDRAL QUASICRYSTAL 173
9.7 AN ELLIPTIC NOTCH/GRIFFITH CRACK IN AN ICOSAHEDRAL QUASICRYSTAL 178
9.8 ELASTICITY OF CUBIC QUASICRYSTALS-THE ANTI-PLANE AND AXISYMMETRIC
DEFORMATION 185
IMAGE 4
X CONTENTS
REFERENCES 189
CHAPTER 10 DYNAMICS OF ELASTICITY AND DEFECTS OF QUASICRYSTALS 191 10.1
ELASTODYNAMICS OF QUASICRYSTALS FOLLOWED THE BAK S ARGUMENT 192 10.2
ELASTODYNAMICS OF ANTI-PLANE ELASTICITY FOR SOME QUASICRYSTALS 192 10.3
MOVING SCREW DISLOCATION IN ANTI-PLANE ELASTICITY 194
10.4 MODE III MOVING GRIFFITH CRACK IN ANTI-PLANE ELASTICITY 197
10.5 ELASTO-/HYDRO-DYNAMICS OF QUASICRYSTALS AND APPROXIMATE ANALYTIC
SOLUTION FOR MOVING SCREW DISLOCATION IN ANTI-PLANE ELASTICITY 199 10.6
ELASTO-/HYDRO-DYNAMICS AND SOLUTIONS OF TWO-DIMENSIONAL DECAGONAL
QUASICRYSTALS 206
10.7 ELASTO-/HYDRO-DYNAMICS AND APPLICATIONS TO FRACTURE DYNAMICS OF
ICOSAHEDRAL QUASICRYSTALS 216
10.8 APPENDIX OF CHAPTER 10: THE DETAIL OF FINITE DIFFERENCE SCHEME 221
REFERENCES 225
CHAPTER 11 COMPLEX VARIABLE FUNCTION METHOD FOR ELASTICITY OF
QUASICRYSTALS 229
11.1 HARMONIC AND QUASI-BIHARMONIC EQUATIONS IN ANTI-PLANE ELASTICITY OF
ONE-DIMENSIONAL QUASICRYSTALS 230
11.2 BIHARMONIC EQUATIONS IN PLANE ELASTICITY OF POINT GROUP 12MM TWO-
DIMENSIONAL QUASICRYSTALS 230
11.3 THE COMPLEX VARIABLE FUNCTION METHOD OF QUADRUPLE HARMONIC
EQUATIONS AND APPLICATIONS IN TWO-DIMENSIONAL QUASICRYSTALS 231 11.4
COMPLEX VARIABLE FUNCTION METHOD FOR SEXTUPLE HARMONIC EQUATION AND
APPLICATIONS TO ICOSAHEDRAL QUASICRYSTALS 243
11.5 COMPLEX ANALYSIS AND SOLUTION OF QUADRUPLE QUASIHARMONIC EQUATION
253
11.6 CONCLUSION AND DISCUSSION 254
REFERENCES 255
CHAPTER 12 VARIATIONAL PRINCIPLE OF ELASTICITY OF QUASICRYSTALS,
NUMERICAL ANALYSIS AND APPLICATIONS 257
12.1 BASIC RELATIONS OF PLANE ELASTICITY OF TWO-DIMENSIONAL
QUASICRYSTALS 258 12.2 GENERALIZED VARIATIONAL PRINCIPLE FOR STATIC
ELASTICITY OF QUASICRYSTALS 259 12.3 FINITE ELEMENT METHOD * * * 263
12.4 NUMERICAL EXAMPLES 267
REFERENCES * 272
CHAPTER 13 SOME MATHEMATICAL PRINCIPLES ON SOLUTIONS OF ELASTICITY OF
QUASICRYSTALS 273
13.1 UNIQUENESS OF SOLUTION OF ELASTICITY OF QUASICRYSTALS 273
IMAGE 5
CONTENTS XI
13.2 GENERALIZED LAX-MILGRAM THEOREM 275
13.3 MATRIX EXPRESSION OF ELASTICITY OF THREE-DIMENSIONAL QUASICRYSTALS
278 13.4 THE WEAK SOLUTION OF BOUNDARY VALUE PROBLEM OF ELASTICITY OF
QUASICRYSTALS 282
13.5 THE UNIQUENESS OF WEAK SOLUTION 283
13.6 CONCLUSION AND DISCUSSION 286
REFERENCES 286
CHAPTER 14 NONLINEAR BEHAVIOUR OF QUASICRYSTALS 289
14.1 MACROSCOPIC BEHAVIOUR OF PLASTIC DEFORMATION OF QUASICRYSTALS 290
14.2 POSSIBLE SCHEME OF PLASTIC CONSTITUTIVE EQUATIONS 292
14.3 NONLINEAR ELASTICITY AND ITS FORMULATION 294
14.4 NONLINEAR SOLUTIONS BASED ON SIMPLE MODELS 295
14.5 NONLINEAR ANALYSIS BASED ON THE GENERALIZED ESHELBY THEORY 301 14.6
NONLINEAR ANALYSIS BASED ON THE DISLOCATION MODEL 305
14.7 CONCLUSION AND DISCUSSION 309
14.8 APPENDIX OF CHAPTER 14: SOME MATHEMATICAL DETAILS 309
REFERENCES 314
CHAPTER 15 FRACTURE THEORY OF QUASICRYSTALS 317
15.1 LINEAR FRACTURE THEORY OF QUASICRYSTALS 317
15.2 MEASUREMENT OF G W 320
15.3 NONLINEAR FRACTURE MECHANICS 322
15.4 DYNAMIC FRACTURE 323
15.5 MEASUREMENT OF FRACTURE TOUGHNESS AND RELEVANT MECHANICAL
PARAMETERS OF QUASICRYSTALLINE MATERIAL 325
REFERENCES 327
CHAPTER 16 REMARKABLE CONCLUSION 329
REFERENCES 330
MAJOR APPENDIX: ON SOME MATHEMATICAL MATERIALS 333
APPENDIX I OUTLINE OF COMPLEX VARIABLE FUNCTIONS AND SOME ADDITIONAL
CALCULATIONS 333
A.I.I COMPLEX FUNCTIONS, ANALYTIC FUNCTIONS 334
A.I.2 CAUCHY S FORMULA 335
A.I.3 POLES 337
A.I.4 RESIDUE THEOREM 337
A.I.5 ANALYTIC EXTENSION 340
A.I.6 CONFORMAL MAPPING 340
A.I.7 ADDITIONAL DERIVATION OF SOLUTION (8.2-19) 341
A.I.8 ADDITIONAL DERIVATION OF SOLUTION (11.3-53) 342
IMAGE 6
XII CONTENTS
A.I.9 DETAIL OF COMPLEX ANALYSIS OF GENERALIZED COHESIVE FORCE MODEL FOR
PLANE ELASTICITY OF TWO-DIMENSIONAL POINT GROUPS 5M, 10MM AND 10, 10
QUASICRYSTALS 345
A.I.10 ON THE CALCULATION OF INTEGRAL (9.2-14) 347
APPENDIX II DUAL INTEGRAL EQUATIONS AND SOME ADDITIONAL CALCULATIONS 348
A.II.L DUAL INTEGRAL EQUATIONS 348
A.II.2 ADDITIONAL DERIVATION ON THE SOLUTION OF DUAL INTEGRAL EQUATIONS
(8.3-8) 353
A.II.3 ADDITIONAL DERIVATION ON THE SOLUTION OF DUAL INTEGRAL EQUATIONS
(9.8-8) 355
REFERENCES 357
I N D EX 359
|
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| id | DE-604.BV037280914 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T00:22:01Z |
| institution | BVB |
| isbn | 9783642146428 9787030256690 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021193720 |
| oclc_num | 724185942 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XII, 363 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Fan, Tianyou Mathematical theory of elasticity of quasicrystals and its applications Elastizitätstheorie (DE-588)4123124-7 gnd Quasikristall (DE-588)4202613-1 gnd |
| subject_GND | (DE-588)4123124-7 (DE-588)4202613-1 |
| title | Mathematical theory of elasticity of quasicrystals and its applications |
| title_auth | Mathematical theory of elasticity of quasicrystals and its applications |
| title_exact_search | Mathematical theory of elasticity of quasicrystals and its applications |
| title_full | Mathematical theory of elasticity of quasicrystals and its applications Tianyou Fan |
| title_fullStr | Mathematical theory of elasticity of quasicrystals and its applications Tianyou Fan |
| title_full_unstemmed | Mathematical theory of elasticity of quasicrystals and its applications Tianyou Fan |
| title_short | Mathematical theory of elasticity of quasicrystals and its applications |
| title_sort | mathematical theory of elasticity of quasicrystals and its applications |
| topic | Elastizitätstheorie (DE-588)4123124-7 gnd Quasikristall (DE-588)4202613-1 gnd |
| topic_facet | Elastizitätstheorie Quasikristall |
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