Configurational forces as basic concepts of continuum physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Schriftenreihe: | Applied mathematical sciences
137 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 239 - 245 |
| Beschreibung: | XIII, 249 S. graph. Darst. |
| ISBN: | 0387986677 9781475774030 |
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Datensatz im Suchindex
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| adam_text | MORTON E. GURTIN CONFIGURATIONAL FORCES AS BASIC CONCEPTS OF CONTINUUM
PHYSICS SPRINGER CONTENTS 1. INTRODUCTION 1 A. BACKGROUND 1 B.
VARIATIONAL DEFINITION OF CONFIGURATIONAL FORCES 2 * INTERFACIAL ENERGY.
A FURTHER ARGUMENT FOR A CONFIGURATIONAL FORCE BALANCE 5 D.
CONFIGURATIONAL FORCES AS BASIC OBJECTS 7 E. THE NATURE OF
CONFIGURATIONAL FORCES 9 F. CONFIGURATIONAL STRESS AND RESIDUAL STRESS.
INTERNAL CONFIGURATIONAL FORCES 10 G. CONFIGURATIONAL FORCES AND
INDETERMINACY 11 H. SCOPE OF THE BOOK 12 I. ON OPERATIONAL DEFINITIONS
AND MATHEMATICS 12 J. GENERAL NOTATION. TENSOR ANALYSIS 13 JL. ON DIRECT
NOTATION 13 J2. VECTORS AND TENSORS. FIELDS 13 J3. THIRD-ORDER TENSORS
(3-TENSORS). THE OPERATION T : * . . 15 J4. FUNCTIONS OF TENSORS 16 A.
CONFIGURATIONAL FORCES WITHIN A CLASSICAL CONTEXT 19 2. KINEMATICS 21 A.
REFERENCE BODY. MATERIAL POINTS. MOTIONS 21 B. MATERIAL AND SPATIAL
VECTORS. THE SETS % *** * AND GATTER 22 C. MATERIAL AND SPATIAL
OBSERVERS 23 D. CONSISTENCY REQUIREMENT. OBJECTIVE FIELDS 23 VIII
CONTENTS 3. STANDARD FORCES. WORKING 25 A. FORCES 25 B. WORKING.
STANDARD FORCE AND MOMENT BALANCES AS CONSEQUENCES OF INVARIANCE UNDER
CHANGES IN SPATIAL OBSERVER 26 4. MIGRATING CONTROL VOLUMES. STATIONARY
AND TIME-DEPENDENT CHANGES IN REFERENCE CONFIGURATION 29 A. MIGRATING
CONTROL VOLUMES P * P(T). VELOCITY FIELDS FOR DP(T) AND DP(T ) 29 B.
CHANGE IN REFERENCE CONFIGURATION 31 BL. STATIONARY CHANGE IN REFERENCE
CONFIGURATION 31 B2. TIME-DEPENDENT CHANGE IN REFERENCE CONFIGURATION
... 32 5. CONFIGURATIONAL FORCES 34 A. CONFIGURATIONAL FORCES 34 B.
WORKING REVISITED 35 * CONFIGURATIONAL FORCE BALANCE AS A CONSEQUENCE OF
INVARIANCE UNDER CHANGES IN MATERIAL OBSERVER 36 D. INVARIANCE UNDER
CHANGES IN VELOCITY FIELD FOR DP(T). CONFIGURATIONAL STRESS RELATION 37
E. INVARIANCE UNDER TIME-DEPENDENT CHANGES IN REFERENCE. EXTERNAL AND
INTERNAL FORCE RELATIONS 38 F. STANDARD AND CONFIGURATIONAL FORMS OF THE
WORKING. POWER BALANCE 39 6. THERMODYNAMICS. RELATION BETWEEN BULK
TENSION AND ENERGY. ESHELBY IDENTITY 41 A. MECHANICAL VERSION OF THE
SECOND LAW 41 B. ESHELBY RELATION AS A CONSEQUENCE OF THE SECOND LAW 42
* THERMOMECHANICAL THEORY 44 D. FLUIDS. CURRENT CONFIGURATION AS
REFERENCE 45 7. INERTIA AND KINETIC ENERGY. ALTERNATIVE VERSIONS OF THE
SECOND LAW 46 A. INERTIA AND KINETIC ENERGY 46 B. ALTERNATIVE FORMS OF
THE SECOND LAW 47 * PSEUDOMOMENTUM 47 D. LYAPUNOV RELATIONS 48 8. CHANGE
IN REFERENCE CONFIGURATION 50 A. TRANSFORMATION LAWS FOR FREE ENERGY AND
STANDARD FORCE .... 50 B. TRANSFORMATION LAWS FOR CONFIGURATIONAL FORCE
51 9. ELASTIC AND THERMOELASTIC MATERIALS 53 A. MECHANICAL THEORY 54 AL.
BASIC EQUATIONS 54 CONTENTS IX A2. CONSTITUTIVE THEORY 54 B.
THERMOMECHANICAL THEORY 56 BL. BASIC EQUATIONS 56 *2. CONSTITUTIVE
THEORY 57 B. THE USE OF CONFIGURATIONAL FORCES TO CHARACTERIZE COHERENT
PHASE INTERFACES 61 10. INTERFACE KINEMATICS 63 11. INTERFACE FORCES.
SECOND LAW 66 A. INTERFACE FORCES 66 B. WORKING 67 * STANDARD AND
CONFIGURATIONAL FORCE BALANCES AT THE INTERFACE . . 68 D. INVARIANCE
UNDER CHANGES IN VELOCITY FIELD FOR Y(T). NORMAL CONFIGURATIONAL BALANCE
69 E. POWER BALANCE. INTERNAL WORKING 70 F. SECOND LAW. INTERNAL
DISSIPATION INEQUALITY FOR THE INTERFACE . . 71 G. LOCALIZATIONS USING A
PILLBOX ARGUMENT 72 12. INERTIA. BASIC EQUATIONS FOR THE INTERFACE 74 A.
RELATIVE KINETIC ENERGY 74 B. DETERMINATION OF B Y AND E Y 75 * STANDARD
AND CONFIGURATIONAL BALANCES WITH INERTIA 77 D. CONSTITUTIVE EQUATION
FOR THE INTERFACE 78 E. SUMMARY OF BASIC EQUATIONS 79 F. GLOBAL ENERGY
INEQUALITY. LYAPUNOV RELATIONS 80 C. AN EQUIVALENT FORMULATION OF THE
THEORY. INFINITESIMAL DEFORMATIONS 81 13. FORMULATION WITHIN A CLASSICAL
CONTEXT 83 A. BACKGROUND. REASON FOR AN ALTERNATIVE FORMULATION IN TERMS
OF DISPLACEMENTS 83 B. FINITE DEFORMATIONS. MODIFIED ESHELBY RELATION 84
* INFINITESIMAL DEFORMATIONS 86 14. COHERENT PHASE INTERFACES 88 A.
GENERAL THEORY 88 B. INFINITESIMAL THEORY WITH LINEAR STRESS-STRAIN
RELATIONS IN BULK . . 89 X CONTENTS D. EVOLVING INTERFACES NEGLECTING
BULK BEHAVIOR 91 15. EVOLVING SURFACES 93 A. SURFACES 93 AL. BACKGROUND.
SUPERFICIAL STRESS 93 A2. SUPERFICIAL TENSOR FIELDS 94 B. SMOOTHLY
EVOLVING SURFACES 97 BL. TIME DERIVATIVE FOLLOWING *. NORMAL TIME
DERIVATIVE. . 97 B2. VELOCITY FIELDS FOR THE BOUNDARY CURVE BF OF A
SMOOTHLY EVOLVING SUBSURFACE OF 5F. TRANSPORT THEOREM .... 99 B3.
TRANSFORMATION LAWS 100 16. CONFIGURATIONAL FORCE SYSTEM. WORKING 101 A.
CONFIGURATIONAL FORCES. WORKING 101 B. CONFIGURATIONAL FORCE BALANCE AS
A CONSEQUENCE OF INVARIANCE UNDER CHANGES IN MATERIAL OBSERVER 102 *
INVARIANCE UNDER CHANGES IN VELOCITY FIELDS. SURFACE TENSION. SURFACE
SHEAR 103 D. NORMAL FORCE BALANCE. INTRINSIC FORM FOR THE WORKING 104 E.
POWER BALANCE. INTERNAL WORKING 105 17. SECOND LAW 108 18. CONSTITUTIVE
EQUATIONS 110 A. FUNCTIONS OF ORIENTATION 110 B. CONSTITUTIVE EQUATIONS
ILL * EVOLUTION EQUATION FOR THE INTERFACE 113 D. LYAPUNOV RELATIONS 114
19. TWO-DIMENSIONAL THEORY 115 A. KINEMATICS 115 B. CONFIGURATIONAL
FORCES. WORKING. SECOND LAW 116 * CONSTITUTIVE THEORY 118 D. EVOLUTION
EQUATION FOR THE INTERFACE 119 E. CORNERS 120 F. ANGLE-CONVEXITY. THE
FRANK DIAGRAM 120 G. CONVEXITY OF THE INTERFACIAL ENERGY AND EVOLUTION
OF THE INTERFACE 124 E. COHERENT PHASE INTERFACES WITH INTERFACIAL
ENERGY AND DEFORMATION 127 20. THEORY NEGLECTING STANDARD INTERFACIAL
STRESS 129 A. STANDARD AND CONFIGURATIONAL FORCES. WORKING 129 CONTENTS
XI B. POWER BALANCE. INTERNAL WORKING 131 C. SECOND LAW 132 CL. SECOND
LAW. INTERFACIAL DISSIPATION INEQUALITY 132 C2. DERIVATION OF THE
INTERFACIAL DISSIPATION INEQUALITY USING A PILLBOX ARGUMENT 132 D.
CONSTITUTIVE EQUATIONS 133 E. CONSTRUCTION OF THE PROCESS USED IN
RESTRICTING THE CONSTITUTIVE EQUATIONS 135 F. BASIC EQUATIONS WITH
INERTIAL EXTERNAL FORCES 135 FL. STANDARD AND CONFIGURATIONAL BALANCES
135 F2. SUMMARY OF BASIC EQUATIONS 136 G. GLOBAL ENERGY INEQUALITY.
LYAPUNOV RELATIONS 137 21. GENERAL THEORY WITH STANDARD AND
CONFIGURATIONAL STRESS WITHIN THE INTERFACE 138 A. KINEMATICS.
TANGENTIAL DEFORMATION GRADIENT 138 B. STANDARD AND CONFIGURATIONAL
FORCES. WORKING 139 * POWER BALANCE. INTERNAL WORKING 142 D. SECOND LAW.
INTERFACIAL DISSIPATION INEQUALITY 144 E. CONSTITUTIVE EQUATIONS 145 F.
BASIC EQUATIONS WITH INERTIAL EXTERNAL FORCES 147 G. LYAPUNOV RELATIONS
147 22. TWO-DIMENSIONAL THEORY WITH STANDARD AND CONFIGURATIONAL STRESS
WITHIN THE INTERFACE 149 A. KINEMATICS 149 B. FORCES. WORKING 150 *
POWER BALANCE. INTERNAL WORKING. SECOND LAW 152 D. CONSTITUTIVE
EQUATIONS 155 E. EVOLUTION EQUATIONS FOR THE INTERFACE 156 F.
SOLIDIFICATION 157 23. SOLIDIFICATION. THE STEFAN CONDITION AS A
CONSEQUENCE OF THE CONFIGURATIONAL FORCE BALANCE 159 A. SINGLE-PHASE
THEORY 159 B. THE CLASSICAL TWO-PHASE THEORY REVISITED. THE STEFAN
CONDITION AS A CONSEQUENCE OF THE CONFIGURATIONAL BALANCE 160 24.
SOLIDIFICATION WITH INTERFACIAL ENERGY AND ENTROPY 163 A. GENERAL THEORY
163 B. APPROXIMATE THEORY. THE GIBBS-THOMSON CONDITION AS A CONSEQUENCE
OF THE CONFIGURATIONAL BALANCE 166 * FREE-BOUNDARY PROBLEMS FOR THE
APPROXIMATE THEORY. GROWM THEOREMS 167 XII CONTENTS CL. THE QUASILINEAR
AND QUASISTATIC PROBLEMS 167 C2. GROWTH THEOREMS 168 G. FRACTURE 173 25.
CRACKED BODIES 175 A. SMOOTH CRACKS. CONTROL VOLUMES 175 B. DERIVATIVES
FOLLOWING THE TIP. TIP INTEGRALS. TRANSPORT THEOREMS . 177 26. MOTIONS
182 27. FORCES. WORKING 184 A. FORCES 184 B. WORKING 186 * STANDARD AND
CONFIGURATIONAL FORCE BALANCES 186 D. INERTIAL FORCES. KINETIC ENERGY
188 28. THE SECOND LAW 190 A. STATEMENT OF THE SECOND LAW 190 B. THE
SECOND LAW APPLIED TO CRACK CONTROL VOLUMES 191 * THE SECOND LAW APPLIED
TO TIP CONTROL VOLUMES. STANDARD FORM OF THE SECOND LAW 191 D. TIP
TRACTION. ENERGY RELEASE RATE. DRIVING FORCE 193 E. THE STANDARD
MOMENTUM CONDITION 194 29. BASIC RESULTS FOR THE CRACK TIP 196 30.
CONSTITUTIVE THEORY FOR GROWING CRACKS 198 A. CONSTITUTIVE RELATIONS AT
THE TIP 198 B. THE GRIFFITH-IRWIN FUNCTION 199 * CONSTITUTIVELY
ISOTROPIC CRACK TIPS. TIPS WITH CONSTANT MOBILITY . 200 31. KINKING AND
CURVING OF CRACKS. MAXIMUM DISSIPATION CRITERION 201 A. CRITERION FOR
CRACK INITIATION. KINK ANGLE 202 B. MAXIMUM DISSIPATION CRITERION FOR
CRACK PROPAGATION 204 32. FRACTURE IN THREE SPACE DIMENSIONS (RESULTS)
208 H. TWO-DIMENSIONAL THEORY OF CORNERS AND JUNCTIONS NEGLECTING
INERTIA 211 33. PRELIMINARIES. TRANSPORT THEOREMS 213 A. TERMINOLOGY 213
B. TRANSPORT THEOREMS 214 1 CONTENTS XIII BL. BULKFIELDS 214 B2.
INTERFACIAL FIELDS 215 34. THERMOMECHANICAL THEORY OF JUNCTIONS AND
CORNERS 218 A. MOTIONS 218 B. NOTATION 219 * FORCES. WORKING 220 D.
SECOND LAW 221 E. BASIC RESULTS FOR THE JUNCTION 222 F. WEAK SINGULARITY
CONDITIONS. NONEXISTENCE OF CORNERS 222 G. CONSTITUTIVE EQUATIONS 223 H.
FINAL JUNCTION CONDITIONS 224 I. APPENDICES ON THE PRINCIPLE OF VIRTUAL
WORK FOR COHERENT PHASE INTERFACES 225 AL. WEAK PRINCIPLE OF VIRTUAL
WORK 227 A. VIRTUAL KINEMATICS 227 B. FORCES. WEAK PRINCIPLE OF VIRTUAL
WORK 228 * PROOF OF THE WEAK THEOREM OF VIRTUAL WORK 229 A2. STRONG
PRINCIPLE OF VIRTUAL WORK 232 A. VIRTUALLY MIGRATING CONTROL VOLUMES 232
B. FORCES. STRONG PRINCIPLE OF VIRTUAL WORK 233 * PROOF OF THE STRONG
THEOREM OF VIRTUAL WORK 234 D. COMPARISON OF THE STRONG AND WEAK
PRINCIPLES 236 REFERENCES 239 INDEX 247
|
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| id | DE-604.BV013074878 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:40Z |
| institution | BVB |
| isbn | 0387986677 9781475774030 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008908270 |
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| physical | XIII, 249 S. graph. Darst. |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Gurtin, Morton E. Verfasser aut Configurational forces as basic concepts of continuum physics Morton E. Gurtin New York [u.a.] Springer 2000 XIII, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 137 Literaturverz. S. 239 - 245 Champs, Théorie des (Physique) ram Fonctions d'onde ram Configuration space Field theory (Physics) Konfigurationsraum (DE-588)4199256-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Kontinuumsmechanik (DE-588)4032296-8 s Konfigurationsraum (DE-588)4199256-8 s DE-604 Applied mathematical sciences 137 (DE-604)BV000005274 137 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008908270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gurtin, Morton E. Configurational forces as basic concepts of continuum physics Applied mathematical sciences Champs, Théorie des (Physique) ram Fonctions d'onde ram Configuration space Field theory (Physics) Konfigurationsraum (DE-588)4199256-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4199256-8 (DE-588)4129367-8 (DE-588)4032296-8 |
| title | Configurational forces as basic concepts of continuum physics |
| title_auth | Configurational forces as basic concepts of continuum physics |
| title_exact_search | Configurational forces as basic concepts of continuum physics |
| title_full | Configurational forces as basic concepts of continuum physics Morton E. Gurtin |
| title_fullStr | Configurational forces as basic concepts of continuum physics Morton E. Gurtin |
| title_full_unstemmed | Configurational forces as basic concepts of continuum physics Morton E. Gurtin |
| title_short | Configurational forces as basic concepts of continuum physics |
| title_sort | configurational forces as basic concepts of continuum physics |
| topic | Champs, Théorie des (Physique) ram Fonctions d'onde ram Configuration space Field theory (Physics) Konfigurationsraum (DE-588)4199256-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Champs, Théorie des (Physique) Fonctions d'onde Configuration space Field theory (Physics) Konfigurationsraum Festkörpermechanik Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008908270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT gurtinmortone configurationalforcesasbasicconceptsofcontinuumphysics |