Non-smooth thermomechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Physics and astronomy online library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 480 S. graph. Darst. |
| ISBN: | 3540665005 |
Internformat
MARC
| LEADER | 00000nam a22000008c 4500 | ||
|---|---|---|---|
| 001 | BV013767714 | ||
| 003 | DE-604 | ||
| 005 | 20180309 | ||
| 007 | t | ||
| 008 | 010605s2002 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 961380098 |2 DE-101 | |
| 020 | |a 3540665005 |9 3-540-66500-5 | ||
| 035 | |a (OCoLC)46858451 | ||
| 035 | |a (DE-599)BVBBV013767714 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-20 |a DE-1046 |a DE-91G |a DE-634 |a DE-11 |a DE-706 | ||
| 050 | 0 | |a QA808 | |
| 082 | 0 | |a 531 |2 21 | |
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a UF 1200 |0 (DE-625)145559: |2 rvk | ||
| 084 | |a UG 2000 |0 (DE-625)145616: |2 rvk | ||
| 084 | |a PHY 200f |2 stub | ||
| 084 | |a PHY 013f |2 stub | ||
| 100 | 1 | |a Frémond, Michel |e Verfasser |0 (DE-588)1112629211 |4 aut | |
| 245 | 1 | 0 | |a Non-smooth thermomechanics |c Michel Frémond |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XVI, 480 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics and astronomy online library | |
| 650 | 4 | |a Inequalities (Mathematics) | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Mechanics, Analytic | |
| 650 | 0 | 7 | |a Nichtglatte Mechanik |0 (DE-588)4201235-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtglatte Mechanik |0 (DE-588)4201235-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009410942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009410942 | |
Datensatz im Suchindex
| _version_ | 1808227533107232768 |
|---|---|
| adam_text |
CONTENTS
1.
THE
DESCRIPTION
OF
A
MATERIAL
.
1
1.1
THE
STATE
QUANTITIES
.
1
1.2
VELOCITIES.
STRAIN
RATES.
RIGID
BODY
VELOCITIES
.
1
2.
THE
PRINCIPLE
OF
VIRTUAL
POWER
.
3
2.1
VIRTUAL
POWER
OF
THE
INTERIOR
FORCES
.
3
2.2
VIRTUAL
POWER
OF
THE
EXTERIOR
FORCES
.
4
2.3
VIRTUAL
POWER
OF
THE
ACCELERATION
FORCES
.
5
2.4
THE
EQUATIONS
OF
MOTION
.
5
3.
THE
CONSTITUTIVE
LAWS.
CASE
OF
NO
CONSTRAINT
ON
THE
STATE
QUANTITIES
OR
THEIR
VELOCITIES
.
7
3.1
INTRODUCTION
AND
DEFINITIONS
.
7
3.2
THE
BALANCE
EQUATIONS
.
7
3.3
THE
CONSTITUTIVE
LAWS
.
9
4.
THE
CONSTITUTIVE
LAWS.
CASE
WITH
CONSTRAINTS
ON
THE
STATE
QUANTITIES
.
15
4.1
INTERNAL
CONSTRAINTS.
THE
FREE
ENERGY
.
15
4.2
THE
BALANCE
LAWS
.
18
4.3
THE
CONSTITUTIVE
LAWS
.
18
4.4
PSEUDOPOTENTIAL
OF
DISSIPATION
.
22
4.4.1
INTERNAL
CONSTRAINTS
ON
QUANTITIES
WHICH
DESCRIBE
THE
EVOLUTION
.
23
4.5
WHEN
THE
TEMPERATURE
CAN
BE
ZERO
.
25
4.6
AN
EXAMPLE
.
27
5.
THE
CONSTITUTIVE
LAWS
ON
A
DISCONTINUITY
SURFACE
.
33
5.1
PSEUDOPOTENTIAL
OF
DISSIPATION
.
40
5.2
WHEN
THE
AVERAGE
TEMPERATURE
CAN
BE
ZERO
.
41
5.3
DEFINITION
OF
A
MATERIAL.
UTILISATION
OF
THE
THEORY
ON
A
DISCONTINUITY
LINE
.
42
5.4
THE
GRADIENT
OF
A
STATE
QUANTITY
IS
INVOLVED
IN
THE
POWER
OF
THE
INTERIOR
FORCES
.
43
X
CONTENTS
5.5
EXAMPLE
1.
SHOCK
IN
AN
ADIABATIC
IDEAL
FLUID
.
44
5.6
EXAMPLE
2.
ADIABATIC
MATERIAL
.
47
5.7
EXAMPLE
3.
SOLID-LIQUID
AND
LIQUID-VAPOUR
PHASE
CHANGE
.
47
5.8
EXAMPLE
4.
THE
TEMPERATURE
IS
DISCONTINUOUS:
RAIN
FALLING
ON
ICE
.
49
5.9
EXAMPLE
5.
SHOCK
IN
PLASTICITY
.
55
5.10
EXAMPLE
6.
CONTACT
SURFACE
.
56
6.
DEFORMABLE
SOLIDS
WITH
INTERACTIONS
AT
A
DISTANCE
.
59
6.1
THE
STRAIN
RATES
.
60
6.1.1
THE
ACTUAL
STRAIN
RATES
.
61
6.2
THE
POWERS
OF
THE
INTERIOR
AND
EXTERIOR
FORCES
.
63
6.3
THE
EQUATIONS
OF
MOTION
.
66
6.4
THE
ENERGY
BALANCE
.
68
6.5
THE
CONSTITUTIVE
LAWS
.
75
6.6
EXAMPLES
OF
MECHANICAL
CONSTITUTIVE
LAWS
.
83
6.7
OTHER
IMPENETRABILITY
CONSTRAINTS
AND
INTERACTIONS
AT
A
DISTANCE
.
84
6.7.1
VOLUME
INTERACTIONS
AT
A
DISTANCE
AND
IMPENETRABILITY
CONSTRAINT
.
84
6.7.2
ANOTHER
IMPENETRABILITY
CONSTRAINT
.
89
6.8
EXAMPLES
OF
THERMAL
CONSTITUTIVE
LAWS
.
90
7.
DEFORMABLE
SOLIDS
WITHOUT
INTERACTION
AT
A
DISTANCE
.
93
7.1
EXAMPLE
1.
UNILATERAL
COULOMB
FRICTION
.
94
7.2
EXAMPLE
2.
COLLISION
OF
A
DEFORMABLE
SOLID
WITH
A
RIGID
HALF-SPACE
.
95
7.3
INSTANTANEOUS
COLLISION
.
98
8.
COLLISION
OF
RIGID
BODIES.
MULTIPLE
COLLISIONS
.
101
8.1
INTRODUCTION
.
101
8.2
THE
DISTANCE
FUNCTION
.
102
8.3
THE
VELOCITIES
AND
THE
STRAIN
RATE
.
102
8.3.1
THE
VIRTUAL
AND
ACTUAL
VELOCITIES
.
103
8.3.2
THE
STRAIN
RATE
.
103
8.3.3
THE
TIME
DERIVATIVES
OF
THE
DISTANCE
AND
THE
SYSTEM
STRAIN
RATE
.
104
8.4
THE
VIRTUAL
WORKS
.
107
8.5
THE
EQUATIONS
OF
MOTION
.
108
8.6
THE
ENERGY
BALANCE
AT
CONSTANT
TEMPERATURE
.
110
8.6.1
SMOOTH
EVOLUTION
AT
CONSTANT
TEMPERATURE
.
ILL
8.6.2
COLLISION
AT
CONSTANT
TEMPERATURE
.
112
8.7
THE
CONSTITUTIVE
LAWS
AT
CONSTANT
TEMPERATURE
.
115
8.7.1
SMOOTH
EVOLUTION
AT
CONSTANT
TEMPERATURE
.
115
8.7.2
COLLISION
AT
CONSTANT
TEMPERATURE
.
116
CONTENTS
XI
8.7.3
THE
IMPENETRABILITY
REACTION
.
118
8.8
THE
ENERGY
BALANCE
WITH
EVOLVING
TEMPERATURE
.
120
8.8.1
SMOOTH
EVOLUTION
WITH
EVOLVING
TEMPERATURE
.
122
8.8.2
COLLISION
WITH
EVOLVING
TEMPERATURE
.
124
8.9
THE
CONSTITUTIVE
LAWS
WITH
EVOLVING
TEMPERATURE
.
127
8.9.1
SMOOTH
EVOLUTION
WITH
EVOLVING
TEMPERATURE
.
127
8.9.2
COLLISION
WITH
EVOLVING
TEMPERATURE
.
129
8.10
FIRST
EXAMPLE
OF
COLLISION
CONSTITUTIVE
LAW
.
133
8.11
SECOND
EXAMPLE
OF
COLLISION
CONSTITUTIVE
LAW
.
135
8.12
THIRD
EXAMPLE
OF
COLLISION
CONSTITUTIVE
LAW
.
138
8.13
FOURTH
EXAMPLE
OF
COLLISION
CONSTITUTIVE
LAW
.
140
8.14
FIFTH
EXAMPLE
OF
COLLISION
CONSTITUTIVE
LAW
.
141
8.15
EXAMPLES
OF
THERMAL
CONSTITUTIVE
LAW
.
143
8.15.1
THERE
IS
NO
COLLISION
.
143
8.15.2
THERE
IS
A
COLLISION
.
143
8.15.3
AN
EXAMPLE
.
144
8.16
CASE
WHERE
THE
SOLID
IS
NOT
CONVEX
.
146
8.17
COLLISION
AT
A
NON-SMOOTH
POINT
.
146
8.17.1
THE
EQUATIONS
OF
MOTION
.
149
8.17.2
THE
ENERGY
BALANCE
IN
A
COLLISION
AT
CONSTANT
TEMPERATURE
.
151
8.17.3
THE
CONSTITUTIVE
LAWS
AT
CONSTANT
TEMPERATURE
.
152
8.17.4
AN
EXAMPLE
.
155
8.17.5
COLLISION
IN
A
REENTRANT
ANGLE
SMALLER
THAN
90
.
155
8.17.6
COLLISION
IN
A
REENTRANT
ANGLE
BETWEEN
90
AND
180
156
8.17.7
COLLISION
WITH
AN
ANGULAR
WEDGE
WHOSE
ANGLE
IS
BETWEEN
180AND
270
.
156
8.17.8
COLLISION
WITH
AN
ANGULAR
WEDGE
WHOSE
ANGLE
IS
BETWEEN
270
AND
360
.
157
8.17.9
COLLISION
WITH
A
PLANE
OR
IN
A
FLAT
ANGLE
.
158
8.17.10
THE
VELOCITY
BEFORE
THE
COLLISION
IS
ZERO
AND
THERE
IS
NO
EXTERIOR
PERCUSSION
.
159
8.18
MULTIPLE
COLLISION
.
159
8.18.1
SITUATION
1.
POINT
A
REMAINS
FIXED
AND
POINT
B
BOUNCES
.
162
8.18.2
SITUATION
2.
THE
POINT
A
MOVES
AND
POINT
B
STOPS
.
162
8.18.3
SITUATION
3.
THE
POINTS
A
AND
B
STOP
.
163
8.18.4
SITUATION
4.
THE
POINTS
A
AND
B
MOVE
.
163
8.18.5
SUMMARY
OF
THE
RESULTS
.
164
8.19
SIMPLE
COLLISION
ON
A
VERTEX
.
165
8.19.1
SITUATION
1.
THE
WHEEL
BOUNCES
.
166
8.19.2
SITUATION
2.
THE
WHEEL
REMAINS
IN
CONTACT
WITH
THE
PLANE
.
166
XII
CONTENTS
8.20
COLLISIONS
OF
TWO
SOLIDS.
THE
GENERAL
SITUATION
.
167
8.20.1
COLLISION
OF
TWO
SMOOTH
SOLIDS
.
167
8.20.2
COLLISION
OF
SOLIDS
AT
IRREGULAR
POINTS
.
173
8.20.3
COLLISIONS
OF
TWO
SOLIDS
ON
A
LINE
.
177
8.20.4
COLLISION
OF
TWO
SOLIDS.
THE
GENERAL
SITUATION
.
179
8.21
COLLISION
OF
THREE
BALLS
.
179
9.
EVOLUTION
OF
TWO
DEFORMABLE
SOLIDS
WITH
COLLISIONS
.
185
9.1
THE
PRINCIPLE
OF
VIRTUAL
WORK
.
185
9.2
THE
ENERGY
BALANCE
.
189
9.3
THE
SECOND
LAW
OF
THERMODYNAMICS
.
200
9.4
THE
CONSTITUTIVE
LAWS
.
202
9.5
EVOLUTION
IN
A
COLLISION
.
206
9.5.1
THE
MECHANICAL
EVOLUTION
WHEN
DECOUPLED
FROM
THE
THERMAL
EVOLUTION
.
209
9.5.2
AN
EXAMPLE.
COLLISION
OF
A
BAR
WITH
A
RIGID
SUPPORT
.
212
9.5.3
THE
THERMAL
EVOLUTION
WHEN
THE
MECHANICAL
EQUATIONS
ARE
DECOUPLED
FROM
THE
THERMAL
EQUATIONS
.
213
9.5.4
THE
VARIATION
OF
THE
TEMPERATURE
IN
A
COLLISION
.
217
10.
MATERIAL
WITH
VOLUME
INTERACTIONS
AT
A
DISTANCE.
FIBRE
REINFORCED
MATERIAL
.
219
10.1
POWER
OF
THE
INTERIOR
FORCES
TO
A
SUBDOMAIN
.
219
10.2
POWER
OF
THE
EXTERIOR
FORCES
TO
A
SUBDOMAIN
.
222
10.3
POWER
OF
THE
ACCELERATION
FORCES
TO
A
SUBDOMAIN
.
222
10.4
THE
EQUATIONS
OF
MOTION
.
222
10.5
THE
ENERGY
BALANCE
.
223
10.6
THE
SECOND
LAW
OF
THERMODYNAMICS
.
226
10.7
THE
FREE
ENERGY
.
227
10.8
THE
CONSTITUTIVE
LAWS
.
229
10.9
AN
EXAMPLE
.
232
10.9.1
THE
FIBRES
CANNOT
BREAK
.
233
10.9.2
THE
FIBRES
CAN
BREAK.
NEW
INTERIOR
FORCES
.
233
10.9.3
THE
FIBRES
CAN
BREAK.
THE
ENERGY
BALANCE
.
235
10.9.4
THE
FIBRES
CAN
BREAK.
THE
SECOND
LAW
OF
THERMODYNAMICS
.
238
10.9.5
THE
FIBRES
CAN
BREAK.
CONSTITUTIVE
LAWS
.
238
10.9.6
NEW
INTERIOR
FORCES
AND
MORE
SOPHISTICATED
THEORIES
.
240
10.9.7
THE
FIBRES
CAN
BREAK.
THE
EQUATIONS
OF
MOTION
.
242
10.9.8
A
NUMERICAL
EXAMPLE
.
245
CONTENTS
XIII
11.
SOLID-LIQUID
PHASE
CHANGE.
SUPERCOOLING.
SOIL
FREEZING.
.
249
11.1
SUPERCOOLING
.
249
11.1.1
INTRODUCTION
.
249
11.1.2
THE
STATE
QUANTITIES
.
251
11.1.3
THE
WATER
MASS
BALANCE
.
251
11.1.4
THE
SEED
MASS
BALANCE
.
252
11.1.5
THE
FREE
ENERGIES
.
252
11.1.6
THE
ENERGY
BALANCE
.
254
11.1.7
THE
SECOND
LAW
OF
THERMODYNAMICS
.
254
11.1.8
THE
CONSTITUTIVE
LAWS
.
254
11.1.9
ICE
.
259
11.1.10
SUPERCOOLED
WATER
.
260
11.1.11
SOLIDIFICATION
OF
SUPERCOOLED
WATER
.
261
11.1.12
SUPERHEATED
ICE?
.
262
11.1.13
MOTION
OF
THE
FREEZING
LINE
.
262
11.1.14
ICE
CANNOT
MELT
AT
A
STRICTLY
NEGATIVE
TEMPERATURE.
264
11.1.15
SUPERCOOLED
WATER
IN
THE
PRESENCE
OF
SEEDS
.
265
11.1.16
INSTANTANEOUS
VOLUME
PHASE
CHANGE
.
265
11.1.17
THE
PREDICTIVE
THEORY
.
269
11.1.18
DISAPPEARANCE
OF
SUPERCOOLING.
VARIATIONAL
FORMULATION
.
270
11.2
THE
CLASSICAL
WATER-ICE
PHASE
CHANGE:
STEFAN
PROBLEM
.
273
11.2.1
THE
FREE
ENERGIES
.
273
11.2.2
THE
CONSTITUTIVE
LAWS
IN
A
DOMAIN
WHERE
THE
EVOLUTION
IS
SMOOTH
.
274
11.2.3
THE
CONSTITUTIVE
LAWS
ON
A
FREEZING
LINE
.
275
11.2.4
ABSENCE
OF
CONSTITUTIVE
LAW
IN
A
DOMAIN
WHERE
THERE
IS
AN
INSTANTANEOUS
VOLUME
PHASE
CHANGE
.
275
11.2.5
THE
EQUATIONS
OF
THE
CLASSICAL
STEFAN
PROBLEM
.
276
11.2.6
THE
FREEZING
INDEX
.
276
11.2.7
THE
EQUATIONS
SATISFIED
BY
THE
FREEZING
INDEX
.
277
11.2.8
VARIATIONAL
FORMULATION
AND
AN
EXISTENCE
THEOREM
.
278
11.3
THE
WATER-ICE
PHASE
CHANGE
IN
A
POROUS
MEDIUM
.
280
11.3.1
THE
CONSTITUTIVE
LAWS
FOR
THE
THERMAL
PREDICTIVE
THEORY
.
281
11.3.2
UNFROZEN
WATER
CONTENT
IN
A
FROZEN
SOIL
.
287
11.4
SOIL
FREEZING
.
288
11.4.1
UNFROZEN
WATER
CONTENT
IN
A
FROZEN
SOIL
.
296
11.4.2
THE
POROSITY
OF
A
FREEZING
SOIL
.
296
11.4.3
AN
EXAMPLE.
THE
SMALL
PERTURBATION
THEORY.
CRYOGENIC
SUCTION
.
298
11.4.4
SOIL
FREEZING.
A
PREDICTIVE
THEORY
.
302
XIV
CONTENTS
11.5
THE
WATER-ICE
PHASE
CHANGE
IN
THE
PRESENCE
OF
SOLUTES
.
308
11.6
DISSIPATIVE
PHASE
CHANGE.
IRREVERSIBLE
PHASE
CHANGE
.
308
12.
DAMAGE.
GRADIENT
OF
DAMAGE
.
313
12.1
INTRODUCTION
.
313
12.2
THE
PRINCIPLE
OF
VIRTUAL
POWER.
EQUATIONS
OF
MOTION
.
314
12.3
THE
BALANCE
LAWS
AND
CONSTITUTIVE
LAWS
.
316
12.4
A
MODEL
WITH
ONE
DAMAGE
QUANTITY
.
319
12.5
A
MODEL
WITH
TWO
DAMAGE
QUANTITIES.
THE
UNILATERAL
PHENOMENON
.
321
12.6
DAMAGE
OF
STRUCTURES
.
325
12.6.1
FIRST
EXAMPLE
.
326
12.6.2
SECOND
EXAMPLE
.
328
12.7
FATIGUE
AND
DAMAGE
.
329
12.8
THE
STRUCTURAL
SIZE
EFFECT
.
334
12.8.1
INTRODUCTION
.
334
12.8.2
THE
EQUATIONS
.
336
12.8.3
A
NUMERICAL
EXAMPLE
.
337
12.8.4
ANALYSIS
OF
THE
STRUCTURAL
SIZE
EFFECT
.
340
12.8.5
THE
SIZE
EFFECT.
AN
EXAMPLE
.
345
12.9
A
NONLOCAL
THEORY
.
347
12.9.1
THE
EQUATIONS
OF
MOTION
.
347
12.9.2
THE
ENERGY
BALANCE
EQUATIONS
.
348
12.9.3
THE
SECOND
LAW
OF
THERMODYNAMICS
.
349
12.9.4
THE
FREE
ENERGY
.
349
12.9.5
THE
CONSTITUTIVE
LAWS
.
350
12.9.6
AN
EXAMPLE
.
353
12.10
DAMAGE
SOURCES
.
355
13.
SHAPE
MEMORY
ALLOYS
.
359
13.1
INTRODUCTION
.
359
13.2
THE
STATE
QUANTITIES
.
359
13.3
THE
PRINCIPLE
OF
VIRTUAL
POWER
AND
THE
EQUATIONS
OF
MOTION
.
360
13.4
THE
ENERGY
BALANCE
.
361
13.5
THE
SECOND
LAW
OF
THERMODYNAMICS
.
362
13.6
THE
FREE
ENERGY
.
362
13.7
THE
CONSTITUTIVE
LAWS
.
365
13.8
THE
NONDISSIPATIVE
CONSTITUTIVE
LAWS
.
367
13.9
TRANSFORMATION
OF
THE
EQUATIONS.
ELIMINATION
OF
FA
.
368
13.10
THE
FIRST
NONDISSIPATIVE
MODEL
.
371
13.11
THE
SECOND
NONDISSIPATIVE
MODEL
.
372
13.12
AN
EXAMPLE
OF
NONDISSIPATIVE
EVOLUTION
.
372
13.12.1
LOW
TEMPERATURE
BEHAVIOUR
(T
TO)
.
373
13.12.2
MEDIUM
TEMPERATURE
BEHAVIOUR
(TO
T
T
C
)
.
374
CONTENTS
XV
13.12.3
LATENT
HEAT
OF
AUSTENITE-MARTENSITE
PHASE
CHANGE
.
376
13.12.4
HIGH
TEMPERATURE
BEHAVIOUR
(T
T
C
)
.
377
13.13
THE
DISSIPATION.
THE
PSEUDO-POTENTIAL
OF
DISSIPATION
.
377
13.14
THE
DISSIPATIVE
CONSTITUTIVE
LAWS
.
378
13.15
DISSIPATIVE
BEHAVIOUR
.
379
13.15.1
EQUILIBRIUM
AT
LOW
TEMPERATURE
(T
TO)
.
379
13.15.2
EQUILIBRIUM
AT
MEDIUM
TEMPERATURE
(TO
T
T
C
)
.
381
13.15.3
EQUILIBRIUM
AT
HIGH
TEMPERATURE
(T
T
C
)
.
381
13.16
EVOLUTION
OF
A
SHAPE
MEMORY
ALLOY
.
383
13.16.1
FIRST
EXPERIMENT
AT
LOW
TEMPERATURE
(T
TO)
.
384
13.16.2
SECOND
EXPERIMENT
AT
LOW
TEMPERATURE
(T
TO)
.
385
13.16.3
THIRD
EXPERIMENT
AT
HIGH
TEMPERATURE
(T
T
C
)
.
387
13.17
THE
ONE-SHAPE
MEMORY
EFFECT
.
388
13.18
THE
TWO-SHAPE
MEMORY
EFFECT
.
388
13.18.1
EQUILIBRIUM
STATES
AT
LOW
TEMPERATURE
(T
TO)
.
389
13.18.2
EQUILIBRIUM
STATES
AT
MEDIUM
TEMPERATURE
(TO
T
T
C
)
.
391
13.18.3
EQUILIBRIUM
STATES
AT
HIGH
TEMPERATURE
(T
T
C
)
.
391
13.18.4
CONSTITUTIVE
LAWS
OF
A
NONDISSIPATIVE,
EDUCATED,
SHAPE
MEMORY
ALLOY
.
392
13.18.5
THE
TWO
SHAPE
MEMORY
EFFECT
.
393
13.19
SMOOTH
CONSTITUTIVE
LAWS
.
394
13.20
EVOLUTIONS
OF
STRUCTURES
MADE
OF
SHAPE
MEMORY
ALLOYS
.
395
13.21
CONCLUSION
.
400
14.
UNILATERAL
CONTACT.
CONTACT
WITH
ADHESION
.
401
14.1
INTRODUCTION
.
401
14.2
THE
PRINCIPLE
OF
VIRTUAL
POWER.
THE
EQUATIONS
OF
MOTION
.
402
14.3
THE
ENERGY
BALANCE
.
407
14.4
THE
SECOND
LAW
OF
THERMODYNAMICS
AND
CONSTITUTIVE
LAWS
.
418
14.5
AN
EXAMPLE
.
431
14.6
THE
SMALL
PERTURBATION
THEORY.
THE
NONLOCAL
FORCES
DEPENDING
ON
THE
ELONGATION
.
434
14.6.1
A
LOCAL
FORCE
AS
A
LIMIT
OF
NONLOCAL
INTERACTIONS
.
436
14.6.2
THE
SMALL
PERTURBATION
THEORY.
THE
LOCAL
FORCES
DEPENDING
ON
THE
DISTANCES
.
438
14.6.3
A
LOCAL
THEORY
EXAMPLE.
THE
ADHESION
OF
TWO
SOLIDS
.
443
14.6.4
THE
LIMIT
CASE
.
445
14.7
OTHER
NONLOCAL
EFFECTS
.
446
14.7.1
NONLOCAL
DISSIPATIVE
FORCES
.
448
14.7.2
NONLOCAL
NONDISSIPATIVE
FORCES
.
450
14.8
SOME
PRACTICAL
RESULTS
.
451
14.8.1
SEPARATION
OF
TWO
GLUED
SOLIDS
.
451
14.8.2
PEELING
OF
SOLIDS
.
452
XVI
CONTENTS
14.8.3
PLATES
DELAMINATION
.
453
14.9
CONCLUSION
.
454
APPENDIX
.
455
A.L
CONVEX
FUNCTIONS
.
455
A.
1.1
SUBGRADIENT
OF
A
CONVEX
FUNCTION.
SUBDIFFERENTIAL
SET
.
455
A.
1.2
INDICATOR
FUNCTION
OF
A
SET
.
457
A.
1.3
INDICATOR
FUNCTION
OF
THE
SET
OF
THE
POSITIVE
NUMBER
R
+
.
457
A.
1.4
INDICATOR
FUNCTION
OF
THE
SET
OF
THE
NEGATIVE
NUMBERS
R~
.
458
A.
1.5
INDICATOR
FUNCTION
OF
THE
SEGMENT
[0,1]
.
458
A.
1.6
INDICATOR
FUNCTION
OF
THE
ORIGIN
OF
R
.
458
A.
1.7
INDICATOR
FUNCTION
OF
A
TRIANGLE
.
458
A.
1.8
THE
INDICATOR
FUNCTION
OF
A
SEGMENT
IN
I?
2
.
459
A.
1.9
A
PROPERTY
OF
THE
SUBDIFFERENTIAL
SET
.
460
A.
1.10
THE
DUAL
FUNCTION
OF
A
CONVEX
FUNCTION
.
461
A.
2
MATERIAL
DERIVATIVES
.
462
A.
2.1
MATERIAL
DERIVATIVE
OF
A
FUNCTION
.
462
A.
2.2
MATERIAL
DERIVATIVE
OF
A
SURFACE
INTEGRAL
.
462
A.
2.3
MATERIAL
DERIVATIVE
OF
A
DOUBLE
SURFACE
INTEGRAL
.
462
A.
2.4
MASS
BALANCE
ON
A
SURFACE
.
463
A.
2.5
MATERIAL
DERIVATIVES
OF
INTEGRALS
OF
MASS
DENSITIES
.
464
REFERENCES
.
465
SUBJECT
INDEX
.
479 |
| any_adam_object | 1 |
| author | Frémond, Michel |
| author_GND | (DE-588)1112629211 |
| author_facet | Frémond, Michel |
| author_role | aut |
| author_sort | Frémond, Michel |
| author_variant | m f mf |
| building | Verbundindex |
| bvnumber | BV013767714 |
| callnumber-first | Q - Science |
| callnumber-label | QA808 |
| callnumber-raw | QA808 |
| callnumber-search | QA808 |
| callnumber-sort | QA 3808 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 UF 1200 UG 2000 |
| classification_tum | PHY 200f PHY 013f |
| ctrlnum | (OCoLC)46858451 (DE-599)BVBBV013767714 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a22000008c 4500</leader><controlfield tag="001">BV013767714</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180309</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010605s2002 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">961380098</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540665005</subfield><subfield code="9">3-540-66500-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)46858451</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013767714</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA808</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">531</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UF 1200</subfield><subfield code="0">(DE-625)145559:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 2000</subfield><subfield code="0">(DE-625)145616:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 200f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 013f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Frémond, Michel</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1112629211</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Non-smooth thermomechanics</subfield><subfield code="c">Michel Frémond</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 480 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Physics and astronomy online library</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Inequalities (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mechanics, Analytic</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtglatte Mechanik</subfield><subfield code="0">(DE-588)4201235-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtglatte Mechanik</subfield><subfield code="0">(DE-588)4201235-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009410942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009410942</subfield></datafield></record></collection> |
| id | DE-604.BV013767714 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T00:42:35Z |
| institution | BVB |
| isbn | 3540665005 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009410942 |
| oclc_num | 46858451 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-1046 DE-91G DE-BY-TUM DE-634 DE-11 DE-706 |
| owner_facet | DE-703 DE-20 DE-1046 DE-91G DE-BY-TUM DE-634 DE-11 DE-706 |
| physical | XVI, 480 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Physics and astronomy online library |
| spelling | Frémond, Michel Verfasser (DE-588)1112629211 aut Non-smooth thermomechanics Michel Frémond Berlin [u.a.] Springer 2002 XVI, 480 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library Inequalities (Mathematics) Mathematical analysis Mechanics, Analytic Nichtglatte Mechanik (DE-588)4201235-1 gnd rswk-swf Nichtglatte Mechanik (DE-588)4201235-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009410942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frémond, Michel Non-smooth thermomechanics Inequalities (Mathematics) Mathematical analysis Mechanics, Analytic Nichtglatte Mechanik (DE-588)4201235-1 gnd |
| subject_GND | (DE-588)4201235-1 |
| title | Non-smooth thermomechanics |
| title_auth | Non-smooth thermomechanics |
| title_exact_search | Non-smooth thermomechanics |
| title_full | Non-smooth thermomechanics Michel Frémond |
| title_fullStr | Non-smooth thermomechanics Michel Frémond |
| title_full_unstemmed | Non-smooth thermomechanics Michel Frémond |
| title_short | Non-smooth thermomechanics |
| title_sort | non smooth thermomechanics |
| topic | Inequalities (Mathematics) Mathematical analysis Mechanics, Analytic Nichtglatte Mechanik (DE-588)4201235-1 gnd |
| topic_facet | Inequalities (Mathematics) Mathematical analysis Mechanics, Analytic Nichtglatte Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009410942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fremondmichel nonsmooththermomechanics |