Plasticity: mathematical theory and numerical analysis
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
[2013]
|
| Edition: | second edition |
| Series: | Interdisciplinary applied mathematics
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 421 Seiten Diagramme |
| ISBN: | 9781461459392 |
Staff View
MARC
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| 245 | 1 | 0 | |a Plasticity |b mathematical theory and numerical analysis |c Weimin Han, B. Daya Reddy |
| 250 | |a second edition | ||
| 264 | 1 | |a New York |b Springer |c [2013] | |
| 264 | 4 | |c © 2013 | |
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| 490 | 1 | |a Interdisciplinary applied mathematics |v 9 | |
| 650 | 4 | |a Elastoplastizität | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Plasticity | |
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Record in the Search Index
| _version_ | 1804150520403722240 |
|---|---|
| adam_text | Titel: Plasticity
Autor: Han, Weimin
Jahr: 2013
Contents
Preface
to
the
Second
Edition.................................
VII
Preface
to
the
First
Edition
...................................
IX
Part
I
Continuum
Mechanics
and
Elastoplasticity
Theory
1
Preliminaries..............................................
3
1.1
Introduction............................................
3
1.2
Some
Historical
Remarks.................................
5
1.3
Notation...............................................
9
2
Continuum
Mechanics
and
Linearized
Elasticity...........
15
2.1
Kinematics.............................................
16
2.2
Balance
of
Momentum;
Stress.............................
22
2.3
Linearly
Elastic
Materials
................................
27
2.4
Isotropic
Elasticity
......................................
29
2.5
A
Thermodynamic
Framework
for
Elasticity................
32
2.6
Initial-Boundary
and
Boundary
Value
Problems
for
Linearized
Elasticity.....................................
36
2.7
Thermodynamics
with
Internal
Variables...................
37
3
Elastoplastic
Media........................................
41
3.1
Physical
Background
and
Motivation.......................
41
3.2
Three-Dimensional
Elastoplastic
Behavior..................
47
3.3
Examples
of
Yield
Criteria................................
61
3.4
Yield
Criteria
for
Dilatant
Materials.......................
66
3.4.1
Examples
........................................
66
3.4.2
A
further
note
on
non-smooth
yield
surfaces..........
69
3.5
Hardening
Laws.........................................
70
3.6
Single-crystal
Plasticity
..................................
74
XIII
XIV
Contents
3.7
Strain-gradient
Plasticity.................................
82
3.7.1
Polycrystalline
plasticity
...........................
82
3.7.2
Gradient
single-crystal
plasticity
....................
87
3.8
Bibliographical
Remarks
.................................
94
4
The
Plastic
Flow
Law
in
a
Convex-Analytic
Setting........
95
4.1
Some
Results
from
Convex
Analysis
.......................
96
4.2
Basic
Plastic
Flow
Relations
of
Elastoplasticity..............106
4.3
Strain-gradient
Plasticity.................................117
4.3.1
The
Aifantis
model................................118
4.3.2
Poly
crystalline
strain-gradient
plasticity..............119
4.3.3
Strain-gradient
single-crystal
plasticity...............121
Part
II
The
Variational
Problems
of
Elastoplasticity
5
Basics
of
Functional
Analysis
and
Function
Spaces
.........125
5.1
Results
from
Functional
Analysis..........................125
5.2
Function
Spaces.........................................135
5.2.1
The
Spaces
C
m
(i2),
C
m
(l2),
and
L
p
{ft)
..............135
5.2.2
Sobolev
Spaces....................................139
5.2.3
Spaces
of
Vector-Valued
Functions...................147
6
Variational
Equations
and
Inequalities
.....................151
6.1
Variational
Formulation
of
Elliptic
Boundary
Value
Problems
.151
6.2
Elliptic
Variational
Inequalities............................163
6.3
Parabolic
Variational
Inequalities..........................171
6.4
Qualitative
Analysis
of
an
Abstract
Problem................174
7
The
Primal
Variational
Problem
of
Elastoplasticity
........187
7.1
Classical
Elastoplasticity
with
Hardening...................189
7.1.1
Variational
formulation
............................189
7.1.2
Analysis
of
the
problem............................195
7.2
Classical
Single-crystal
Plasticity..........................201
7.3
Strain-gradient
Plasticity.................................203
7.3.1
The
Aifantis
model................................203
7.3.2
The
Gurtin
model
of
strain-gradient
plasticity
........204
7.4
Strain-gradient
Single-crystal
Plasticity
....................213
7.4.1
Weak
formulation
of
the
problem....................213
7.4.2
Well-posedness....................................215
7.5
Stability
Analysis........................................219
Contents
XV
8
The
Dual
Variational
Problem
of
Classical
Elastoplasticity.
225
8.1
The
Dual
Variational
Problem............................226
8.2
Analysis
of
the
Stress
Problem............................230
8.3
Analysis
of
the
Dual
Problem.............................242
8.4
Rate
Form
of
Stress-Strain
Relation.......................246
Part
III
Numerical
Analysis
of
the
Variational
Problems
9
Introduction
to
Finite
Element
Analysis
...................251
9.1
Basics
of
the
Finite
Element
Method.......................253
9.2
Affine
Families
of
Finite
Elements.........................255
9.3
Local
Interpolation
Error
Estimates........................259
9.4
Global
Interpolation
Error
Estimates
......................265
10
Approximation
of
Variational
Problems
....................269
10.1
Approximation
of
Elliptic
Variational
Equations.............269
10.2
Numerical
Approximation
of
Elliptic
Variational
Inequalities
..
273
10.3
Approximation
of
Parabolic
Variational
Inequalities..........282
11
Approximations
of
the
Abstract
Problem..................285
11.1
Spatially
Discrete
Approximations.........................286
11.2
Time-Discrete
Approximations............................288
11.3
Fully
Discrete
Approximations............................295
11.4
Convergence
Under
Minimal
Regularity....................301
12
Numerical
Analysis
of
the
Primal
Problem
................319
12.1
Error
Analysis
of
Discrete
Approximations
of
the
Primal
Problem................................................320
12.1.1
Problems
of
classical
elastoplasticity
with
hardening
...
320
12.1.2
Problems
of
strain-gradient
plasticity................329
12.2
Solution
Algorithms
.....................................337
12.3
Convergence
Analysis
of
the
Solution
Algorithms............348
12.4
Regularization
Technique
and
A
Posteriori
Error
Analysis
....
355
12.5
Fully
Discrete
Schemes
with
Numerical
Integration..........363
13
Numerical
Analysis
of
the
Dual
Problem
..................371
13.1
Time-Discrete
Approximations
of
the
Stress
Problem
........373
13.2
Time-Discrete
Approximations
of
the
Dual
Problem
.........379
13.3
Fully
Discrete
Approximations
of
the
Dual
Problem..........383
13.4
Predictor-Corrector
Algorithms...........................393
13.5
Computation
of
the
Closest-Point
Projections...............401
References.....................................................405
Index
415
|
| any_adam_object | 1 |
| author | Han, Weimin 1963- Reddy, B. Dayanand 1953- |
| author_GND | (DE-588)121177971 (DE-588)118128965 |
| author_facet | Han, Weimin 1963- Reddy, B. Dayanand 1953- |
| author_role | aut aut |
| author_sort | Han, Weimin 1963- |
| author_variant | w h wh b d r bd bdr |
| building | Verbundindex |
| bvnumber | BV041128294 |
| classification_rvk | SK 950 UF 3100 |
| ctrlnum | (OCoLC)827677933 (DE-599)BVBBV041128294 |
| dewey-full | 531.385 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.385 |
| dewey-search | 531.385 |
| dewey-sort | 3531.385 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik Geographie |
| edition | second edition |
| format | Book |
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| id | DE-604.BV041128294 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:40:14Z |
| institution | BVB |
| isbn | 9781461459392 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026104170 |
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| owner | DE-11 DE-706 DE-188 DE-384 DE-29T |
| owner_facet | DE-11 DE-706 DE-188 DE-384 DE-29T |
| physical | XV, 421 Seiten Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | Han, Weimin 1963- Verfasser (DE-588)121177971 aut Plasticity mathematical theory and numerical analysis Weimin Han, B. Daya Reddy second edition New York Springer [2013] © 2013 XV, 421 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 9 Elastoplastizität Numerical analysis Plasticity Plastizität (DE-588)4046283-3 gnd rswk-swf Elastoplastizität (DE-588)4204381-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Plastizität (DE-588)4046283-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Elastoplastizität (DE-588)4204381-5 s Reddy, B. Dayanand 1953- Verfasser (DE-588)118128965 aut Erscheint auch als Online-Ausgabe 978-1-4614-5940-8 Interdisciplinary applied mathematics 9 (DE-604)BV004216726 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026104170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Han, Weimin 1963- Reddy, B. Dayanand 1953- Plasticity mathematical theory and numerical analysis Interdisciplinary applied mathematics Elastoplastizität Numerical analysis Plasticity Plastizität (DE-588)4046283-3 gnd Elastoplastizität (DE-588)4204381-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4046283-3 (DE-588)4204381-5 (DE-588)4114528-8 |
| title | Plasticity mathematical theory and numerical analysis |
| title_auth | Plasticity mathematical theory and numerical analysis |
| title_exact_search | Plasticity mathematical theory and numerical analysis |
| title_full | Plasticity mathematical theory and numerical analysis Weimin Han, B. Daya Reddy |
| title_fullStr | Plasticity mathematical theory and numerical analysis Weimin Han, B. Daya Reddy |
| title_full_unstemmed | Plasticity mathematical theory and numerical analysis Weimin Han, B. Daya Reddy |
| title_short | Plasticity |
| title_sort | plasticity mathematical theory and numerical analysis |
| title_sub | mathematical theory and numerical analysis |
| topic | Elastoplastizität Numerical analysis Plasticity Plastizität (DE-588)4046283-3 gnd Elastoplastizität (DE-588)4204381-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Elastoplastizität Numerical analysis Plasticity Plastizität Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026104170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
| work_keys_str_mv | AT hanweimin plasticitymathematicaltheoryandnumericalanalysis AT reddybdayanand plasticitymathematicaltheoryandnumericalanalysis |