Functional and numerical methods in viscoplasticity:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford u.a.
Oxford Univ. Press
1993
|
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 265 S. graph. Darst. |
| ISBN: | 0198535902 |
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MARC
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| 100 | 1 | |a Ionescu, Ioan R. |0 (DE-588)1223375293 |4 aut | |
| 245 | 1 | 0 | |a Functional and numerical methods in viscoplasticity |c Ioan R. Ionescu and Mircea Sofonea |
| 264 | 1 | |a Oxford u.a. |b Oxford Univ. Press |c 1993 | |
| 300 | |a XVII, 265 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Oxford science publications | |
| 650 | 7 | |a Viscoplasticité |2 ram | |
| 650 | 4 | |a Viscoplasticity | |
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| 700 | 1 | |a Sofonea, Mircea |d 1957- |0 (DE-588)1028214723 |4 aut | |
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Record in the Search Index
| _version_ | 1804122610301140992 |
|---|---|
| adam_text | CONTENTS
Summary of notations
xv
Chapter
1
Preliminaries on mechanics of continuous media
1
1
Kinematics of continuous media
1
1.1
Material and spatial description
1
1.2
Deformation and strain tensors
3
1.3
The rate of deformation tensor
7
2
Balance laws and stress tensors
8
2.1
The balance law of mass
8
2.2
The balance laws of momentum
9
2.3
The Cauchy stress tensor
10
2.4
The Piola-Kirehhoff stress tensors and the linearized theory
11
3
Some experiments and models for solids
13
3.1
Standard tests and elastic laws
14
3.2
Loading and unloading tests. Plastic laws
16
3.3
Long-range tests and viscoplastic laws
18
Bibliographical notes
21
Chapter
2
Functional spaces in viscoplasticity
22
1
Functional spaces of scalar-valued functions
22
1.1
Test functions, distributions, and
U
spaces
22
1.2
Sobolev spaces of integer order
24
2
Functional spaces attached to some linear differential
operators of first order
27
2.1
Linear differential operators of first order
27
2.2
Functional spaces associated with the deformation operator
29
2.3
A Hubert space associated with the divergence operator
32
3
Functional spaces of vector-valued functions defined on real intervals
35
3.1
Weak and strong measurability and
U
spaces
35
3.2
Absolutely continuous
vectorial
functions and
Ak p
spaces
37
3.3
Vectorial
distributions and Wk-P spaces
38
Bibliographical notes
41
Chapter
3
Quasistatic processes for rate-type viscoplastic materials
42
1
Discussion of a quasistatic elastic-viscoplastic problem
42
1.1
Rate-type constitutive equations
42
1.2
Statement of the problem
47
1.3
An existence and uniqueness result
49
1.4
The dependence of the solution upon the input data
54
XU CONTENTS
2
Behaviour of the solution in the viscoelastic case
57
2.1
Asymptotic stability
57
2.2
Periodic solutions
61
2.3
An approach to elasticity
62
2.4
Long-term behaviour of the solution
66
3
An approach to perfect plasticity
67
3.1
A convergence result
68
3.2
Quasistatic processes in perfect plasticity
73
3.3
Some pathological examples
75
4
A numerical approach <9
4.1
Error estimates over a finite time interval
80
4.2
Error estimation over an infinite time interval in the
viscoelastic case
81
4.3
Numerical examples
83
5
Quasistatic processes for rate-type viscoplastic materials with
internal state variables
89
5.1
Rate-type constitutive equations with internal state variables
89
5.2
Problem statement
91
5.3
Existence, uniqueness, and continuous dependence of the solution
93
5.4
A numerical approach
94
6
An application to a mining engineering problem
96
6.1
Constitutive assumptions and material constants
97
6.2
Boundary conditions and initial data
98
6.3
Numerical results
100
6.4
Failure
104
Bibliographical notes
105
Chapter
4
Dynamic processes for rate-type elastic-viscoplastic
materials
108
1
Discussion of a dynamic elastic-viscoplastic problem
108
1.1
Problem statement
108
1.2
An existence and uniqueness result
109
1.3
The dependence of the solutions upon the input data
112
1.4
Weak solutions
115
2
The behaviour of the solution in the viscoelastic case
118
2.1
The energy function
118
2.2
An energy bound for isolated bodies
121
2.3
An approach to linear elasticity
122
3
An approach to perfect plasticity
127
3.1
A convergence result
128
3.2
Dynamic processes in perfect plasticity
133
4
Dynamic processes for rate-type elastic-viscoplastic materials with
internal state variables
134
4.1
Problem statement and constitutive assumptions
134
4.2
Existence, uniqueness and continuous dependence of the solution
135
4.3
A local existence result
136
PREFACE
ХІІІ
5
Other functional methods in the study of dynamic problems
143
5.1
Monotony methods
143
5.2
A fixed point method
147
6
Perturbations of homogeneous simple shear and strain localization
152
6.1
Problem statement
153
6.2
Existence and uniqueness of smooth solutions
154
6.3
Perturbations of the homogeneous solutions
157
6.4
Numerical results
161
Bibliographical notes
167
Chapter
5
The flow of the Bingham fluid with friction
169
1
Boundary value problems for the Bingham fluid with friction
169
1.1
The constitutive equations of the Bingham fluid
169
1.2
Statement of the problems and friction laws
173
1.3
An existence and uniqueness result in the local friction law case
178
1.4
An existence result in the non-local friction law case
180
2
The blocking property of the solution
183
2.1
Problem statements and blocking property
184
2.2
The blocking property for abstract variational inequalities
185
2.3
The blocking property in the case without friction
191
2.4
The blocking property in the case with friction
193
3
A numerical approach
194
3.1
The penalized problem
195
3.2
The discrete and regularized problem
197
3.3
A Newton iterative method
199
3.4
An application to the wire drawing problem
201
Bibliographical notes
205
Appendix
206
1
Elements of linear analysis
206
1.1
Normed linear spaces and linear operators
206
1.2
Duality and weak topologies
208
1.3
Hubert spaces
209
2
Elements of non-linear analysis
211
2.1
Convex functions
212
2.2
Elliptic variational inequalities
215
2.3
Maximal monotone operators in Hubert spaces
218
3
Evolution equations in Banach spaces
222
3.1
Ordinary differential equations in Banach spaces
222
3.2
Linear evolution equations
223
3.3
Lipschitz perturbation of linear evolution equations
228
3.4
Non-linear evolution equations in Hubert spaces
236
4
Some numerical methods and complements
238
4.1
Numerical methods for elliptic problems
238
4.2
Euler s method for ordinary differential equations in
Hubert spaces
241
xiv CONTENTS
4.3
A numerical method for a non-linear evolution equation
244
4.4
Some technical results
248
Bibliographical notes
253
References
255
Index
263
|
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| author | Ionescu, Ioan R. Sofonea, Mircea 1957- |
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| institution | BVB |
| isbn | 0198535902 |
| language | English |
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| physical | XVII, 265 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publications |
| spelling | Ionescu, Ioan R. (DE-588)1223375293 aut Functional and numerical methods in viscoplasticity Ioan R. Ionescu and Mircea Sofonea Oxford u.a. Oxford Univ. Press 1993 XVII, 265 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Viscoplasticité ram Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd rswk-swf Viskoplastizität (DE-588)4136051-5 s DE-604 Sofonea, Mircea 1957- (DE-588)1028214723 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005427938&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ionescu, Ioan R. Sofonea, Mircea 1957- Functional and numerical methods in viscoplasticity Viscoplasticité ram Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd |
| subject_GND | (DE-588)4136051-5 |
| title | Functional and numerical methods in viscoplasticity |
| title_auth | Functional and numerical methods in viscoplasticity |
| title_exact_search | Functional and numerical methods in viscoplasticity |
| title_full | Functional and numerical methods in viscoplasticity Ioan R. Ionescu and Mircea Sofonea |
| title_fullStr | Functional and numerical methods in viscoplasticity Ioan R. Ionescu and Mircea Sofonea |
| title_full_unstemmed | Functional and numerical methods in viscoplasticity Ioan R. Ionescu and Mircea Sofonea |
| title_short | Functional and numerical methods in viscoplasticity |
| title_sort | functional and numerical methods in viscoplasticity |
| topic | Viscoplasticité ram Viscoplasticity Viskoplastizität (DE-588)4136051-5 gnd |
| topic_facet | Viscoplasticité Viscoplasticity Viskoplastizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005427938&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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