Alexandrov Singular Solutions in Plasticity

1. Auflage 2018
ISBN: 978-981-10-5227-9
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 115 Seiten

Reihe: SpringerBriefs in Continuum Mechanics

This book deals with singular solutions that appear in the vicinity of maximum friction surfaces for several rigid plastic models. In particular, it discusses precise asymptotic expansions as a necessary ingredient for the development of efficient numerical methods to solve boundary value problems that involve the maximum friction law as a boundary condition. An applied aspect of the singular solutions considered is that these solutions are capable of predicting the development of narrow hard layers near frictional interfaces in manufacturing processes.

Autoren/Hrsg.

Alexandrov, Sergei

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgements;8
3;Contents;9
4;Symbols;11
5;1 Introduction;12
5.1;1.1 Definition of the Subject;12
5.2;1.2 Coordinate Systems and Fundamental Equations;13
5.3;1.3 Material Models;16
5.4;1.4 Maximum Friction Law;19
5.5;References;21
6;2 Rigid Perfectly Plastic Material;23
6.1;2.1 Plane Strain Deformation;23
6.2;2.2 Axisymmeric Deformation;26
6.3;2.3 Compression of a Layer Between Rough Plates;30
6.3.1;2.3.1 Statement of the Problem;31
6.3.2;2.3.2 Solution;32
6.4;References;35
7;3 Rigid Viscoplastic Material;36
7.1;3.1 Plane Strain Deformation [6-8];36
7.2;3.2 Axisymmeric Deformation [9];45
7.3;3.3 Compression of a Layer Between Rough Plates;55
7.4;References;58
8;4 Anisotropic Rigid Plastic Material;59
8.1;4.1 Plane Strain Deformation 1;59
8.2;4.2 Compression of a Layer Between Rough Plates 2;64
8.3;References;68
9;5 Numerical Method;69
9.1;5.1 The Strain Rate Intensity Factor in Characteristic Coordinates;69
9.2;5.2 Benchmark Problem;73
9.3;5.3 Numerical Solution;77
9.3.1;5.3.1 General Numerical Scheme for the Boundary Value Problem of Section 2.3;77
9.3.2;5.3.2 Verification of the Accuracy of the Numerical Scheme;81
9.3.3;5.3.3 The Strain Rate Intensity Factor in Compression of a Finite Layer;84
9.4;References;88
10;6 Applications;89
10.1;6.1 Generation of Fine Grain Layers Near Frictional Interfaces;89
10.2;6.2 Upper Bound Method;100
10.2.1;6.2.1 Statement of the Problem;101
10.2.2;6.2.2 General Approach;102
10.2.3;6.2.3 Illustrative Example;109
10.3;References;113
11;Index;115