Singular Solutions in Plasticity (eBook)

Sergei Alexandrov (Autor)

eBook Download: PDF

2017 | 1st ed. 2018
XI, 107 Seiten
Springer Singapore (Verlag)
978-981-10-5227-9 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 12.7.2017
• Reihe/Serie: SpringerBriefs in Applied Sciences and Technology
• Reihe/Serie: SpringerBriefs in Applied Sciences and Technology
• Reihe/Serie: SpringerBriefs in Continuum Mechanics
• Reihe/Serie: SpringerBriefs in Continuum Mechanics
• Reihe/Serie: SpringerBriefs in Continuum Mechanics
• Zusatzinfo: XI, 107 p. 40 illus.
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Double shearing model • Maximum friction law • Rigid perfectly plastic solids • Rigid viscoplastic solids • singular velocity field • Strain rate intensity factor • Stress intensity factor
• ISBN-10: 981-10-5227-1 / 9811052271
• ISBN-13: 978-981-10-5227-9 / 9789811052279