Chapter
1.3. The Theory of Plasticity
1.4. The Nature of Physical Theories
1.5. The Conceptual Simplicity and Power of Plastic Theory
1.6. Uniqueness, Indeterminacy and Freedom
CHAPTER II. SPECIFICATION OF AN IDEAL PLASTIC MATERIAL
2.1. Observations on a Tension Test
2.2. Behaviour of Metals on the Atomic Scale
2.3. Tension and Compression Tests
2.4. Instability in the Tension Test
2.5. Materials with Upper and Lower Yield Points
2.6. The Bauschinger Effect
2.8. Yield Surface for Three-dimensional Stress
2.9. Symmetry of the C-curve
2.10. The Tresca Yield Condition
2.11. Plastic Deformation
2.12. The "Normality" Rule
2.13. The Mises Yield Condition and Associated Flow Rule
2.14. Tresca or Mises Yield Condition?
2.15. The Experiments of Taylor and Quinney
2.16. Correlation between Tension and Shear Tests
2.17. Perfectly Plastic Material
CHAPTER III.
FEATURES OF THE BEHAVIOUR OF STRUCTURES MADE OF IDEALISED ELASTIC-PLASTIC MATERIAL
3.1. Ideal Elastic-plastic Material
3.2. Equations of the Problem
3.4. Elastic-plastic Deformation
3.5. Behaviour under Rising and Falling Pressure
3.6. The Effect of Residual Stresses
3.8. A "Work" Calculation
CHAPTER IV.
THEOREMS OF PLASTIC THEORY
4.1. Lower and Upper Bounds on Collapse Loads
4.2. The Lower-bound ("Safe") Theorem
4.3. Proof of the Lower-bound Theorem
4.4. Loads other than Point Loads
4.5· The Upper-bound Theorem
4.6. Calculation of Dissipation of Energy
4.7. Simpler Form of the Proofs
4.8. Corollaries of the Bound Theorems
4.9. Problems solved in Terms of Stress Resultants
CHAPTER V.
ROTATING DISCS
5.2. The Flat Disc with No Central Hole
5.3. A Physical Interpretation
5.4. Discs with Central Holes
5.5. Mechanisms of Collapse
5.6. Discs with Edge Loading
5.8. Discs of Variable Thickness
5.9. Reinforcement of Central Holes
6.1. Torsion of Thin-walled Tubes of Arbitrary Cross-section
6.2. Lower-bound Analysis of Thick-walled Tubes and Solid Cross-sections
6.3. The Sand-hill Analogy
6.5. Other Aspects of Plastic Torsion
6.6. Combined Torsion and Tension
6.7. Combined Torsion, Bending and Tension
CHAPTER VII.
INDENTATION PROBLEMS
7.1. Upper-bound Approach
7.2. Lower-bound Approach
7.4. Experimental Confirmation: the Hardness Test
7.5. Indentation of Finite Blocks of Plastic Material
7.6 The Effects of Friction
7.7. Compression of a Thin Sheet between Broad Dies
CHAPTER VIII. INTRODUCTION TO SLIP-LINE FIELDS
8.1. Equilibrium Equations
8.2. Geometry of α, β nets
8.3. Hyperbolic Equations
8.4. Extension of α, β nets
8.5. The Indentation Problem
8.6. Choice of Approach: Slip Lines or Bound Theorems?
CHAPTER IX. CIRCULAR PLATES UNDER TRANSVERSE LOADING
9.1. Validity of the Simple Plastic Theory
9.2. Collapse of a Simply Supported Circular Plate under Uniform Transverse Pressure
9.3. Yield Locus for an Element of Plate
9.4. Lower-bound Analysis
9.5. A Clamped Circular Plate: Lower-bound Analysis
9.6. Upper-bound Calculations
9.7. Modes of Deformation
9.8. Reinforced Concrete Slabs
9.10. Experimental Behaviour
CHAPTER X. METAL-FORMING PROCESSES: WIRE-DRAWING AND EXTRUSION
10.2. A Simple Mode of Deformation
10.4. Presentation of Results
10.5. Drawing with Small Die Angles
10.6. Sheet Drawing in the Presence of Friction
10.7. Extrusion through Square Dies
10.8. Hydrostatic Extrusion
10.9. Allowance for Work-hardening
10.10. Axisymmetric Wire-drawing
10.11. Diffuse Shear in Region B
10.12. Evaluation of "Diffuse Shear" Work
10.13. Optimum Die Angles
10.14. Axisymmetric Extrusion for α = 90°
CHAPTER XI.
EFFECTS OF CHANGES IN GEOMETRY
11.1. Three Broad Classes of Structural Behaviour
11.2. An Approach to Geometry-change Effects in Plastic Deformation
11.4. Geometry-change Effects in Simple Structures
11.5. Summary and Concluding Remarks
CHAPTER XII. THE WIDER SCOPE OF PLASTIC THEORY AND DESIGN
12.1. Interrelation with Other Aspects of Design
12.2. The Role of Computers in Structural Design
12.3. Application of Plastic Theory to Other Fields of Design
APPENDIX I: THE MOHR CIRCLE OF STRESS
APPENDIX II: VIRTUAL WORK
APPENDIX III: ''CORRESPONDING" LOADS AND DEFLECTIONS
APPENDIX IV: PROPORTIONAL LOADING
APPENDIX V: NOTATION FOR THREE-DIMENSIONAL STRESS
APPENDIX VI: SYMBOLS, UNITS AND CONVERSION FACTORS
Engineering Plasticity
：The Commonwealth and International Library: Structures and Solid Body Mechanics Division
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