Theory of Plasticity

Plasticity is concerned with the mechanics of materials deformed beyond their elastic limit. A strong knowledge of plasticity is essential for engineers dealing with a wide range of engineering problems, such as those encountered in the forming of metals, the design of pressure vessels, the mechanics of impact, civil and structural engineering, as well as the understanding of fatigue and the economical design of structures.

Theory of Plasticity is the most comprehensive reference on the subject as well as the most up to date -- no other significant Plasticity reference has been published recently, making this of great interest to academics and professionals. This new edition presents extensive new material on the use of computational methods, plus coverage of important developments in cyclic plasticity and soil plasticity.

• A complete plasticity reference for graduate students, researchers and practicing engineers; no other book offers such an up to date or comprehensive reference on this key continuum mechanics subject
• Updates with new material on computational analysis and applications, new end of chapter exercises
• Plasticity is a key subject in all mechanical engineering disciplines, as well as in manufacturing engineering and civil engineering. Chakrabarty is one of the subject's leading figures.

Graduate level students in aeronautical, mechanical, materials & metallurgical engineering & related disciplines including structural mechanics, solid mechanics, elasticity, plasticity, mechanics of materials, metal forming mechanics, civil engineering; Secondary audience: Research students/scientists; professional engineers in structural engineering (esp. aeronautical, but also marine engineering & more general structural/civil engineering applications; engineers dealing with pressure vessels & other loaded structures; fabrication engineers)

Preface Preface to the third edition Chapter 1: Stresses and Strains 1.1 Introduction 1.2 The Stress–Strain Behavior 1.3 Analysis of Stress 1.4 Mohr’s Representation of Stress 1.5 Analysis of Strain Rate 1.6 Concepts of Stress Rate Problems Chapter 2: Foundations of Plasticity 2.1 The Criterion of Yielding 2.2 Strain-Hardening Postulates 2.3 The Rule of Plastic Flow 2.4 Particular Stress–Strain Relations 2.5 The Total Strain Theory 2.6 Theorems of Limit Analysis 2.7 Uniqueness Theorems 2.8 Extremum Principles Problems Chapter 3: Elastoplastic Bending and Torsion 3.1 Plane Strain Compression and Bending 3.2 Cylindrical Bars Under Torsion and Tension 3.3 Thin-Walled Tubes Under Combined Loading 3.4 Pure Bending of Prismatic Beams 3.5 Bending of Beams Under Transverse Loads 3.6 Torsion of Prismatic Bars 3.7 Torsion of Bars of Variable Diameter 3.8 Combined Bending and Twisting of Bars Problems Chapter 4: Plastic Analysis of Beams and Frames 4.1 Introduction 4.2 Limit Analysis of Beams 4.3 Limit Analysis of Plane Frames 4.4 Displacements in Plane Frames 4.5 Variable Repeated Loading 4.6 Minimum Weight Design 4.7 Influence of Axial Forces 4.8 Limit Analysis of Space Frames Problems Chapter 5: Further Solutions of Elastoplastic Problems 5.1 Expansion of a Thick Spherical Shell 5.2 Expansion of a Thick-Walled Tube 5.3 Thermal Stresses in a Thick-Walled Tube 5.4 Thermal Stresses in a Thick Spherical Shell 5.5 Pure Bending of a Curved Bar 5.6 Rotating Discs and Cylinders 5.7 Infinite Plate with a Circular Hole 5.8 Yielding Around a Cylindrical Cavity Problems Chapter 6: Theory of the Slipline Field 6.1 Formulation of the Plane Strain Problem 6.2 Properties of Slipline Fields and Hodographs 6.3 Stress Discontinuities in Plane Strain 6.4 Construction of Slipline Fields and Hodographs 6.5 Analytical and Matrix Methods of Solution 6.6 Explicit Solutions for Direct Problems 6.7 Some Mixed Boundary-Value Problems 6.8 Superposition of Slipline Fields Problems Chapter 7: Steady Problems in Plane Strain 7.1 Symmetrical Extrusion Through Square Dies 7.2 Unsymmetrical and Multihole Extrusion 7.3 Sheet Drawing Through Tapered Dies 7.4 Extrusion Through Tapered Dies 7.5 Extrusion Through Curved Dies 7.6 Ideal Die Profiles in Drawing and Extrusion 7.7 Limit Analysis of Plane Strain Extrusion 7.8 Cold Rolling of Strips 7.9 Analysis of Hot Rolling 7.10 Mechanics of Machining Problems Chapter 8: Nonsteady Problems in Plane Strain 8.1 Indentation by a Flat Punch 8.2 Indentation by a Rigid Wedge 8.3 Compression of a Wedge by a Flat Die 8.4 Cylindrical Depression in a Large Block 8.5 Compression Between Smooth Platens 8.6 Compression Between Rough Platens 8.7 Yielding of Notched Bars in Tension 8.8 Bending of Single-Notched Bars 8.9 Bending of Double-Notched Bars 8.10 Bending of Beams and Curved Bars 8.11 Large Bending of Wide Sheets Problems Chapter 9: Computational Methods 9.1 Numerical Mathematics 9.2 Finite Difference Method 9.3 Finite Element Discretization 9.4 Finite Element Procedure 9.5 Illustrative Examples Problems Appendices: A Tables on Slipline Fields B Orthogonal Curvilinear Coordinates C Fundamentals of Soil Plasticity