Theory of Plasticity


  • Jagabanduhu Chakrabarty, Professor of Mechanical Engineering, Penn State University, USA, Previously University of Birmingham, UK

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, and is accompanied by a fully worked solutions manual.
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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)


Book information

  • Published: March 2006
  • ISBN: 978-0-7506-6638-1


“This is a well-established, graduate level text designed for mechanical, civil and materials engineers. The style adopted is very clear and the text gives very good explanations of complex ideas, such as slip line field theory. A significant feature of the text is the extensive referencing to original articles, reviews and other texts.” — Brian Ralph, Emeritus Professor, School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UK

Table of Contents

PrefacePreface to the third editionChapter 1: Stresses and Strains1.1 Introduction1.2 The Stress–Strain Behavior1.3 Analysis of Stress1.4 Mohr’s Representation of Stress1.5 Analysis of Strain Rate1.6 Concepts of Stress RateProblemsChapter 2: Foundations of Plasticity2.1 The Criterion of Yielding2.2 Strain-Hardening Postulates2.3 The Rule of Plastic Flow2.4 Particular Stress–Strain Relations2.5 The Total Strain Theory2.6 Theorems of Limit Analysis2.7 Uniqueness Theorems 2.8 Extremum PrinciplesProblemsChapter 3: Elastoplastic Bending and Torsion3.1 Plane Strain Compression and Bending3.2 Cylindrical Bars Under Torsion and Tension 3.3 Thin-Walled Tubes Under Combined Loading3.4 Pure Bending of Prismatic Beams3.5 Bending of Beams Under Transverse Loads3.6 Torsion of Prismatic Bars3.7 Torsion of Bars of Variable Diameter3.8 Combined Bending and Twisting of BarsProblemsChapter 4: Plastic Analysis of Beams and Frames4.1 Introduction4.2 Limit Analysis of Beams4.3 Limit Analysis of Plane Frames4.4 Displacements in Plane Frames4.5 Variable Repeated Loading4.6 Minimum Weight Design4.7 Influence of Axial Forces4.8 Limit Analysis of Space FramesProblemsChapter 5: Further Solutions of Elastoplastic Problems5.1 Expansion of a Thick Spherical Shell5.2 Expansion of a Thick-Walled Tube5.3 Thermal Stresses in a Thick-Walled Tube5.4 Thermal Stresses in a Thick Spherical Shell5.5 Pure Bending of a Curved Bar5.6 Rotating Discs and Cylinders5.7 Infinite Plate with a Circular Hole5.8 Yielding Around a Cylindrical CavityProblemsChapter 6: Theory of the Slipline Field6.1 Formulation of the Plane Strain Problem6.2 Properties of Slipline Fields and Hodographs6.3 Stress Discontinuities in Plane Strain6.4 Construction of Slipline Fields and Hodographs6.5 Analytical and Matrix Methods of Solution6.6 Explicit Solutions for Direct Problems6.7 Some Mixed Boundary-Value Problems6.8 Superposition of Slipline FieldsProblemsChapter 7: Steady Problems in Plane Strain7.1 Symmetrical Extrusion Through Square Dies7.2 Unsymmetrical and Multihole Extrusion7.3 Sheet Drawing Through Tapered Dies7.4 Extrusion Through Tapered Dies7.5 Extrusion Through Curved Dies7.6 Ideal Die Profiles in Drawing and Extrusion7.7 Limit Analysis of Plane Strain Extrusion7.8 Cold Rolling of Strips7.9 Analysis of Hot Rolling7.10 Mechanics of MachiningProblemsChapter 8: Nonsteady Problems in Plane Strain8.1 Indentation by a Flat Punch8.2 Indentation by a Rigid Wedge8.3 Compression of a Wedge by a Flat Die8.4 Cylindrical Depression in a Large Block8.5 Compression Between Smooth Platens8.6 Compression Between Rough Platens8.7 Yielding of Notched Bars in Tension8.8 Bending of Single-Notched Bars8.9 Bending of Double-Notched Bars8.10 Bending of Beams and Curved Bars8.11 Large Bending of Wide SheetsProblemsChapter 9: Computational Methods9.1 Numerical Mathematics9.2 Finite Difference Method9.3 Finite Element Discretization9.4 Finite Element Procedure9.5 Illustrative ExamplesProblemsAppendices:A Tables on Slipline FieldsB Orthogonal Curvilinear CoordinatesC Fundamentals of Soil Plasticity