Introduction to Engineering Plasticity

Introduction to Engineering Plasticity

Fundamentals with Applications in Metal Forming, Limit Analysis and Energy Absorption

1st Edition - June 24, 2022

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  • Authors: Tongxi Yu, Pu Xue
  • Paperback ISBN: 9780323989817

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The theory of plasticity is a branch of solid mechanics that investigates the relationship between permanent deformation and load, and the distribution of stress and strains of materials and structures beyond their elastic limit. Engineering plasticity underpins the safety of many modern systems and structures. Realizing the full potential of materials as well as designing precise metal processing and energy absorption structures requires mastery of engineering plasticity. Introduction to Engineering Plasticity: Fundamentals with Applications in Metal Forming, Limit Analysis and Energy Absorption presents both fundamental theory on plasticity and emphasizes the latest engineering applications. The title combines theory and engineering applications of plasticity, elaborating on problem solving in real-world engineering tasks such as in metal forming, limit analysis of structures, and understanding the energy absorption of structures and materials. The five main parts of the book cover: Plastic properties of materials and their characterization; Fundamental theory in plasticity; Elastic-plastic problems and typical solutions; and Rigid-plastic problems under plane-stress conditions. This title provides students and engineers alike with the fundamentals and advanced tools needed in engineering plasticity.

Key Features

  • Brings together plasticity theory with engineering applications and problem solving
  • Elaborates problem solving methods and demonstrates plasticity in various engineering fields
  • Covers the recent decades of research on metal forming and limit analysis
  • Includes energy absorption of new structures and materials where plasticity dominates analysis and design
  • Gives a systematic account of the theory of plasticity alongside its engineering applications


Advanced students and researchers in applied mechanics, materials science and engineering, structural analysis, metal forming, and aerospace engineering. Engineers and researchers in various engineering fields

Table of Contents

  • Chapter 1  Plasticity of Metallic Materials
    1.1 Introduction
    1.2 Plastic properties of metallic materials
    1.2.1 Simple tensile tests
    1.2.2 Hydrostatic pressure test
    1.3 Physical basis of plastic deformation
    1.4 Plastic instability during axial tension
    1.5 Idealization of plastic behavior of materials
    1.5.1 Basic assumptions about plastic behavior of materials
    1.5.2 Idealized model for stress-strain relationship
    1.5.3 Strain-hardening model

    Chapter 2 Basic Characteristics of Structural Plasticity
    2.1 Three-bar truss structure made of elastic, perfectly plastic material
    2.2 Three-bar truss structure made of linear hardening elastic-plastic material
    2.3 Influence of large deformation on the load-carrying capacity of truss
    2.4 Effect of loading path on stress and strain of the truss
    2.5 Yield curve and limit curve on load plane
    2.5.1 Load plane
    2.5.2 Yield curve
    2.5.3 Limit curve
    2.5.4 Subsequent yield curve

    Chapter 3 Stress and Strain
    3.1 Stress analysis
    3.1.1 Stress tensor and its decomposition
    3.1.2 Principal stresses and stress invariants
    3.1.3 Stress on an octahedral plane
    3.1.4 Effective stress
    3.1.5 Three-dimensional Mohr’s circle and lode parameters
    3.1.6 Stress space and principal stress space
    3.2 Strain analysis
    3.2.1 Displacement and strain
    3.2.2 Decomposition of strain tensor and invariants of strain tensor
    3.2.3 Equivalent strain and lode strain parameter
    3.2.4 Strain rate tensor and strain increment tensor

    Chapter 4 Yield Criteria
    4.1 Initial yield criteria
    4.2 Two widely used yield criteria
    4.2.1 Tresca yield criterion
    4.2.2 von Mises yield criterion
    4.2.3 Comparison between the two yield criteria
    4.2.4 Other yield criteria
    4.3 Experimental verification of yield criteria
    4.4 Subsequent yield criteria

    Chapter 5 Plastic Constitutive Equations
    5.1 Elastic constitutive equations
    5.2 Drucker’s Postulate
    5.3 Loading and unloading criteria
    5.3.1 Loading and unloading criteria for perfectly plastic materials
    5.3.2 Loading and unloading criteria for hardening materials
    5.4 Incremental Theory (Flow Theory)
    5.4.1 Overview
    5.4.2 Flow rules of perfectly plastic materials associated with von Mises criterion
    5.4.3 Flow rules of perfectly plastic materials associated with Tresca criterion
    5.4.4 Incremental constitutive relationship of hardening materials
    5.5 Deformation Theory (Total Theory of Plasticity)
    5.5.1 Илъюшин theory
    5.5.2 Simple loading and unique curve assumption
    5.5.3 Theorem on simple loading
    5.5.4 Summary and comparison of plastic constitutive relationships
    5.6 Coulomb yield criterion and flow rule in rock mechanics

    Chapter 6 Simple Elastic-plastic Problems
    6.1 Formulation of elastic-plastic boundary value problems
    6.1.1 Boundary value problems based on the elastic-plastic deformation theory
    6.1.2 Boundary value problems based on the incremental theory of plasticity
    6.2 Deformation of thin-walled cylinder under combination of tension and torsion
    6.3 Elastic-plastic bending of beams (Engineering Theory)
    6.3.1 Pure bending of elastic-plastic beams
    6.3.2 Elastic-plastic bending of beams under transverse loads
    6.3.3 Combined loading of bending moment and axial force
    6.4 Plastic bending of plate under plane strain condition (accurate theory)
    6.4.1 Stress distribution
    6.4.2 Deformation during bending
    6.4.3 Movement of layers inside the plate
    6.5 Free torsion of elastic-plastic cylinder
    6.5.1 Scope and basic equations
    6.5.2 Elastic torsion and membrane analogy
    6.5.3 Fully plastic torsion and sand heap analogy
    6.5.4 Elastic-plastic torsion and membrane-glass cover analogy
    6.5.5 Unloading, springback and residual stress
    6.5.6 Torsion of cylinder made of elastic-plastic strain-hardening material
    6.6 Thick-walled cylinder under internal pressure
    6.6.1 Basic equations
    6.6.2 Elastic solution
    6.6.3 Elastic-plastic solution for perfectly plastic material
    6.6.4 Unloading and residual stress
    6.6.5 Influence of geometric change on load-carrying capacity
    6.6.6 Analysis for long thick-walled cylinder made of strain-hardening material
    6.7 Rotating disc
    6.7.1 Elastic solution
    6.7.2 Elastic-plastic Solution

    Chapter 7 Plane Strain Problems for Rigid Perfectly Plastic Materials
    7.1 Basic concepts
    7.2 Basic equations of plane strain problems
    7.3 Slip line and its geometric properties
    7.3.1 Stress equation and slip line
    7.3.2 Velocity equations
    7.3.3 Hencky’s First Theorem
    7.3.4 Hencky's Second Theorem
    7.3.5 Stress discontinuity theorem
    7.3.6 Summary
    7.4 Boundary condition
    7.4.1 Stress boundary
    7.4.2 Rigid-plastic boundary
    7.4.3 Boundary between two plastic regions
    7.5 Applications of slip line field theory
    7.5.1 Wedge under unilateral compression
    7.5.2 A half plane pressed by a rigid stamper
    7.5.3 Limit load of uniform pressure acting along a circular hole
    7.5.4 Notched specimens in tension
    7.6 Steady plastic flow problems
    7.6.1 Slip line field of strip drawing
    7.6.2 Stress distribution and drawing force
    7.6.3 Velocity distribution
    7.6.4 Check of rigid region

    Chapter 8 Principles of Limit Analysis
    8.1 Limit state and limit analysis
    8.2 Principle of virtual work-rate
    8.3 Principle of limit analysis
    8.3.1 Kinematically admissible velocity field and static field
    8.3.2 Limit analysis theorems
    8.3.3 Inferences of bound theorems
    8.3.4 Summary
    8.4 Applications of bound theorems

    Chapter 9 Limit Analysis of Beams and Frames
    9.1 Collapse mechanism including plastic hinges
    9.2 Bound theorems in limit analysis of beams and frames
    9.3 Kinematical method and statical method
    9.3.1 Kinematical method
    9.3.2 Statical method
    9.3.3 Limit curve and its applications
    9.4 Limit curve and its application
    Chapter 10 Limit Analysis of Plates
    10.1 Fundamental equations of plate
    10.1.1 Basic assumptions on bending of thin plates 
    10.1.2 Generalized stress and strain 
    10.1.3 Generalized yield criteria 
    10.2 Limit analysis of axisymmetric bending of circular plates 
    10.2.1 Principal directions and general stresses
    10.2.2 Limit load of simply supported circular plates 
    10.2.3 Limit load of clamped circular plate 
    10.3 Kinematic solutions of non-circular plates 
    10.4 Load-carrying capacity of plates under large deformation
    10.4.1 Overview 
    10.4.2 Calladine method 
    10.4.3 Membrance Factor Method (MFM) 
    10.5 Stamping of circular plates 

    Chapter 11 Utilzing Plastic Deformation for Energy Absorption
    11.1 Introduction
    11.2 Ring and circular tube under transverse compression
    11.2.1 Rings compressed by two flat plates
    11.2.2 Rings under a pair of compressive forces
    11.2.3 Laterally constrained rings
    11.2.4 Ring and tube systems
    11.3 Circular and square tubes under axial compression
    11.3.1 Axial crushing modes and typical force vs. displacement curves
    11.3.2 Theoretical models of circular tube under axial crushing
    11.3.3 Square tube under axial crushing
    11.4 Comparison of various energy absorption elements
    11.5 Energy absorption of cellular materials

    Chapter 12 Introduction to Dynamic Plasticity
    12.1 Introduction
    12.2 Propagation of elastic-plastic stress waves
    12.2.1 One-dimensional wave equation
    12.2.2 Propagation of elastic stress wave
    12.2.3 Reflection and transmission of elastic waves
    12.2.4 Elastic-plastic wave and formation of shock wave
    12.3 Dynamic characteristics of materials under high strain rate
    12.3.1 Strain rate
    12.3.2 Strain rate sensitivity
    12.3.3 Hopkinson bar technology
    12.4 Dynamic response of rigid perfectly plastic beam
    12.4.1 Basic assumptions
    12.4.2 Cantilever beam subjected to a pulse load at free end
    12.5 Effects of loading speed on energy absorption
    12.5.1 Effects of loading speed on the deformation mode
    12.5.2 Sensitivity of structural deformation to impact velocity
    12.5.3 Static and dynamic behavior of Type II structure

Product details

  • No. of pages: 362
  • Language: English
  • Copyright: © Elsevier 2022
  • Published: June 24, 2022
  • Imprint: Elsevier
  • Paperback ISBN: 9780323989817

About the Authors

Tongxi Yu

Tongxi Yu is Professor Emeritus in the Department of Mechanical and Aerospace Engineering and University Honorary Fellow at The Hong Kong University of Science and Technology, Hong Kong, China. He received his PhD from Cambridge University, UK. He was professor at Peking University and UMIST (now University of Manchester) before moved to Hong Kong. He is a Fellow of ASME, the IMechE and HKIE, as well as an honorary member of the International Association of Impact Engineering. He is an overseas fellow of Churchill College, Cambridge, and a recipient of a Doctor of Science (DSc) from Cambridge University as well as a recipient of a China Higher Education Science and Technology Award (1st Class).

Affiliations and Expertise

Professor Emeritus in the Department of Mechanical and Aerospace Engineering at The Hong Kong University of Science and Technology, Hong Kong

Pu Xue

Pu Xue is Professor in the School of Aeronautics at Northwestern Polytechnical University, China. She received her PhD from the Department of Mechanical and Aerospace Engineering, at The Hong Kong University of Science and Technology. She was also a Postdoctoral Fellow at the Hong Kong Polytechnic University, as well as at Northwestern University, USA.

Affiliations and Expertise

Professor in the School of Aeronautics at Northwestern Polytechnical University, Hong Kong

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