The Mechanical and Thermodynamical Theory of Plasticity

The Mechanical and Thermodynamical Theory of Plasticity

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Features

    • Includes more than 200 figures and an extensive number of exercises and computer simulation problems
    • Reviews background mathematics, continuum thermodynamics, and the extension of bars, to provide a broad perspective for student readers
    • Offers a look at special advanced topics, including infinitesimal theory and solutions; the finite deformation theories; and the common perspective that connects them
    • Explores the common perspectives and similarities of the mechanical and thermodynamical theories, with extensive use of analogs to help connect the ideas
    • Connects the first gradient theory to elasticity, plasticity, visicoelasticity, visicoplasticity, and crystal plasticity
    • Demonstrates extensive use of the representation theory to provide tools for constructing complex models

    Summary

    Born out of 15 years of courses and lectures on continuum mechanics, nonlinear mechanics, continuum thermodynamics, viscoelasticity, plasticity, crystal plasticity, and thermodynamic plasticity, The Mechanical and Thermodynamical Theory of Plasticity represents one of the most extensive and in-depth treatises on the mechanical and thermodynamical aspects of plastic and visicoplastic flow. Suitable for student readers and experts alike, it offers a clear and comprehensive presentation of multi-dimensional continuum thermodynamics to both aid in initial understanding and introduce and explore advanced topics.

    Covering a wide range of foundational subjects and presenting unique insights into the unification of disparate theories and practices, this book offers an extensive number of problems, figures, and examples to help the reader grasp the subject from many levels. Starting from one-dimensional axial motion in bars, the book builds a clear understanding of mechanics and continuum thermodynamics during plastic flow. This approach makes it accessible and applicable for a varied audience, including students and experts from engineering mechanics, mechanical engineering, civil engineering, and materials science.

    Table of Contents

    Plasticity In The 1-D Bar
    Introduction to Plastic Response
    The Bar and The Continuum Assumption
    Motion and Temperature of Points on a Bar
    Stretch Ratio, Strain, Velocity Gradient, Temperature Gradient
    Superposition of Deformations
    Elastic, Plastic, and Thermal Strains
    Examples of Constitutive Models
    Mechanical Theory of Rate-Independent Plasticity
    Mechanical Models for Plasticity
    Temperature-Dependent Plasticity
    An Infinitesimal Theory of Thermoplasticity
    Rate-Dependent Models for Plasticity
    Load Control as Opposed to Strain Control
    Numerical Integration of Constitutive Equations
    The Balance Laws
    Thermodynamic Restrictions on Constitutive Equations
    Heat Generation and Flow
    Equilibrium and Quasi-Equilibrium Problems
    Dynamic Loading Problems: Numerical Solution
    Dealing with Discontinuities: Jump Conditions
    Plastic Drawing of Bars
    Elastic and Plastic (Shock) Waves in a Bar
    General Comment on Selection of Moduli
    Notation and Summary

    Vectors and Tensors
    Matrix algebra
    Vectors
    Tensors
    Tensor calculus
    Notation

    Describing Motion, Deformation and Temperature
    Position, Velocity, Acceleration And Temperature
    Configurations of Material Bodies
    Streamlines and Pathlines
    Deformation Gradient and Temperature Gradient
    Stretch and Strain Tensors
    Velocity Gradient
    Relative Deformation
    Triaxial Extension, Simple Shear, Bending and Torsion
    Small Deformations
    Notation

    Elastic, Plastic And Thermal Deformation
    Elastic and Plastic Deformation Gradients
    Elastic and Plastic Strains
    Elastic and Plastic Velocity Gradients
    Infinitesimal Elastic and Plastic Deformations
    Large Rigid Body Rotations
    Thermal Deformation and Thermal Strain
    Notation

    Traction, Stress and Heat Flux
    The Traction Vector
    The Relation between Tractions on Different Surfaces
    The Stress Tensor
    Isotropic Invariants and the Deviatoric Stress
    Examples of Elementary States of Stress
    True Stress as Opposed to Engineering Stress
    The Piola-Kirchhoff, Rotated and Convected Stresses
    Heat Flux
    Notation

    Balance Laws and Jump Conditions
    Introduction
    Transport Relations
    Conservation of Mass
    Balance of Linear Momentum
    Balance of Angular Momentum
    Balance of Work snd Energy
    Entropy and the Entropy Production Inequality
    Heat Flow and Thermodynamic Processes
    Infinitesimal Deformations
    The Generalized Balance Law
    Jump Conditions
    Perturbing a Motion
    Initial and Boundary Conditions
    Notation

    Infinitesimal Plasticity
    A Mechanical Analog for Plasticity
    Elastic Perfectly-Plastic Response
    Common Assumptions
    Von Mises Yield Function with Combined Isotropic and Kinematic Hardening
    Thermoplasticity
    Free-Energy of Quadratic Form
    Scalar Stress and Hardening Functions
    Multiple Elements in Parallel
    Multiple Elements in Series
    Rate-Dependent Plasticity
    Deformation Plasticity
    Notation

    Solutions for Infinitesimal Plasticity
    Homogeneous Deformations
    Torsion-Extension of a Thin Circular Cylindrical Tube
    Compression in Plane Strain
    Bending
    Torsion of Circular Members
    Unloading
    Torsion of Prismatic Sections
    Non-Uniform Loading of Bars
    Cylindrical and Spherical Symmetry
    Two-Dimensional Problems
    Heat and Its Generation

    First-Gradient Thermo-Mechanical Materials
    First-Gradient Theories
    Superposition of Pure Translations
    Superposition of Rigid Body Rotations
    Material Symmetry
    First-Gradient State Variable Models
    Higher Gradient and Non-Local Models
    Notation

    Elastic And Thermoelastic Solids
    The Thermoelastic Solid
    The Influence of Pure Rigid-Body Translation on the Constitutive Response
    The Influence of Pure Rigid-Body Rotation on the Constitutive Response
    Material Symmetry
    Change of Reference Configuration
    A Thermodynamically Consistent Model
    Models Based on Fe And FӨ
    Specific Free-Energy of Quadratic Form in Strain
    Heat Generation and Heat Capacity
    Material Constraints
    Multiple Material Constraints
    Superposition of Deformations
    Notation

    Finite Deformation Mechanical Theory of Plasticity
    General Mechanical Theory of Plasticity
    Rigid Body Motions
    Material Symmetry
    Stress Depending Only on Elastic Deformation Gradient
    Stress Depending on both Elastic Deformation and Plastic Strain
    General Comments
    Deformation Plasticity
    Notation

    Thermoplastic Solids
    A Simple Thermo-Mechanical Analog
    Thermoplasticity
    Thermodynamic Constraint
    Isotropic Examples with J2 Type Yield Functions
    Superposition of Rigid Body Motions
    Material Symmetry
    An Initially Isotropic Material
    Models Depending on Cp
    Heat Generation and Heat Flow
    Specific Free-Energy of Quadratic Form in Strain
    Plasticity Models Based on Green Strains
    Heat Flux Vector
    Material Constraints
    Models Based on F = Fefөfp
    Notation

    Viscoelastic Solids
    One-Dimensional Linear Viscoelasticity
    One-Dimensional Nonlinear Viscoelasticity
    Three-Dimensional Linear Viscoelasticity
    A One-Element Thermo-Viscoelastic Model
    Multi-Element Thermodynamic Viscoelastic Model
    Initially Isotropic Models: Free-Energy and Thermodynamic Stresses
    Quasi-Linear Viscoelastic Model
    Material Constraints
    Models Based on F = Fefөfve
    Notation

    Rate-Dependent Plasticity
    Infinitesimal Mechanical and Thermo-Mechanical Models with Viscoplastic Flow
    Nonlinear Thermoelastic-Viscoplastic Model
    Single-Element Viscoelastic-Viscoplastic
    Full Viscoelastic-Viscoplastic Model
    Material Constraints
    Models Based on F = Fefөfvp
    Notation

    Crystal plasticity
    Crystal Structures and Slip Systems
    Elastic Crystal Distortion
    Kinematics of Single-Crystal Deformation
    Resolved Shear Stress and Overstress
    Yield Function
    Thermo-Mechanical Models
    Rate-Dependent Models
    Notation

    A Representation of functions
    Isotropic
    Transversely Isotropic
    Orthotropic

    B Representation for fourth order constants
    Isotropic
    Transversely Isotropic
    Crystal Classes

    C Basic Equations
    Basic Equations
    Curvilinear Coordinates
    Rectangular Coordinates
    Cylindrical Coordinates
    Spherical Coordinates

    Index

    Editorial Reviews

    "an excellent text for a graduate-level course in plasticity…the approach and selection of topics are appropriate for the audience. Professor Negahban has done an excellent job in presenting a unified approach to include thermal effects in the theory of finite deformation of plastic solids. The simple thermo-mechanical analog presented at the beginning of the chapter is also very instructive to the reader. {presented figures are] particularly helpful in understanding the mechanisms in a simple (one-dimensional) setting… The learning features included in this chapter are excellent (the figures are clear and illustrative). The table of contents is well-balanced and very clear…The in-depth and unified approach to many topics discussed in the text (e.g., thermoplasticity under finite deformation) is of particular interest..."
    Ken Zuo, University of Alabama in Huntsville, USA

    "… takes a modern, in depth approach to the subject of thermoplasticity. The chapters are written to be somewhat self-contained. …. can be adapted to satisfy a variety of courses and subjects. The author has done an admirable job of pointing out how the text would satisfy these competing requirements."
    Ronald E. Smelser, The University of North Carolina at Charlotte, USA

     
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