Plasticity theory 1st edition by Jacob Lubliner ISBN ‎ 0486462900 ‎ 978-0486462905

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ISBN 10: ‎ 0486462900
ISBN 13: ‎ 978-0486462905
Author: Jacob Lubliner

The aim of Plasticity Theory is to provide a comprehensive introduction to the contemporary state of knowledge in basic plasticity theory and to its applications. It treats several areas not commonly found between the covers of a single book: the physics of plasticity, constitutive theory, dynamic plasticity, large-deformation plasticity, and numerical methods, in addition to a representative survey of problems treated by classical methods, such as elastic-plastic problems, plane plastic flow, and limit analysis; the problem discussed come from areas of interest to mechanical, structural, and geotechnical engineers, metallurgists and others.
The necessary mathematics and basic mechanics and thermodynamics are covered in an introductory chapter, making the book a self-contained text suitable for advanced undergraduates and graduate students, as well as a reference for practitioners of solid mechanics.

Plasticity theory 1st  Table of contents:

Chapter 1: Introduction to Continuum Thermomechanics

Section 1.1 Mathematical Fundamentals

1.1.1 Notation

1.1.2 Cartesian Tensors

1.1.3 Vector and Tensor Calculus

1.1.4 Curvilinear Coordinates

Section 1.2 Continuum Deformation

1.2.1 Displacement

1.2.2 Strain

1.2.3 Principal Strains

1.2.4 Compatibility Conditions

Section 1.3 Mechanics of Continuous Bodies

1.3.1 Introduction

1.3.2 Stress

1.3.3 Mohr’s Circle

1.3.4 Plane Stress

1.3.5 Boundary-Value Problems

Section 1.4 Constitutive Relations: Elastic

1.4.1 Energy and Thermoelasticity

1.4.2 Linear Elasticity

1.4.3 Energy Principles

Section 1.5 Constitutive Relations: Inelastic

1.5.1 Inelasticity

1.5.2 Linear Viscoelasticity

1.5.3 Internal Variables: General Theory

1.5.4 Flow Law and Flow Potential

Chapter 2: The Physics of Plasticity

Section 2.1 Phenomenology of Plastic Deformation

2.1.1 Experimental Stress-Strain Relations

2.1.2 Plastic Deformation

2.1.3 Temperature and Rate Dependence

Section 2.2 Crystal Plasticity

2.2.1 Crystals and Slip

2.2.2 Dislocations and Crystal Plasticity

2.2.3 Dislocation Models of Plastic Phenomena

Section 2.3 Plasticity of Soils, Rocks and Concrete

2.3.1 Plasticity of Soil

2.3.2 “Plasticity” of Rock and Concrete

Chapter 3: Constitutive Theory

Section 3.1 Viscoplasticity

3.1.1 Internal-Variable Theory of Viscoplasticity

3.1.2 Transition to Rate-Independent Plasticity

3.1.3 Viscoplasticity Without a Yield Surface

Section 3.2 Rate-Independent Plasticity

3.2.1 Flow Rule and Work-Hardening

3.2.2 Maximum-Dissipation Postulate and Normality

3.2.3 Strain-Space Plasticity

Section 3.3 Yield Criteria, Flow Rules and Hardening Rules

3.3.1 Introduction

3.3.2 Yield Criteria Independent of the Mean Stress

3.3.3 Yield Criteria Dependent on the Mean Stress

3.3.4 Yield Criteria Under Special States of Stress or Deformation

3.3.5 Hardening Rules

Section 3.4 Uniqueness and Extremum Theorems

3.4.1 Uniqueness Theorems

3.4.2 Extremum and Variational Principles

3.4.3 Rigid–Plastic Materials

Section 3.5 Limit-Analysis and Shakedown Theorems

3.5.1 Standard Limit-Analysis Theorems

3.5.2 Nonstandard Limit-Analysis Theorems

3.5.3 Shakedown Theorems

Chapter 4: Problems in Contained Plastic Deformation

Section 4.1 Elementary Problems

4.1.1 Introduction: Statically Determinate Problems

4.1.2 Thin-Walled Circular Tube in Torsion and Extension

4.1.3 Thin-Walled Cylinder Under Pressure and Axial Force

4.1.4 Statically Indeterminate Problems

Section 4.2 Elastic—Plastic Torsion

4.2.1 The Torsion Problem

4.2.2 Elastic Torsion

4.2.3 Plastic Torsion

Section 4.3 The Thick-Walled Hollow Sphere and Cylinder

4.3.1 Elastic Hollow Sphere Under Internal and External Pressure

4.3.2 Elastic–Plastic Hollow Sphere Under Internal Pressure

4.3.3 Thermal Stresses in an Elastic–Plastic Hollow Sphere

4.3.4 Hollow Cylinder: Elastic Solution and Initial Yield Pressure

4.3.5 Elastic–Plastic Hollow Cylinder

Section 4.4 Elastic—Plastic Bending

4.4.1 Pure Bending of Prismatic Beams

4.4.2 Rectangular Beams Under Transverse Loads

4.4.3 Plane-Strain Pure Bending of Wide Beams or Plates

Section 4.5 Numerical Methods

4.5.1 Integration of Rate Equations

4.5.2 The Finite-Element Method

4.5.3 Finite-Element Methods for Nonlinear Continua

Chapter 5: Problems in Plastic Flow and Collapse I: Theories and “Exact” Solutions

Introduction

Section 5.1 Plane Problems

5.1.1 Slip-Line Theory

5.1.2 Simple Slip-Line Fields

5.1.3 Metal-Forming Problems

Section 5.2 Collapse of Circular Plates

5.2.1 Introduction to Plate Theory

5.2.2 Elastic Plates

5.2.3 Yielding of Plates

Section 5.3 Plastic Buckling

5.3.1 Introduction to Stability Theory

5.3.2 Theories of the Effective Modulus

5.3.3 Plastic Buckling of Plates and Shells

Chapter 6: Problems in Plastic Flow and Collapse II: Applications of Limit Analysis

Introduction

Section 6.1 Limit Analysis of Plane Problems

6.1.1 Blocks and Slabs with Grooves or Cutouts

6.1.2 Problems in Bending

6.1.3 Problems in Soil Mechanics

Section 6.2 Beams Under Combined Stresses

6.2.1 Generalized Stress

6.2.2 Extension and Bending

6.2.3 Combined Extension, Bending and Torsion

6.2.4 Bending and Shear

Section 6.3 Limit Analysis of Trusses, Beams and Frames

6.3.1 Trusses

6.3.2 Beams

6.3.3 Limit Analysis of Frames

6.3.4 Limit Design of Frames

Section 6.4 Limit Analysis of Plates and Shells

6.4.1 Limit Analysis of Plates

6.4.2 Limit Analysis of Shells: Theory

6.4.3 Limit Analysis of Shells: Examples

Chapter 7: Dynamic Problems

Section 7.1 Dynamic Loading of Structures

7.1.1 Introduction

7.1.2 Dynamic Loading of Beams

7.1.3 Dynamic Loading of Plates and Shells

Section 7.2 One-Dimensional Plastic Waves

7.2.1 Theory of One-Dimensional Waves

7.2.2 Waves in Elastic–Plastic bars

7.2.3 Rate Dependence

7.2.4 Application of the Method of Characteristics

Section 7.3 Three-Dimensional Waves

7.3.1 Theory of Acceleration Waves

7.3.2 Special Cases

Chapter 8: Large-Deformation Plasticity

Section 8.1 Large-Deformation Continuum Mechanics

8.1.1 Continuum Deformation

8.1.2 Continuum Mechanics and Objectivity

Section 8.2 Large-Deformation Constitutive Theory

8.2.1 Thermoelasticity

8.2.2 Inelasticity: Kinematics

8.2.3 Inelasticity: Thermomechanics

8.2.4 Yield Condition and Flow Rule

Section 8.3 Numerical Methods in Large-Deformation Plasticity

8.3.1 Rate-Based Formulations

8.3.2 “Hyperelastic” Numerical Methods

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