\"This book goes back a long way. There is a tradition of research and teaching in inelasticity at Stanford that goes back at least to Wilhelm Flugge and Erastus Lee.I joined the faculty in 1980, and shortly thereafter the Chairman of the Applied Mechanics Division, George Herrmann, asked me to present a course in plasticity.I decided to develop a new two-quarter sequence entitled Theoretical and Computational Plasticity which combined the basic theory I had learned as a graduate student at the University of California at Berkeley from David Bogy, James Kelly,Jacob Lubliner, and Paul Naghdi with new computational techniques from the finite-element literature and my personal research. I taught the course a couple of times and developed a set of notes that 1 passed on to Juan Simo when he joined the faculty in 1985.1 was Chairman at that time and I asked Juan to furthdr develop the course into a full year covering inelasticity from a more comprehensive per-spectiye.\"

\"Preface Chapter I Motivation. One-Dimensional Plasticity and Viscoplasticity. 1.1 Overview 1.2 Motivation. One-Dimensional Frictional Models 1.2.1 Local Governing Equations 1.2.2 An Elementary Model for (Isotropic) Hardening Plasticity 1.2.3 Aitemative Form of the Loading/Unloading Conditions 1.2.4 Further Refinements of the Hardening Law 1.2.5 Geometric Properties of the Elastic Domain 1.3 The Initial Boundary-Value Problem 1.3.1 The Local Form of the IBVP 1.3.2 The Weak Formulation of the IBVP 1.3.3 Dissipation. A priori Stability Estimate 1:3.4 Uniqueness of the Solution to the IBVE Contractivity 1.3.5 Outline of the Numerical Solution of the IBVP 1.4 Integration Algorithms for Rate-Independent Plasticity 1.4.1 The Incremental Form of Rate-Independent Plasticity 1.4,2 Return-Mapping Algorithms.1sotropic Hardening 1..3 Discrete Variational Formulation. Convex Optimization 1.4.4 Extension to the Combined lsotropic/Kinematic Hardening Model 1.5 Finite-Element Solution of the Elastoplastic IBVP. An Illustration 1.5.1Spatial Discretization. Finite-Element Approximation 1.5.2 Incremental Solution Procedure 1.6 Stability Analysis of the Algorithmic IBVP 1.6.1 Algorithmic Approximation to the Dynamic Weak Form 1.7 One-\'Dimensional Viscoplasticity 1.7.1 One-Dimensional Rheological Model 1.7.2 Dissipation. A Priori Stability Estimate 1.7.3 An Integration Algorithm for Viscoplasticity Chapter 2 Classical Rate-independent Plasticity and Viscoplasticity. 2.1 Review of Some Standard Notation 2.1.1 The Local Form of the IBVP. Elasticity 2.2 Classical Rate-Independent Plasticity 2.2.1 Strain-Space and Stress-Space Formulations 2.2.2 Stress-Space Governing Equations 2.2.3 Strain-Space Formulation 2.2.4 An Elementary Example: I-D Plasticity 2.3 Plane Strain and 3-D, Classical /2 Flow Theory 2.3.1 Perfect Plasticity 2.3.2 -/2 Flow Theory with lsotropic/Kinematic Hardening 2.4 Plane-Stress -/2 Flow Theory 2.4.1 Projection onto the Plane-Str\"