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Plasticity

Mathematical Theory and Numerical Analysis

  • Book
  • © 2013

Overview

Authors:
  1. Weimin Han

    1. University of Iowa City, Iowa City, USA

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    You can also search for this author in PubMed   Google Scholar

  2. B. Daya Reddy

    1. , Faculty of Science, University of Cape Town, Rondebosch, South Africa

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    You can also search for this author in PubMed   Google Scholar

  • Book bridging mechanics and mathematics
  • Provides a comprehensive and unified treatment of the mathematical theory and numerical analysis
  • Focuses on theoretical aspects of the small-strain theory of hardening elastoplasticity
  • Includes supplementary material: sn.pub/extras

Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 9)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xv
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  2. Continuum Mechanics and Elastoplasticity Theory

    1. Front Matter

      Pages 1-1
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    2. Preliminaries

      • Weimin Han, B. Daya Reddy
      Pages 3-13

    3. Continuum Mechanics and Linearized Elasticity

      • Weimin Han, B. Daya Reddy
      Pages 15-39

    4. Elastoplastic Media

      • Weimin Han, B. Daya Reddy
      Pages 41-94

    5. The Plastic Flow Law in a Convex-Analytic Setting

      • Weimin Han, B. Daya Reddy
      Pages 95-122

  3. The Variational Problems of Elastoplasticity

    1. Front Matter

      Pages 123-123
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    2. Basics of Functional Analysis and Function Spaces

      • Weimin Han, B. Daya Reddy
      Pages 125-150

    3. Variational Equations and Inequalities

      • Weimin Han, B. Daya Reddy
      Pages 151-185

    4. The Primal Variational Problem of Elastoplasticity

      • Weimin Han, B. Daya Reddy
      Pages 187-223

    5. The Dual Variational Problem of Classical Elastoplasticity

      • Weimin Han, B. Daya Reddy
      Pages 225-248

  4. Numerical Analysis of the Variational Problems

    1. Front Matter

      Pages 249-249
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    2. Introduction to Finite Element Analysis

      • Weimin Han, B. Daya Reddy
      Pages 251-267

    3. Approximation of Variational Problems

      • Weimin Han, B. Daya Reddy
      Pages 269-283

    4. Approximations of the Abstract Problem

      • Weimin Han, B. Daya Reddy
      Pages 285-317

    5. Numerical Analysis of the Primal Problem

      • Weimin Han, B. Daya Reddy
      Pages 319-370

    6. Numerical Analysis of the Dual Problem

      • Weimin Han, B. Daya Reddy
      Pages 371-404

  5. Back Matter

    Pages 405-421
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Keywords

About this book

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: “The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory.” (ZAMM, 2002) “In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field.” (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Reviews

“The book is unique in its broad consideration of analytical and numerical aspects of plasticity. … The book is well written and carefully presented overall. It presents a wealth of useful material otherwise absent from other plasticity books. It exposes both the interested mechanician and the interested mathematician to mathematical problems in plasticity in a unified manner, albeit to be pursued in their own way.” (Anurag Gupta, SIAM Review, Vol. 58 (4), December, 2016)

Authors and Affiliations

  • University of Iowa City, Iowa City, USA

    Weimin Han

  • , Faculty of Science, University of Cape Town, Rondebosch, South Africa

    B. Daya Reddy

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