© 2013


Mathematical Theory and Numerical Analysis


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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Continuum Mechanics and Elastoplasticity Theory

    1. Front Matter
      Pages 1-1
    2. Weimin Han, B. Daya Reddy
      Pages 3-13
    3. Weimin Han, B. Daya Reddy
      Pages 15-39
    4. Weimin Han, B. Daya Reddy
      Pages 41-94
    5. Weimin Han, B. Daya Reddy
      Pages 95-122
  3. The Variational Problems of Elastoplasticity

    1. Front Matter
      Pages 123-123
    2. Weimin Han, B. Daya Reddy
      Pages 125-150
    3. Weimin Han, B. Daya Reddy
      Pages 151-185
    4. Weimin Han, B. Daya Reddy
      Pages 187-223
    5. Weimin Han, B. Daya Reddy
      Pages 225-248
  4. Numerical Analysis of the Variational Problems

    1. Front Matter
      Pages 249-249
    2. Weimin Han, B. Daya Reddy
      Pages 251-267
    3. Weimin Han, B. Daya Reddy
      Pages 269-283
    4. Weimin Han, B. Daya Reddy
      Pages 285-317
    5. Weimin Han, B. Daya Reddy
      Pages 319-370
    6. Weimin Han, B. Daya Reddy
      Pages 371-404
  5. Back Matter
    Pages 405-421

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)


Continuum Mechanics Finite Element Analysis Functional Analysis Linear Elasticity

Authors and affiliations

  1. 1.University of Iowa CityIowa CityUSA
  2. 2., Faculty of ScienceUniversity of Cape TownRondeboschSouth Africa

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


“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)