Nonlinear Continuum Mechanics and Large Inelastic Deformations

  • Yuriy I. Dimitrienko

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 174)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Yuriy I. Dimitrienko
    Pages 5-88
  3. Yuriy I. Dimitrienko
    Pages 89-159
  4. Yuriy I. Dimitrienko
    Pages 161-346
  5. Yuriy I. Dimitrienko
    Pages 347-375
  6. Yuriy I. Dimitrienko
    Pages 377-460
  7. Yuriy I. Dimitrienko
    Pages 461-496
  8. Yuriy I. Dimitrienko
    Pages 497-589
  9. Yuriy I. Dimitrienko
    Pages 591-706
  10. Back Matter
    Pages 707-721

About this book

Introduction

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Keywords

theories of large viscoelastic and plastic deformations anisotropic co-rotational derivatives constitutive relations deformation compatibility foundations of nonlinear continuum mechanics, inelastic deformations nonlinear continuum mechanics theory of large elastic deformations, viscoelastic

Authors and affiliations

  • Yuriy I. Dimitrienko
    • 1
  1. 1.Moscow State Technical UniversityMoskvaRussian Federation

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-0034-5
  • Copyright Information Springer Science+Business Media B.V. 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-94-007-0033-8
  • Online ISBN 978-94-007-0034-5
  • Series Print ISSN 0925-0042
  • About this book