Solid Mechanics and Its Applications

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Authors: Dimitrienko, Yuriy I.

  • Presents a rigorous axiomatic approach to continuum mechanics
  • Introduces a new approach to the formulation of constitutive equations for nonlinear continua
  • Includes advanced models for visco-elastic materials under large deformation
  • Explores advanced models for plastic materials under large deformation
  • Provides a comparison of experimental data and results computed by different models
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eBook $259.00
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  • ISBN 978-94-007-0034-5
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  • Immediate eBook download after purchase
Hardcover $329.00
price for USA
  • ISBN 978-94-007-0033-8
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Softcover $329.00
price for USA
  • ISBN 978-94-007-3413-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this book

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.

Reviews

From the reviews:

“The present book is a textbook for master and PhD students studying the mathematical continuum mechanics. Based on a strong mathematical framework, the author presents the basics of continuum mechanics and materials theory. … For further studies 60 references are given.” (Holm Altenbach, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 92 (6), 2012)

Table of contents (9 chapters)

  • Introduction: Fundamental Axioms of Continuum Mechanics

    Dimitrienko, Yuriy I.

    Pages 1-4

  • Kinematics of Continua

    Dimitrienko, Yuriy I.

    Pages 5-88

  • Balance Laws

    Dimitrienko, Yuriy I.

    Pages 89-159

  • Constitutive Equations

    Dimitrienko, Yuriy I.

    Pages 161-346

  • Relations at Singular Surfaces

    Dimitrienko, Yuriy I.

    Pages 347-375

Buy this book

eBook $259.00
price for USA (gross)
  • ISBN 978-94-007-0034-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $329.00
price for USA
  • ISBN 978-94-007-0033-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $329.00
price for USA
  • ISBN 978-94-007-3413-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Continuum Mechanics and Large Inelastic Deformations
Authors
Series Title
Solid Mechanics and Its Applications
Series Volume
174
Copyright
2011
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-007-0034-5
DOI
10.1007/978-94-007-0034-5
Hardcover ISBN
978-94-007-0033-8
Softcover ISBN
978-94-007-3413-5
Series ISSN
0925-0042
Edition Number
1
Number of Pages
XXIV, 721
Topics