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Nonlinear Continuum Mechanics and Large Inelastic Deformations

  • Book
  • © 2011

Overview

Authors:
  1. Yuriy I. Dimitrienko

    1. Moscow State Technical University, Moskva, Russian Federation

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  • Rgorous axiomatic approach to continuum mechanics
  • New approach to the formulation of constitutive equations for nonlinear continua
  • Advanced models for visco-elastic materials under large deformation
  • Advanced models for plastic materials under large deformation
  • Comparison of experimental data and results computed by different models
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. Introduction: Fundamental Axioms of Continuum Mechanics

    • Yuriy I. Dimitrienko
    Pages 1-4

  3. Kinematics of Continua

    • Yuriy I. Dimitrienko
    Pages 5-88

  4. Balance Laws

    • Yuriy I. Dimitrienko
    Pages 89-159

  5. Constitutive Equations

    • Yuriy I. Dimitrienko
    Pages 161-346

  6. Relations at Singular Surfaces

    • Yuriy I. Dimitrienko
    Pages 347-375

  7. Elastic Continua at Large Deformations

    • Yuriy I. Dimitrienko
    Pages 377-460

  8. Continua of the Differential Type

    • Yuriy I. Dimitrienko
    Pages 461-496

  9. Viscoelastic Continua at Large Deformations

    • Yuriy I. Dimitrienko
    Pages 497-589

  10. Plastic Continua at Large Deformations

    • Yuriy I. Dimitrienko
    Pages 591-706

  11. Back Matter

    Pages 707-721
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Keywords

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)

Authors and Affiliations

  • Moscow State Technical University, Moskva, Russian Federation

    Yuriy I. Dimitrienko

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