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Zhilin’s Method and Its Modifications

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Encyclopedia of Continuum Mechanics

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Synonyms

Chemical potential; Entropy introduction; Zhilin’s approach

Definitions

The main idea of the method consists in transformation of the energy balance equation to a special form called the reduced equation of energy balance. This form is obtained by separation of the stress tensors into elastic and dissipative components and introduction of quantities characterizing the physical processes associated with neglected degrees of freedom. As a result the energy balance equation is divided into two or more parts: one of them is the reduced equation of energy balance and the rest carrying the meaning of heat conduction equation and equation of structural transformations.

Introduction

To describe inelastic processes associated with phase transitions and structural transformations, plastic flow, dynamics of bulk solids, dynamics of granular media, fragmentation and defragmentation of materials, particle diffusion, chemical reactions, etc., it is important to introduce additional state...

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References

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Author information

Authors and Affiliations

  1. Department of Theoretical Mechanics, Peter the Great St.Petersburg Polytechnic University, St.Petersburg, Russia

    Elena A. Ivanova & Elena N. Vilchevskaya

  2. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, St.Petersburg, Russia

    Elena A. Ivanova & Elena N. Vilchevskaya

Authors
  1. Elena A. Ivanova
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  2. Elena N. Vilchevskaya
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Corresponding author

Correspondence to Elena A. Ivanova .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Department of Theoretical Mechanics, Peter the Great St.Petersburg Polytechnic University, St.Petersburg, Russia

    Elena A. Ivanova

  2. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, St.Petersburg, Russia

    Elena A. Ivanova

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Ivanova, E.A., Vilchevskaya, E.N. (2018). Zhilin’s Method and Its Modifications. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_59-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_59-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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