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Description of Thermal and Micro-Structural Processes in Generalized Continua: Zhilin’s Method and its Modifications

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Generalized Continua as Models for Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 22))

Abstract

The method of description of thermal and micro-structural processes, developed by P.A.Zhilin is discussed. The main idea of the method consists of 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 have a sense of heat conduction equation, diffusion equation, equation of structural transformations, etc. We discuss the applicability of this method to generalized continua, in particular, to media with rotational degrees of freedom and media with microstructure. Comparative analysis of various modifications of Zhilin’s method, differed in the way of temperature, entropy and chemical potential introduction, is carried out.

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Notes

  1. 1.

    Details are presented in E.N. Vilchevskaya. Appendix: Formula calculus in [35].

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Authors and Affiliations

  1. Saint-Petersburg State Polytechnical University (SPbSPU), Politekhnicheskaja 29, Saint-Petersburg, 195251, Russia

    Elena Ivanova

  2. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bolshoy pr. 61, Saint-Petersburg, 199178, Russia

    Elena Vilchevskaya

Authors
  1. Elena Ivanova
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  2. Elena Vilchevskaya
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Correspondence to Elena Ivanova .

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Editors and Affiliations

  1. , Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Magdeburg, 39112, Germany

    Holm Altenbach

  2. , Centre des Materiaux CNRS UMR 7633, Mines ParisTech, BP 87, EVRY Cedex, 91003, France

    Samuel Forest

  3. University, Dep. of Theoretical Mechanics, St. Petersburg State Polytechnical, Politekhnicheskaya, 29, St. Petersburg, 195251, Russia

    Anton Krivtsov

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Ivanova, E., Vilchevskaya, E. (2013). Description of Thermal and Micro-Structural Processes in Generalized Continua: Zhilin’s Method and its Modifications. In: Altenbach, H., Forest, S., Krivtsov, A. (eds) Generalized Continua as Models for Materials. Advanced Structured Materials, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36394-8_10

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