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State of the Art and Future Trends in Material Modeling pp 421–442Cite as

On Micropolar Theory with Inertia Production

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 100))

Abstract

This paper presents a new aspect in generalized continuum theory, namely micropolar media showing structural change. Initially the necessary theoretical framework for a micropolar continuum is presented. To this end the standard macroscopic equations for mass and linear and angular momentum are complemented by a recently proposed balance equation for the moment of inertia tensor containing a production term. The new balance and, in particular, the production is interpreted mesoscopically by taking the inner structure of micropolar media into account. Various of examples for the term are presented.

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Acknowledgements

The author is deeply grateful to E.A. Ivanova and W.H. Müller for useful discussions on the subject.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, Politechnicheskaya 29, 195251, St. Petersburg, Russia

    Elena Vilchevskaya

  2. Laboratory of Mathematical Methods in Mechanics of Materials, Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Bolshoy pr. V.O. 61, 199178, St. Petersburg, Russia

    Elena Vilchevskaya

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  1. Elena Vilchevskaya
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Correspondence to Elena Vilchevskaya .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany

    Andreas Öchsner

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Vilchevskaya, E. (2019). On Micropolar Theory with Inertia Production. In: Altenbach, H., Öchsner, A. (eds) State of the Art and Future Trends in Material Modeling . Advanced Structured Materials, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-30355-6_18

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