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Material Symmetry Group and Consistently Reduced Constitutive Equations of the Elastic Cosserat Continuum

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Generalized Continua as Models for Materials

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

Abstract

We discuss the material symmetry group of the polar-elastic continuum and related consistently simplified constitutive equations. Following [1] we extent the definition of the group proposed by Eringen and Kafadar [2] by taking into account the microstructure curvature tensor as well as different transformation properties of polar and axial tensors. Our material symmetry group consists of ordered triples of tensors which make the strain energy density of the polar-elastic continuum invariant under change of the reference placement. Within the polar-elastic solids we discuss the isotropic, hemitropic, orthotropic, transversely isotropic and cubic-symmetric materials and give explicitly the consistently reduced representations of the strain energy density.

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Acknowledgments

The first author was supported by the DFG grant No. AL 341/33-1 and by the RFBR with the grant No. 12-01-00038.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Otto-von-Guericke-University, 39106 , Magdeburg, Germany

    Victor A. Eremeyev

  2. South Scientific Center of RASci and South Federal University, Milchakova St. 8a, Rostov on Don, 344090, Russia

    Victor A. Eremeyev

  3. Institute of Fluid-Flow Machinery, PASci, ul. Gen. J. Fiszera 14, 80-952, Gdańsk, Poland

    Wojciech Pietraszkiewicz

Authors
  1. Victor A. Eremeyev
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  2. Wojciech Pietraszkiewicz
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Correspondence to Victor A. Eremeyev .

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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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Eremeyev, V.A., Pietraszkiewicz, W. (2013). Material Symmetry Group and Consistently Reduced Constitutive Equations of the Elastic Cosserat Continuum. 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_5

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