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On Strain Rate Tensors and Constitutive Equations of Inelastic Micropolar Materials

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Book cover Generalized Continua as Models for Classical and Advanced Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 42))

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Abstract

Following Altenbach and Eremeyev (Int J Plast 63:3–17, 2014) we introduce a new family of strain rate tensors for micropolar materials. With the help of introduced strain rates we discuss the possible forms of constitutive equations of the nonlinear inelastic micropolar continuum, that is micropolar viscous and viscoelastic fluids and solids, hypo-elastic and viscoelastoplastic materials. Considering the fact that some of strain rates are not true tensors but pseudotensors we obtain some constitutive restrictions following from the material frame indifference principle. Using the theory of tensorial invariants we present the general form of constitutive equations of some types of inelastic isotropic micropolar materials including several new constitutive equations.

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Authors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universtät Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holm Altenbach

  2. Faculty of Mechanical Engineering, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959, Rzeszów, Poland

    Victor A. Eremeyev

Authors
  1. Holm Altenbach
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  2. Victor A. Eremeyev
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Correspondence to Victor A. Eremeyev .

Editor information

Editors and Affiliations

  1. Universität Magdeburg, Otto‐von‐Guericke, Magdeburg, Germany

    Holm Altenbach

  2. Mines ParisTech, Paris, France

    Samuel Forest

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Altenbach, H., Eremeyev, V.A. (2016). On Strain Rate Tensors and Constitutive Equations of Inelastic Micropolar Materials. In: Altenbach, H., Forest, S. (eds) Generalized Continua as Models for Classical and Advanced Materials. Advanced Structured Materials, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-31721-2_1

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  • DOI: https://doi.org/10.1007/978-3-319-31721-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31719-9

  • Online ISBN: 978-3-319-31721-2

  • eBook Packages: EngineeringEngineering (R0)

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