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Foundations of Micropolar Mechanics pp 35–70Cite as

Constitutive Equations

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Abstract

For an arbitrary part of the body, Eqs. (3.30) and (3.31) express the balance equations for the moment and the moment of momentum. These six scalar equations contain 18 unknown quantities that are the components of tensors \(\mathbf{ T} \) and \(\mathbf{ M} \). The dependence of \(\mathbf{ T} \) and \(\mathbf{ M} \) on medium deformations is determined by the constitutive equations or constitutive relations that depend on the material properties. They are determined experimentally. The constitutive equations must obey some principles that restrict their form, see [1].

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Authors and Affiliations

  1. Halle-Wittenberg, Martin-Luther-Universität, Kurt-Mothes-Str. 1, 06120, Halle, Germany

    Victor A. Eremeyev

  2. Universidad Nacional de Colombia, Bogotá, Colombia

    Leonid P. Lebedev

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

    Holm Altenbach

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Eremeyev, V.A., Lebedev, L.P., Altenbach, H. (2013). Constitutive Equations. In: Foundations of Micropolar Mechanics. SpringerBriefs in Applied Sciences and Technology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28353-6_4

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