Generalized Continua as Models for Materials pp 77-90

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 22) | Cite as

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

Chapter

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Victor A. Eremeyev
    • 2
    • 1
  • Wojciech Pietraszkiewicz
    • 3
  1. 1.Faculty of Mechanical EngineeringOtto-von-Guericke-UniversityMagdeburgGermany
  2. 2.South Scientific Center of RASci and South Federal UniversityRostov on DonRussia
  3. 3.Institute of Fluid-Flow Machinery, PASciGdańskPoland

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