Material symmetry group and constitutive equations of micropolar anisotropic elastic solids

Author:

Eremeyev Victor A1,Pietraszkiewicz Wojciech2

Affiliation:

1. Institute of Mechanics, Otto von Guericke University Magdeburg, Germany; South Scientific Center of RASci & South Federal University, Rostov-on-Don, Russia

2. Institute of Fluid-Flow Machinery, PASci, Gdańsk, Poland

Abstract

We discuss the material symmetry group of the micropolar continuum and related consistently simplified constitutive equations. Following Eremeyev and Pietraszkiewicz ( Int J Solid Struct 2012; 49: 1993–2005; Generalized continua as models for materials, Heidelberg: Springer, 2013, 77–90) we extend the definition of the group proposed by Eringen and Kafadar ( Continuum physics, vol. 4, New York, NY: Academic Press, 1976, 1–75) by taking into account the microstructure curvature tensor as well as different transformation properties of polar (true) and axial (pseudo) tensors. Our material symmetry group consists of ordered triples of tensors which make the strain energy density of the micropolar continuum invariant under change of the reference placement. Within micropolar solids we discuss the isotropic, hemitropic, orthotropic, transversely isotropic and clinotropic materials and give explicitly the consistently reduced representations of the strain energy density.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

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