Material symmetry group of the non-linear polar-elastic continuum

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:49

Article

Eremeyev, Victor A.^2,3,4  Pietraszkiewicz, Wojciech¹ 

[1] PASci, Inst Fluid Flow Machinery, PL-80952 Gdansk, Poland

[2] Univ Magdeburg, D-39106 Magdeburg, Germany

[3] RASci, S Sci Ctr, Rostov Na Donu, Russia

[4] S Fed Univ, Rostov Na Donu, Russia

关键词: Material symmetry;    Symmetry group;    Polar-elastic continuum;    Cosserat continuum;    Non-linear theory;    Constitutive equations;   

DOI  :  10.1016/j.ijsolstr.2012.04.007

来源: Elsevier

【 摘 要 】

We extend the material symmetry group of the non-linear polar-elastic continuum by taking into account microstructure curvature tensors as well as different transformation properties of polar and axial tensors. The group consists of an ordered triple of tensors which makes the strain energy density of polar-elastic continuum invariant under change of reference placement. An analog of the Noll rule is established. Four simple specific cases of the group with corresponding reduced forms of the strain energy density are discussed. Definitions of polar-elastic fluids, solids, liquid crystals and subfluids are given in terms of members of the symmetry group. Within polar-elastic solids we discuss in more detail isotropic, hemitropic, cubic-symmetric, transversely isotropic, and orthotropic materials and give explicitly corresponding reduced representations of the strain energy density. For physically linear polar-elastic solids, when the density becomes a quadratic function of strain measures, reduced representations of the density are established for monoclinic, allotropic, cubic-symmetric, hemitropic and isotropic materials in terms of appropriate joint scalar invariants of stretch, wryness and undeformed structure curvature tensors. (C) 2012 Elsevier Ltd. All rights reserved.

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