Material symmetry group and constitutive equations of micropolar anisotropic elastic solids. (February 2016)

• Record Type: Journal Article
• Authors: Eremeyev, Victor A; Pietraszkiewicz, Wojciech
• Other Names: Eremeyev Victor A guest-editor.; Porubov Alexey V guest-editor.; Placidi Luca guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 21:Number 2(2016:Mar.)
• Page Start: 210
• Page End: 221
• Publication Date: 2016-02
• Subjects: Micropolar solid -- Cosserat continuum -- material symmetry group -- orthotropy -- isotropy -- strain energy density; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286515582862
• Languages: English
• ISSNs: 1081-2865

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.