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Material symmetry group and constitutive equations of micropolar anisotropic elastic solids. (English) Zbl 1332.74003

Summary: We discuss the material symmetry group of the micropolar continuum and related consistently simplified constitutive equations. Following V. A. Eremeyev and W. Pietraszkiewicz [“Material symmetry group of the non-linear polar-elastic continuum”, Int. J. Solid. Struct. 49, No. 14, 1993–2005 (2012; doi:10.1016/j.ijsolstr.2012.04.007); “Material symmetry group and consistently reduced constitutive equations of the elastic cosserat continuum”, in: Generalized continua as models for materials. Heidelberg: Springer. 77–90 (2013)] we extend the definition of the group proposed by A. C. Eringen and C. B. Kafadar [“Polar field theories”, in: Continuum physics, Vol. 4. New York, NY: Academic Press. 1–75 (1976)] 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.

MSC:

74A20 Theory of constitutive functions in solid mechanics
74E10 Anisotropy in solid mechanics
74A35 Polar materials
74A60 Micromechanical theories
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