Universal solutions for isotropic incompressible micropolar solids

摘要

The significance of universal solutions consists in the fact that they can be used efficiently for the experimental determination of equations of state of a material. The model of the micropolar medium is applied to the description of composites, polymers, and also nano-structural, high-porous, magnetic, and other materials. Due to the fact that the rotation field of the Cosserat continuum is kinematically independent of the displacement field, the set of universal solutions of the micropolar elasticity considerably exceeds the set of universal deformations of the classical theory of elasticity for nonpolar materials. For these orthogonal coordinates, it is convenient to apply the orthonormalized vector bases, the vectors of which are tangential to the coordinate lines.