Two-dimensional Nye figures for hemitropic micropolar elastic solids

Abstract

The paper is devoted to a wide range of problems related to the two-dimensional Nye figures for micropolar continua. The method of two-dimensional matrix representation of fourth-rank tensors is well known from monographs on crystallography. Such representations are used to simplify tensor notation of the equations of anisotropic solids. This method allows us to represent the asymmetric constitutive tensors and pseudotensors of the fourth, third and second ranks in the form of specific two-dimensional figures. The Nye figures for the constitutive hemitropic tensors of the fourth and second ranks are given. The matrix form of the constitutive equations of a hemitropic micropolar solid in the athermal case is obtained. The transformation of the pseudotensor governing equations of the micropolar theory to a formulation in terms of absolute tensors is carried out via the  pseudoscalar units and their integer powers. The study is carried out in terms of absolute tensors in a Cartesian rectangular coordinate system.

Keywords

• elastic energy potential
• constitutive tensor
• pseudotensor unit
• hemitropic micropolar continuum
• nye figure
• matrix notation