On the constitutive pseudoscalars of hemitropic micropolar media in inverse coordinate frames

Abstract

The paper is devoted to the constitutive pseudoscalars associated with the theory of hemitropic micropolar continuum. The basic concepts of pseudotensor algebra are presented. The pseudotensor form of the hemitropic micropolar elastic potential is given, based on 9 constitutive pseudoscalars (3 are pseudoscalars and 6 are absolute scalars). The weights of the constitutive pseudoscalars are calculated. The fundamental orienting pseudoscalar of weight \(+1\) is used to formulate transformation rules for constitutive pseudoscalars. The governing equations of the hemitropic micropolar elastic continuum are derived. The equations of the dynamics of the hemitropic micropolar continuum are discussed in terms of pseudotensors in right- and left-handed Cartesian coordinate systems. The presence of inverse modes along with normal ones is shown for wave propagation across the hemitropic micropolar continuum.

Keywords

• micropolar hemitropic continuum
• microrotation
• pseudoscalar
• relative tensor
• fundamental orienting pseudoscalar
• inversion of space
• polarisation