Tensors with Constant Components in the Constitutive Equations of a Hemitropic Micropolar Solids

The present paper is devoted to elastic potentials and the constitutive equations of mechanics of anisotropic micropolar solids, the kinematics of which can be specified by two independent vector fields: a contravariant field of translational displacements and a contravariant pseudovector field of microrotations of weight +1. The quadratic stress potential is represented by three constitutive tensors of the fourth rank, two of which are pseudotensor in nature and can be assigned weights –2 and –1. Such a solid is completely specified by the 171st micropolar elastic modulus. The main attention is focused on the model of a hemitropic (half-isotropic, demitropic) micropolar elastic solid characterized by nine constitutive constants. The components of the constitutive pseudo-tensor of weight ‒1 turn out to be sensitive to mirror reflection transformations in three-dimensional space. A peculiar algebraic structure of the constitutive tensors of a hemitropic solid, more precisely, their absolute analogues obtained by multiplying by integer powers of a pseudoscalar unity, is studied. It is shown that these tensors can always be constructed from isomers (isomer) of a tensor with constant components (generally insensitive to any transformations of the coordinate system) and one additional fourth-rank tensor constructed, in turn, from the components of the metric tensor.