On the theory of fourth-rank hemitropic tensors in three-dimensional Euclidean spaces

The paper is devoted to problems concerning the tensors with constant components, hemitropic tensors and pseudotensors that are of interest from the point of view of micropolar continuum mechanics. The properties and coordinate representations of tensors and pseudotensors with constant components are discussed. Based on an unconventional definition of a hemitropic fourth-rank tensor, a coordinate representations in terms of Kronecker deltas and metric tensors are given. A comparison of an arbitrary hemitropic fourth-rank tensor and a tensor with constant components are discussed. The coordinate representations for constitutive tensors and pseudotensors used in mathematical modeling of linear hemitropic micropolar continuums are given in terms of the metric tensor.The covariant constancy of fourth-rank pseudotensors with constant components and hemitropic tensors is considered and discussed.