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

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Abstract

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.

About the authors

Eugenii V. Murashkin

Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Email: evmurashkin@gmail.com
ORCID iD: 0000-0002-3267-4742
SPIN-code: 4022-4305
Scopus Author ID: 12760003400
ResearcherId: F-4192-2014
http://www.mathnet.ru/person53045

Cand. Phys. & Math. Sci., PhD, MD; Senior Researcher; Lab. of Modeling in Solid Mechanics

101–1, pr. Vernadskogo, Moscow, 119526, Russian Federation

Yuri N. Radayev

Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Author for correspondence.
Email: y.radayev@gmail.com
ORCID iD: 0000-0002-0866-2151
SPIN-code: 5886-9203
Scopus Author ID: 6602740688
ResearcherId: J-8505-2019
http://www.mathnet.ru/person39479

D.Sc. (Phys. & Math. Sci.), Ph.D., M.Sc., Professor; Leading Researcher; Lab. of Modeling in Solid Mechanics

Russian Federation, 101–1, pr. Vernadskogo, Moscow, 119526, Russian Federation

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