pseudotensor, fundamental orienting pseudoscalar, micropolar hemitropic continuum, M-cell, frame, Stokes theorem

Oriented continua play an important role in the micropolar theory of elasticity, all realizations of which are possible only within the framework of the pseudotensor formalism and the orientable manifold concept. This especially concerns the theory of micropolar hemitropic elastic media. In this paper, we consider various formulations of the Stokes integral theorem for an asymmetric covariant pseudotensor field of a given weight. This extends the well-known Stokes integral formula to the case of pseudotensors. The latter circumstance makes it possible to use the manifistated generalization for micropolar continua. The study relies heavily on the class of special coordinate systems.

Evgenii V. Murashkin, Cand. Sc., PhD, MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences,

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

Yuri N. Radayev, D. Sc., PhD, MSc, Professor of Continuum Mechanics, Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.