Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state

Bulletin of the Yakovlev Chuvash State Pedagogical University. Series: Mechanics of Limit State


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Kovalev V.A., Murashkin E.V., Stadnik N.E. On a multiweight formulation of boundary conditions for surface growth theories // Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state . 2024. № 1(59). p. 5-20
Author(s):Kovalev V.A., Murashkin E.V., Stadnik N.E.
Index of UDK:539.374
DOI:10.37972/chgpu.2024.59.1.013
Title:On a multiweight formulation of boundary conditions for surface growth theories
Keywords:algebraic weight, pseudotensor, nanoscale, microscale, micropolarity, pseudotensor volume element, multiweight formulation, constitutive pseudotensor function, growing surface,rational pseudoinvariant.
Abstracts:In this paper, we consider a method for constructing a multiweight theory of surface growth in terms of pseudotensors. The mathematical theory proposed for consideration is substantially based on the achievements of modern pseudotensor calculus. Definitions of multiweight pseudotensor elements of area and volume are given. The general multiweight form of the pseudotensor relation on a growing surface is derived, taking into account the additional selected direction. The necessary system of independent multiweight pseudotensor arguments of the defining pseudotensor function on the growing surface is determined. A complete multiweight set of joint rational pseudoinvariants of force and couple stress pseudotensors is determined. A pseudoinvariant complete formulation of the constitutive relations on the growing surface is given.
The contact details of authors:Kovalev Vladimir Alexandrovich, Dr. Sci. Phys. & Math., Professor, Moscow City University of Management, Moscow, Russia; e-mail: vlad_koval@mail.ru; https://orcid.org/0000-0003-2991-9531; AuthorID: 782898 Evgenii V. Murashkin, Cand. Sci. Phys. & Math., MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; e-mail: evmurashkin@gmail.ru; https://orcid.org/0000-0002-3267-4742; AuthorID: 129570 Nikita E. Stadnik, MD, Minor Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; e-mail: nik-122@mail.ru; https://orcid.org/0000-0002-0187-8048; AuthorID: 961836
Pages:5-20
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