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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2020, Volume 24, Number 3, Pages 424–444
DOI: https://doi.org/10.14498/vsgtu1792
(Mi vsgtu1792)
 

This article is cited in 24 scientific papers (total in 24 papers)

Mechanics of Solids

On a micropolar theory of growing solids

E. V. Murashkin, Yu. N. Radayev

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The present paper is devoted to the problem of boundary conditions formulation in the growing micropolar solid mechanics. The static equations of the micropolar continuum in terms of relative tensors (pseudotensors) are derived due to virtual work principle for a solid of constant staff. The constitutive quadratic form of the elastic potential (treated as an absolute scalar) for a linear hemitropic micropolar solid is presented and discussed. The constitutive equations for symmetric and antisymmetric parts of force and couple stress tensors are given. The final forms of the static equations for the hemitropic micropolar continuum in terms of displacements and microrotations rates are obtained including the case of growing processes. A transformation of the equilibrium equations is proposed to obtain boundary conditions on the propagating growing surface in terms of relative tensors in the form of differential constraints. Those are valid for a wide range of materials and metamaterials. The algebra of rational relative invariants is intensively used for deriving the constitutive relations on the growing surface. Systems of joint algebraic rational relative invariants for force, couple stress tensors and also unit normal and tangent vectors to propagating growing surface are obtained, including systems of invariants sensitive to mirror reflections and 3D-space inversions.
Keywords: micropolar hemitropic continuum, microrotation, pseudoscalar, relative tensor, 3D printing, propagating growing surface, stress, constitutive equation, rational relative invariant, differential constraint, complete system.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-00844
19-51-60001
20-01-00666
Russian Academy of Sciences - Federal Agency for Scientific Organizations АААА-А20-120011690132-4
This study was in part financially supported by the Ministry of Science and Higher Education of the Russian Federation (State Registration Number AAAA–A20–120011690132–4) and by the Russian Foundation for Basic Research projects nos. 18–01–00844, 19–51–60001, 20–01–00666.
Received: June 15, 2020
Revised: August 17, 2020
Accepted: September 14, 2020
First online: September 30, 2020
Bibliographic databases:
Document Type: Article
UDC: 539.319
Language: English
Citation: E. V. Murashkin, Yu. N. Radayev, “On a micropolar theory of growing solids”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:3 (2020), 424–444
Citation in format AMSBIB
\Bibitem{MurRad20}
\by E.~V.~Murashkin, Yu.~N.~Radayev
\paper On a micropolar theory of growing solids
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 3
\pages 424--444
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\crossref{https://doi.org/10.14498/vsgtu1792}
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\elib{https://elibrary.ru/item.asp?id=45631179}
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  • https://www.mathnet.ru/eng/vsgtu/v224/i3/p424
  • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :233
    References:43
     
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