Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2013-5pp.553-560

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Total articles in the database: 4675
In Russian (. . ): 2249
In English (Mech. Solids): 2426

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S.A. Lychev and A.V. Manzhirov, "Reference Configurations of Growing Bodies," Mech. Solids. 48 (5), 553-560 (2013)
Year 2013 Volume 48 Number 5 Pages 553-560
DOI 10.3103/S0025654413050117
Title Reference Configurations of Growing Bodies
Author(s) S.A. Lychev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-tVernadskogo101, str.1, Moscow, 119526 Russia,
A.V. Manzhirov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-tVernadskogo101, str.1, Moscow, 119526 Russia,
Abstract The growing bodies are considered as bodies with induced inhomogeneity caused by junction of inconsistently deformed parts. The body is formalized as an abstract smooth manifold, and all possible affine connections on it are classified. A method is shown for introducing a special connection-material connection-for which neighborhoods of all material points of a growing body pass into a stress-free state. A method for constructing a global stress-free reference configuration of a growing body as an embedding in a space with absolute parallelism is proposed. It is shown that in the case of layered accretion, the material connection corresponding to the stress-free embedding is determined by three independent functions and is in general non-Euclidean. The property of being non-Euclidean is determined by the fact that the torsion of the material connection is nonzero. We suggest to formalize the growing body as a fibration of a three-dimensional smooth manifold over a one-dimensional base, and this formalization characterizes the structure of the material connection.
Keywords growing body, deformation inconsistency, inhomogeneity, natural configuration, internal geometry, absolute parallelism
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Received 26 June 2013
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