 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, lychevsa@mail.ru)
A.V. Manzhirov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, manzh@ipmnet.ru) |
| 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 |
| References |
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|
| Received |
26 June 2013 |
| Link to Fulltext |
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