Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

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S.A. Lychev, "Universal Deformations of Growing Solids," Mech. Solids. 46 (6), 863-876 (2011)
Year 2011 Volume 46 Number 6 Pages 863-876
DOI 10.3103/S0025654411060069
Title Universal Deformations of Growing Solids
Author(s) S.A. Lychev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia,
Abstract A class of universal deformations of accreted hyperelastic incompressible bodies is studied. Accretion is realized by adding prestrained layers [1-4]. The deformations correspond layerwise to the transformation of a parallelepiped to a hollow circular cylinder. Discrete and continuous accretion modes are considered and classified. Solutions of the boundary-value problems for the elastic Mooney-Rivlin potential are constructed. The solutions of the discrete accretion problems are shown to converge to solutions of the corresponding problems of continuous accretion as the number of layers increases and the layer thickness decreases.
Keywords finite deformations, growing solids, universal deformations, discrete accretion, continuous accretion, incompatibility, residual stresses
1.  N. Kh. Arutyunyan and A. V. Manzhirov, Contact Problems of Creep Theory (Inst. Mekh. NAN, Erevan, 1999) [in Russian].
2.  N. Kh. Arutyunyan, A. V. Manzhirov, and V. E. Naumov, Contact Problems of Mechanics of Growing Bodies (Nauka, Moscow, 1991) [in Russian].
3.  A. V. Manzhirov and D. A. Parshin, "Modeling the Accretion of Cylindrical Bodies on a Rotating Mandrel with Centrifugal Forces Taken into Account," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 149-166 (2006) [Mech. Solids (Engl. Transl.) 41 (6), 121-134 (2006)].
4.  S. A. Lychev, T. N. Lycheva, and A. V. Manzhirov, "Unsteady Vibration of a Growing Circular Plate," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 199-208 (2011) [Mech. Solids (Engl. Transl.) 46 (2), 325-333 (2011)].
5.  V. N. Kukudzhanov, Computational Continuum Mechanics (Fizmatgiz, Moscow, 2008) [in Russian].
6.  C. A. Truesdell, A First Course in Rational Continuum Mechanics (The Johns Hopkins University Press, Baltimore, Maryland, 1972; Mir, Moscow, 1975).
7.  A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].
8.  W. Noll, "Materially Uniform Simple Bodies with Inhomogeneities," Arch. Rat. Mech. Anal., No. 2, 1-32 (1967).
Received 17 August 2011
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