Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2006-4pp.118-129

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Total articles in the database: 10864
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R. V. Goldstein and G. A. Shatalov, "Modeling of rupture processes in the framework of the generalized model of atomistic normal separation cracks," Mech. Solids. 41 (4), 118-129 (2006)
Year 2006 Volume 41 Number 4 Pages 118-129
Title Modeling of rupture processes in the framework of the generalized model of atomistic normal separation cracks
Author(s) R. V. Goldstein (Moscow)
G. A. Shatalov (Moscow)
Abstract We propose a generalized atomic model of a Thomson type crack. We assume that an edge crack separates four half-infinite chains of atoms. The interaction between atoms within each of the chains is characterized by springs with flexural rigidity, while the interaction between atoms in neighboring chains is modeled by bilinear bonds (springs) working in tension. The loading is realized by lumped tensile forces acting on the extreme atoms in the chains. We perform analytical-numerical modeling of the deformation and bond rupture processes near the crack tip and obtain an estimate for the dimensions of the adhesion region depending on the crack length and the bond parameters. We analyze the role of the additional (compared with the Thomson model) atomic chains and their influence on the redistribution of stresses and displacements in the adhesion region as well as the dimensions of the adhesion region itself.
1.  G. I. Barenblatt, "On equilibrium cracks formed in the process of brittle fracture," PMM [Applied Mathematics and Mechanics], Vol. 23, No. 3, pp. 434-444 (General ideas and hypothesis. Axially symmetric cracks); No. 4, pp. 706-721 (Rectilinear cracks in plane plates); No. 5, pp. 893-900 (Stability of isolated cracks. Relationship between energy theories), 1959.
2.  D. S. Dugdale, "Yielding of steel sheets containing slits," J. Mech. Phys. Solids, Vol. 8, No. 2, pp. 100-104, 1960.
3.  M. Ya. Leonov and V. V. Panasyuk, "Development of cracks in solids," PM [Applied Mechanics], Vol. 5, No. 4, pp. 391-401, 1959.
4.  R. Thomson, "Physics of Fracture," in R. V. Goldstein (Editor), Atomistics of Destruction [in Russian], pp. 104-144, Mir, Moscow, 1987.
5.  E. R. Fuller and R. M. Thomson, "Lattice theories of fracture," in R. C. Brandt (Editor), Fracture Mechanics of Ceramics, Vol. 4, pp. 507-548, Plenum Press, New York, 1978.
6.  N. F. Morozov and M. V. Paukshto, Discrete and Hybrid Models of Fracture [in Russian], Idz-vo SPbGU, St. Petersburg, 1995.
7.  R. V. Goldstein and G. A. Shatalov, "On the coupling domain near the crack edge in the process of brittle fracture," Doklady RAN, Vol. 389, No. 5, pp. 608-610, 2003.
8.  R. V. Goldstein and G. A. Shatalov, "Brittle fracture in the one-dimensional model of atomistic crack," Izv. RAN. MTT [Mechanics of Solids], No. 3, pp. 135-147, 2003.
9.  R. Thomson, C. Hsiek, and V. Rana, "Lattice trapping of fracture cracks," J. Appl. Phys., Vol. 42, No. 8, pp. 3154-3160, 1971.
10.  A. O. Gelfond, Calculus of Finite Differences [in Russian], Nauka, Moscow, 1967.
11.  R. V. Goldstein and G. A. Shatalov, Modeling Destruction Processes in Atomistic Normal Separation Crack. Preprint No. 710 [in Russian], In-t Problem Mekhaniki RAN, Moscow, 2002.
Received 20 July 2005
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