Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2014-6pp.713-724

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Total articles in the database: 10864
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K.B. Ustinov, "On Shear Separation of a Thin Strip from the Half-Plane," Mech. Solids. 49 (6), 713-724 (2014)
Year 2014 Volume 49 Number 6 Pages 713-724
DOI 10.3103/S0025654414060132
Title On Shear Separation of a Thin Strip from the Half-Plane
Author(s) K.B. Ustinov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr.†Vernadskogo†101, str.†1, Moscow, 119526 Russia,
Abstract A homogeneous solution of the problem of semi-infinite shear crack along the interface between a thin layer and an elastic half-plane made of a material with different properties is obtained and studied. Under the assumption that the influence of normal shear stresses can be neglected, the problem is reduced to the Riemann problem by using the two-sided Laplace transform. The factorization procedure is used to obtain asymptotic expressions for displacements of the crack shores near its tip and at a large distance from it. It is shown that the leading terms of the asymptotics of the crack shore displacements at a large distance from its tip correspond to displacements of a rod under boundary conditions of elastic fixation type, i.e., under the assumption that the displacements at the fixation point are proportional to the longitudinal force. The obtained results agree well with known numerical results.
Keywords separation, interface crack, factorization, elastic fixation
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4.  A. A. Khrapkov, Wiener-Hopf Method in Mixed Elasticity Theory Problems (VNIIG, St. Petersburg, 2001).
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7.  A. I. Kalandiia, "Stress Conditions in Plates Reinforced by Stiffening Ribs," "On Stress State in Plated Reinforces by Stiffeners," Prikl. Mat. Mekh. 33 (3), 538-543 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (3), 523-529 (1969)].
8.  A. I. Kalandiya, Mathematical Methods of Two-Dimensional Elasticity (Nauka, Moscow, 1973) [in Russian].
9.  G. Ya. Popov and L. Ya. Tikhonenko, "Two-Dimensional Problem of the Contact between a Semi-Infinite Beam and an Elastic Wedge," Prikl. Mat. Mekh. 38 (2), 312-320 (1974) [J. Appl. Math. Mech. (Engl. Transl.) 38 (2), 284-292 (1974)].
10.  R. D. Bantsuri, "A Contact Problem for a Wedge with Elastic Bracing," Dokl. Akad. Nauk SSSR 211 (4), 797-800 (1973) [Sov. Math. Dokl. (Engl. Transl.) 18, 561-562 (1973)].
11.  R. Muki and E. Sternberg, "On the Diffusion of Load From a Transverse Tension Bar Into a Semi-Infinite Elastic Sheet," J. Appl. Mech. 35 (4), 737-746 (1968) [Prikl. Mekh. Tr. Amer. Obshch. Inzh.-Mekh. Ser. E (Russ. Transl.) 35 (4), 124-135 (1968)].
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14.  M. A. Grekov, Singular Plane Problem of Elasticity (Izd-vo SPb. Univ., St. Petersburg, 2001) [in Russian].
15.  H.-H. Yu and J. W. Hutchinson, "Influence of Substrate Compliance on Buckling Delamination of Thin Films," Int. J. Fract. 113, 39-55 (2002).
16.  B. Cotterell and Z. Chen, "Buckling and Cracking of Thin Films on Compliant Substrates under Compression," Int. J. Fract. 104 (2), 169-179 (2000).
17.  B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London etc., 1958; Mir, Moscow, 1962).
18.  V. M. Entov and R. L. Salganik, "On the Prandtl Brittle Fracture Model," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 87-99 (1968) [Mech. Solids (Engl. Transl.)].
19.  R. L. Salganik, "Thin Layer with Jumpwise Characteristics in and Infinite Elastic Body," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 154-163 (1977) [Mech. Solids (Engl. Transl.)].
20.  G. Doetsch, Handbook der Laplace-Transformation (Birkhäuser, Basel, 1946; Fizmatlit, Moscow, 1958).
21.  R. L. Salganik, "The Brittle Fracture of Cemented Bodies," Prikl. Mat. Mekh. 27 (5), 957-962 (1963) [J. Appl. Math. Mech. (Engl. Transl.) 27 (5), 1468-1478 (1963)].
22.  B. M. Malyshev and R. L. Salganik, "The Strength of Adhesive Joints Using the Theory of Crack," Int. J. Fract. Mech. 1 (2), 114-128 (1965).
Received 04 August 2013
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