 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| K.B. Ustinov, "On Separation of a Layer from the Half-Plane: Elastic Fixation Conditions for a Plate Equivalent to the Layer," Mech. Solids. 50 (1), 62-80 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
1 |
Pages |
62-80 |
| DOI |
10.3103/S0025654415010070 |
| Title |
On Separation of a Layer from the Half-Plane: Elastic Fixation Conditions for a Plate Equivalent to the Layer |
| Author(s) |
K.B. Ustinov (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, ustinov@ipmnet.ru) |
| Abstract |
The solution of the homogeneous problem on a half-infinite crack passing along the interface between a thin layer and an elastic half-plane made of materials with distinct properties is obtained and analyzed. Following [1-4], the two-sided Laplace transform is used to reduce the problem to a matrix Riemann problem. The class of combinations of elastic constants of the materials for which the matrix coefficient can be factorized by the method proposed in [1-4] is singled out. This factorization is used to generalize the problem studied in [1-4] to the case of distinct elastic constants of the layer and the half-plane (although they satisfy an additional condition). An asymptotic expression for the crack shore displacements far from the tip are obtained. It is shown that the leading terms of the asymptotics of the crack shore displacements correspond to the cantilever (plate) displacements under boundary conditions of the rigid fixation type, i.e., to the conditions that the displacements and the angle of rotation at the fixation point are proportional to the components of the resultant and the bending moment of the load. Some expressions for the entries of the matrix of elastic fixation coefficients are obtained. |
| Keywords |
separation, interface crack, factorization, elastic fixation |
| References |
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|
| Received |
23 July 2013 |
| Link to Fulltext |
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