 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 50, Issue 3 / 2015 | Next article >> |
| I.M. Peshkhoev and B.V. Sobol, "Spatial Problem of Crack Theory for a Prestressed Incompressible Elastic Layer," Mech. Solids. 50 (3), 345-352 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
3 |
Pages |
345-352 |
| DOI |
10.3103/S0025654415030103 |
| Title |
Spatial Problem of Crack Theory for a Prestressed Incompressible Elastic Layer |
| Author(s) |
I.M. Peshkhoev (Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000 Russia, peshkhoev@rambler.ru)
B.V. Sobol (Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000 Russia, b.sobol@mail.ru) |
| Abstract |
The three-dimensional elasticity problem of loading the shores of an elliptic crack by normal pressure keeping the crack in the open state is considered. The crack is located in the midplane of a layer under the action of a preliminary finite deformation in the direction of the crack symmetry axes. The model of incompressible neo-Hookean material is considered. The two-dimensional integral Fourier transform is used to reduce the problem to a singular integro-differential equation of the first kind for the crack opening function. An asymptotic solution of the problem is constructed in the form of an expansion in two parameters characterizing the relative thickness of the layer and the difference between the coefficients of the preliminary finite deformation. It is shown that the initial stress does not change the order of the stress field singularity near the crack edge and influences only the normal stress intensity factor. The influence of the layer thickness and the preliminary stress parameters on the intensity of normal stresses in the crack plane is investigated. |
| Keywords |
flat elliptic crack, prestressed elastic layer, asymptotic solution, stress intensity |
| References |
| 1. | A. I. Lurie,
Nonlinear Theory of Elasticity. (Nauka, Moscow, 1980)
[in Russian]. |
| 2. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko,
Nonclassical Mixed Problems of Elasticity. (Nauka, Moscow, 1974)
[in Russian]. |
| 3. | A. N. Guz',
"Theory of Cracks in Elastic Bodies with Initial Stresses
(Spatial Static Problems),"
Prikl. Mekh.
17 (6), 3-20 (1981). |
| 4. | R. S,. Dhalival, B. M. Singh, and J. G. Rokne,
"Axisymmetric Contact and Crack Problems for an Initially Stressed Neo-Hookean Elastic Layer,"
Int. J. Engng Sci.
18 (1), 169-179 (1980). |
| 5. | D. M. Haughton,
"Penny-Shaped Cracks in a Finitely Deformed Elastic Solid,"
Int. J. Solid Struct.
18 (8), 699-704 (1982). |
| 6. | A. R. S. Selvadurai,
"The Penny-Shaped Crack Problem in a Finitely Deformed Incompressible Elastic Solid,"
Int. J. Fract.
16 (4), 327-333 (1980). |
| 7. | K. M. Filippova,
"On the Effect of Initial Stresses on the Opening of a Circular Crack,"
Prikl. Mat. Mekh.
47 (2), 286-290 (1983)
[J. Appl. Math. Mech. (Engl. Transl.)
47 (2), 240-243 (1983)]. |
| 8. | K. M. Filippova,
"Stability of a Compressed Elastic Layer Weakened by a Circular Crack,"
Prikl. Mat. Mekh.
52 (2), 327-330 (1988)
[J. Appl. Math. Mech. (Engl. Transl.)
52 (2), 257-260 (1988)]. |
| 9. | V. M. Alexandrov and B. V. Sobol',
"Equilibrium of a Prestressed Elastic Body Weakened by a Plane Elliptical Crack,"
Prikl. Mat. Mekh.
49 (2), 348-352 (1985)
[J. Appl. Math. Mech. (Engl. Transl.)
49 (2), 268-272 (1985)]. |
| 10. | B. I. Smetanin and B. V. Sobol',
"Equilibrium of an Elastic Layer Weakened by Plane Cracks,"
Prikl. Mat. Mekh.
48 (6), 1030-1038 (1984)
[J. Appl. Math. Mech. (Engl. Transl.)
48 (6), 757-764 (1984)]. |
| 11. | V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol'
Thin Stress Concentrators in Elastic Bodies. (Nauka, Moscow, 1993)
[in Russian]. |
| 12. | B. V. Sobol',
"On Asymptotic Solutions of Three-Dimensional Static Problems of Elasticity
with Mixed Boundary Conditions,"
Vestnik Nizhegorod. Univ.,
No. 4, 1778-1789 (2011). |
| 13. | K. M. Filippova,
"Three-Dimensional Contact Problem for a Prestressed Elastic Body,"
Prikl. Mat. Mekh.
42 (6), 1080-1084 (1978)
[J. Appl. Math. Mech. (Engl. Transl.)
42 (6), 1183-1188 (1978)]. |
| 14. | V. M. Alexandrov,
"Spatial Contact Problems for a Prestressed Incompressible Elastic Layer,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 141-146 (2011)
[Mech. Solids (Engl. Transl.)
46 (2), 275-279 (2011)]. |
| 15. | V. M. Alexandrov and V. S. Poroshin,
"Contact Problem for Prestressed Physically Nonlinear Elastic Layer,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 79-85 (1984)
[Mech. Solids (Engl. Transl.)]. |
| 16. | Yu. A. Brychkov and A. P. Prudnikov,
Integral Transformations of Generalized Functions. (Nauka, Moscow, 1977)
[in Russian]. |
|
| Received |
11 February 2013 |
| Link to Fulltext |
|
| << Previous article | Volume 50, Issue 3 / 2015 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English