 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 74, Issue 2 / 2010 | Next article >> |
| E.V. Teodorovich, "Self-similar solution of the plane problem of the evolution of a hydraulic fracture crack in an elastic medium," J. Appl. Math. Mech. 74 (2), 181-187 (2010) |
| Year |
2010 |
Volume |
74 |
Issue |
2 |
Pages |
181-187 |
| Title |
Self-similar solution of the plane problem of the evolution of a hydraulic fracture crack in an elastic medium |
| Author(s) |
E.V. Teodorovich (Moscow, Russia, teodor@ipmnet.ru) |
| Abstract |
The plane problem of the evolution of a hydraulic fracture crack in an elastic medium is considered. It is established that a self-similar solution is only possible at a constant rate of fluid injection. The solution for the value of the crack opening is presented in the form of a series expansion in Chebyshev polynomials of the second kind, and expansion coefficients are obtained as a solution of the algebraic set of equations which arise when projecting the balance equation for injected fluid mass on Chebyshev polynomials. When there is no part of the region unfilled with fluid (a fluid lag), the gradient of the crack opening at the crack tip turns out to be singular when the finiteness of the medium stress intensity factor is taken into account. According to the estimate made, the rate of convergence of the series expansion for the solution in Chebyshev polynomials is fairly rapid for a small injection intensity. |
| Received |
27 October 2009 |
| Link to Fulltext |
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