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Russian Academy of Sciences
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IssuesArchive of Issues2010-2pp.181-187

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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 http://www.sciencedirect.com/science/journal/00218928
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