 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| G. Iovane and M. A. Sumbatyan, "Periodic system of collinear cracks in an elastic porous medium," Mech. Solids. 44 (3), 400-408 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
400-408 |
| DOI |
10.3103/S0025654409030091 |
| Title |
Periodic system of collinear cracks in an elastic porous medium |
| Author(s) |
G. Iovane (D.I.I.M.A., University of Salerno, Via Ponte don Melillo, Fisciano (SA), 84084 Italy, iovane@diima.unisa.it)
M. A. Sumbatyan (South Federal University, Mil'chakova 8a, Rostov-on-Don, 344090 Russia, sumbat@math.rsu.ru) |
| Abstract |
We consider a problem for cracks in a specific porous elastic material described by the Cowin-Goodman-Nunziato model. For an arbitrary set of collinear cracks, the problem is reduced to an integral equation over the crack surface. In the special case of a periodic crack arrangement, the kernel of the integral equation is written in the form of a Fourier series. By explicitly summing the leading part of the kernel, we can show that it exhibits hypersingular behavior as the argument tends to zero. Further, we solve the main integral equation by using the direct numerical method proposed in our preceding paper. In conclusion, we study the stress concentration at the crack tips and compare this case with the case of a single isolated crack. |
| References |
| 1. | M.A. Biot,
"Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I: Low Frequency Range,"
J. Acoust. Soc. America 28 (2), 168-178 (1956). |
| 2. | M.A. Biot and D.G. Willis,
"Elastic Coefficients of the Theory of Consolidation,"
J. Appl. Mech. 24 (4), 594-601 (1957). |
| 3. | C. Atkinson and R. Craster,
"A Singular Perturbation Approach to Integral Equations Occurring in Poroelasticity,"
IMA J. Appl. Math. 52 (3), 221-252 (1994). |
| 4. | E. Detournay and A.H.-D. Cheng,
"Plane Strain Analysis of a Stationary Hydraulic Fracture in a Poroelastic Medium,"
Intern. J. Solids Struct. 27 (13), 1645-1662 (1991). |
| 5. | S.C. Cowin and J.W. Nunziato,
"Linear Elastic Materials with Voids,"
J. Elasticity 13 (2), 125-147 (1983). |
| 6. | M.A. Goodman and S.C. Cowin,
"A Continuum Theory for Granular Materials,"
Arch. Rat. Mech. Anal. 44 (4), 249-266 (1972). |
| 7. | I.N. Sneddon,
Mixed Boundary Value Problems in Potential Theory
(North-Holland, Amsterdam, 1966). |
| 8. | G. Iovane, I.K. Lifanov, and M.A. Sumbatyan,
"On Direct Numerical Treatment of Hypersingular Integral Equations Arising in Mechanics and Acoustics,"
Acta Mech. 162 (1-4), 99-110 (2003). |
| 9. | E. Scarpetta,
"In-Plane Problems for Wave Propagation through Elastic Solids with a Periodic Array of Cracks,"
Acta Mech. 154 (1-4), 179-187 (2002). |
| 10. | M. Ciarletta, V.M. Alexandrov, and M.A. Sumbatyan,
"Low-Frequency Penetration of a Plane Elastic Wave through the Periodic Array of Interface Cracks,"
ZAMM 82 (2), 137-141 (2002). |
| 11. | E. Scarpetta and M.A. Sumbatyan,
"Explicit Analytical Results for One-Mode Normal Reflection and Transmission by a Periodic Array of Screens,"
J. Math. Anal. Appl. 195 (3), 736-749 (1995). |
| 12. | E. Scarpetta and M.A. Sumbatyan,
"Explicit Analytical Results for One-Mode Oblique Penetration into a Periodic Array of Screens,"
IMA J. Appl. Math. 56 (2), 109-120 (1996). |
| 13. | J.D. Achenbach and Z.L. Li,
"Propagation of Horizontally Polarized Transverse Waves in a Solid with a Periodic Distribution of Cracks,"
Wave Motion 8 (4), 371-379 (1986). |
| 14. | Y.C. Angel and J.D. Achenbach,
"Harmonic Waves in an Elastic Solid Containing a Doubly Periodic Array of Cracks,"
Wave Motion 9 (5), 377-385 (1987). |
| 15. | E. Scarpetta and M.A. Sumbatyan,
"On Wave Propagation in Elastic Solids with a Doubly Periodic Array of Cracks,"
Wave Motion 25 (1), 61-72 (1997). |
| 16. | A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev,
Integrals and Series: Elementary Functions
(Nauka, Moscow, 1981) [in Russian]. |
| 17. | I.M. Gelfand and G.E. Shilov,
Generalized Functions and Operations over Them
(Fizmatgiz, Moscow, 1959) [in Russian]. |
|
| Received |
07 September 2006 |
| Link to Fulltext |
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