 | | 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 45, Issue 3 / 2010 | Next article >> |
| O.Ya. Izvekov and V.I. Kondaurov, "Scattered Fracture of Porous Materials with Brittle Skeleton," Mech. Solids. 45 (3), 445-464 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
3 |
Pages |
445-464 |
| DOI |
10.3103/S0025654410030155 |
| Title |
Scattered Fracture of Porous Materials with Brittle Skeleton |
| Author(s) |
O.Ya. Izvekov (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow oblast, 141700 Russia)
V.I. Kondaurov (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow oblast, 141700 Russia, vk@mipt.ru, v_kondaurov47@mail.ru) |
| Abstract |
A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated. |
| Keywords |
porous medium, damage, surface energy, kinetics, constitutive relations |
| References |
| 1. | R. V. Goldstein and N. M. Osipenko,
Brittle Failure of Highly Porous Bodies under Compression,
Preprint No. 812
(IPMekh RAN, Moscow, 2006)
[in Russian]. |
| 2. | R. V. Goldstein, N. M. Osipenko, and A. V. Chentsov,
"To Determination of the Strength of Nanodimensional Objects,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 164-181 (2008)
[Mech. Solids (Engl. Transl.)
43 (3), 453-469 (2008)]. |
| 3. | V. I. Karev and K. B. Ustinov,
"Seepage of a Gas Condensate Mixture When Using the Geoloosening Method,"
Prikl. Mat. Mekh.
73 (5), 787-798 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (5), 566-573 (2009)]. |
| 4. | O. Coussy,
Poromechanics
(Wiley, New York, 2004). |
| 5. | R. de Boer,
Trends in Continuum Mechanics of Porous Media
(Springer, Berlin, 2005). |
| 6. | S. S. Grigorian,
"Some Problems of the Mathematical Theory of Deformation and Fracture of Hard Rocks,"
Prikl. Mat. Mekh.
31 (4), 643-669 (1967)
[J. Appl. Math. Mech. (Engl. Transl.)
31 (4), 665-686 (1967)]. |
| 7. | V. N. Nikolaevskii,
Mechanics of Porous and Cracked Media
(Nedra, Moscow, 1984)
[in Russian]. |
| 8. | M. Aubertin, L. Li. and R. Simon,
"A Multiaxial Stress Criterion for Short- and Long-Term Strength of Isotropic Rock Media,"
Int. J. Rock. Mech. Mining Sci.
37, 1169-1193 (2000). |
| 9. | L. I. Sedov,
Continuum Mechanics, Vol. 2
(Nauka, Moscow, 1970)
[in Russian]. |
| 10. | V. I. Kondaurov and N. V. Kutlyarova,
"Damage and Rheological Instability of Initially Porous Materials,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 99-109 (2000)
[Mech. Solids (Engl. Transl.)
35 (4), 83-92 (2000)]. |
| 11. | V. I. Kondaurov and V. E. Fortov,
Foundations of Thermomechanics of Condensed Media
(Izd-vo MFTI, Moscow, 2002)
[in Russian]. |
| 12. | R. I. Nigmatulin,
Foundations of Mechanics of Heterogeneous Media,
(Nauka, Moscow, 1978)
[in Russian]. |
| 13. | C. A. Truesdell,
A First Course in Rational Continuum Mechanics
(The Johns Hopkins University Press, Baltimore, Maryland, 1972; Mir, Moscow, 1975). |
| 14. | M. A. Biot,
"Mechanics of Deformation and Acoustic Propagation in Porous Media,"
J. Appl. Phys.
33 (4), 1482-1498 (1962). |
| 15. | V. I. Kondaurov,
"The Thermodynamically Consistent Equations of a Thermoelastic Saturated Porous Medium,"
Prikl. Mat. Mekh.
71 (4), 616-635 (2007)
[J. Appl. Math. Mech. (Engl. Transl.)
71 (4), 562-579 (2007)]. |
| 16. | P. Germain,
Course of Continuum Mechanics
(Vysshaya Shkola, Moscow, 1983)
[in Russian]. |
| 17. | B. L. Rozhdestvenskii and N. N. Yanenko,
Systems of Quasilinear Equations and Their Applications to Gas Dynamics,
(Nauka, Moscow, 1978)
[in Russian]. |
|
| Received |
25 January 2010 |
| Link to Fulltext |
|
| << Previous article | Volume 45, Issue 3 / 2010 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English