 | | 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 |
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| E. M. Rudoi, "Differentiation of energy functionals in the problem on a curvilinear crack with possible contact between the shores," Mech. Solids. 42 (6), 935-946 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
6 |
Pages |
935-946 |
| Title |
Differentiation of energy functionals in the problem on a curvilinear crack with possible contact between the shores |
| Author(s) |
E. M. Rudoi (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090, Russia, rem@hydro.nsc.ru) |
| Abstract |
We consider the N-dimensional (N=2 or 3) model of a one-dimensional anisotropic elastic body containing a curvilinear or surface crack. On the crack shores, the nonpenetration conditions in the form of inequalities (Signorini type conditions) are posed. For the general form of a sufficiently smooth perturbation of the domain, we obtain the derivative of the energy functional with respect to the perturbation parameter. We derive sufficient conditions for the existence of invariant integrals over an arbitrary closed contour. In particular, we obtain an invariant Cherepanov-Rice integral for curvilinear cracks. |
| References |
| 1. | V. Z. Parton and E. M. Morozov,
Mechanics of Elastoplastic Fracture
(Nauka, Moscow, 1974) [in Russian]. |
| 2. | G. P. Cherepanov,
Mechanics of Brittle Fracture
(Nauka, Moscow, 1974; McGraw-Hill, New York, 1979). |
| 3. | A. M. Khludnev and V. A. Kovtunenko,
Analysis of Cracks in Solids
(WIT-Press, Southampton-Boston, 2000). |
| 4. | R. V. Goldstein and A. A. Spektor,
"Variational Estimates of Solutions of Some Mixed Spatial Problems
of Elasticity with Unknown Boundary,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 82-94 (1978)
[Mech. Solids (Engl. Transl.)]. |
| 5. | R. V. Goldstein and Yu. V. Zhitnikov, "Equilibrium of Cavities and
Cracks-Cuts with Domains of Overlapping and Opening in an Elastic
Medium," Prikl. Mat. Mekh. 50 (5), 826-834 (1986)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 6. | V. A. Kovtunenko,
"Shape Sensitivity of a Plane Crack Front,"
Math. Meth. Appl. Sci.
26 (5), 359-374 (2003). |
| 7. | K. Ohtsuka,
"Mathematics of Brittle Fracture,"
in Theoretical Studies on Fracture Mechanics in Japan
(Hiroshima-Denki Inst. Technol., Hiroshima, 1997). |
| 8. | V. G. Maz'ya and S. A. Nazarov,
"Asymptotics of Energy Integrals under Small Perturbations of the Boundary
Close to Angular and Conic Points,"
Trudy Moskov. Mat. Obshch.
50, 79-129 (1987)
[Trans. Mosc. Math. Soc. (Engl. Transl.)]. |
| 9. | N. V. Banichuk, "Determination of the Shape of a Curved Crack by
the Small-Parameter Method,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 130-137
(1970) [Mech. Solids (Engl. Transl.)]. |
| 10. | R. V. Goldstein and R. L. Salganik, "The Plane Problem on Curved
Cracks in Elastic Body," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 3, 69-82 (1970) [Mech. Solids (Engl. Transl.)]. |
| 11. | R. V. Goldstein and R. L. Salganik,
"Brittle Fracture of Bodies with Arbitrary Cracks,"
in Progress in Mechanics of Strains Media
(Nauka, Moscow, 1975)
[in Russian]. |
| 12. | B. Cotterell and J. R. Rice,
"Slightly Curved or Kinked Cracks,"
Intern. J. Fract.
16 (2), 155-169 (1980). |
| 13. | M. Amestoy and J. B. Leblond,
"Crack Paths in Plane Situations - II: Detailed Form of the Expansion
of the Stress Intensity Factors,"
Intern. J. Solids and Structures
29 (4), 465-501 (1992). |
| 14. | J. B. Leblond,
"Crack Paths in Three-Dimensional Elastic Solids. I: Two-Term
Expansion of the Stress Intensity Factors - Application to Cracks Path
Stability in Hydraulic Fracturing,"
Intern. J. Solids and Structures
36 (1), 79-103 (1999). |
| 15. | D. Leguillon,
"Asymptotic and Numerical Analysis of a Crack Branching in Non-Isotropic
Materials,"
Eur. J. Mech. A / Solids
12 (1), 33-51 (1993). |
| 16. | H. Gao and C.-H. Chiu,
"Slightly Curved or Kinked Cracks in Anisotropic Elastic Solids,"
Intern. J. Solids and Structures
29 (8), 947-972 (1992). |
| 17. | P. A. Martin,
"Perturbed Cracks in Two-Dimensions: An Integral-Equation Approach,"
Intern. J. Fract.
104 (4), 317-327 (2000). |
| 18. | A. M. Khludnev and J. Sokolowski,
"The Griffith Formula and the Rice-Cherepanov Integral for Crack Problems
with Unilateral Conditions in Nonsmooth Domains,"
Euro. J. Appl. Math.
10 (4), 379-394 (1999). |
| 19. | V. A. Kovtunenko, "Invariant Energy Integrals for the Non-Linear
Crack Problem with Possible Contact of the Crack Surfaces,"
Prikl. Mat. Mekh.
67 (1), 109-123 (2003)
[J. Appl. Math. Mech. (Engl. Transl.)
67 (1), 99-110 (2003)]. |
| 20. | J. Sokolowski and A. M. Khludnev,
"On the Differentiation of Energy Functionals in Crack Theory with
Possible Contact of the Crack Faces,"
Dokl. Ross. Akad. Nauk
374 (6), 776-779 (2000)
[Russian Acad. Sci. Dokl. Math. (Engl. Transl.)]. |
| 21. | E. M. Rudoi,
"The Griffith Formula for a Plate with a Crack,"
Sibirsk. Zh. Industr. Mat.
5 (3), 155-161 (2002). |
| 22. | V. A. Kovtunenko,
"Shape Sensitivity of Curvilinear Cracks on Interface
to Non-Linear Perturbations,"
ZAMP
54 (4), 410-423 (2003). |
| 23. | V. A. Kovtunenko,
"Sensitivity of Interfacial Cracks to Non-Linear Crack Front Perturbation,"
ZAMM
82 (6), 387-398 (2002). |
| 24. | A. M. Khludnev, K. Ohtsuka, and J. Sokolowski,
"On Derivative of Energy Functional for Elastic Bodies with
Cracks and Unilateral Conditions,"
Quart. Appl. Math.
60 (2), 99-109 (2002). |
| 25. | E. M. Rudoi,
"Invariant Integrals for the Equilibrium Problem for a Plate with a Crack,"
Sibirsk. Mat. Zh.
45 (2), 466-477 (2004)
[Siberian Math. J. (Engl. Transl.)
45 (2), 388-397 (2004)]. |
| 26. | E. M. Rudoi,
"Differentiation of Energy Functionals in Two-Dimensional
Elasticity Theory for Solids with Curvilinear Cracks,"
Zh. Prikl. Mekh. Tekhn. Fiz.
45 (6), 83-94 (2004)
[J. Appl. Mech. Tech. Phys.
45 (6), 843-852 (2004)]. |
| 27. | L. C. Evans and R. F. Gariepy,
Measure Theory and Fine Properties of Functions
(Boca Raton, Ann Arbor, and London, 1992; Nauchnaya Kniga, Novosibirsk, 2002). |
| 28. | G. Duvaut and J.-L. Lions,
Les Inequations en Mecanique et Physique
(Dunod, Paris, 1972; Nauka, Moscow, 1980). |
| 29. | J. K. Knowles and E. Sternberg,
"On a Class of Conservation Laws in Linearized and Finite Elastoplastic,"
Arch. Ration. Mech. and Analysis
44 (3), 187-211 (1972). |
|
| Received |
25 April 2005 |
| Link to Fulltext |
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