 | | 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
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| S. A. Nazarov, "Damage tensor and damage measures. 2. Invariant integrals in bodies with disperse of defects," Mech. Solids. 36 (2), 104-113 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
104-113 |
| Title |
Damage tensor and damage measures. 2. Invariant integrals in bodies with disperse of defects |
| Author(s) |
S. A. Nazarov (St. Petersburg) |
| Abstract |
The value of the familiar invariant integral M is calculated over the
surface of a three-dimensional body with small defects (M=0 for a
homogeneous body). The value of M is related to the potential energy
increment due to damage. The defects under consideration are cavities
(cracks) or elastic (rigid) inclusions. We study the case of finitely many
defects of arbitrary distribution and the case of a defect cluster with a
periodic structure. |
| References |
| 1. | G. P. Cherepanov, "Propagation of cracks in continuous media,"
PMM [Applied Mathematics and Mechanics], Vol. 31, No. 3, pp. 476-488,
1967. |
| 2. | J. R. Rice, "A path independent integral and the approximate
analysis of strain concentration by notches and cracks," Trans. ASME. Ser.
E.J. Appl. Mech., Vol. 35, No. 2, pp. 379-386, 1968. |
| 3. | J. K. Knowles and E. Sternberg, "On a class of conservation laws
in linearized and finite elastostatics," Arch. Rat. Mech. Anal., Vol. 44,
No. 3, pp. 187-211, 1972. |
| 4. | B. Budianskii and J. R. Rice, "Conservation laws and energy release
rates," Trans. ASME, Eer. E. J. Appl. Mech., Vol. 40, No. 1, pp. 201-203,
1973. |
| 5. | S. A. Nazarov, "Damage tensor and measures. I. Asymptotic
analysis of anisotropic media with defects," Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 113-124,
2000. |
| 6. | S. A. Nazarov and O. P. Polyakova, "Weight functions and higher
order invariant integrals," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 104-119, 1995. |
| 7. | S. A. Nazarov, "Invariant integrals and Leonov-Panasyuk-Dugdale
crack models," Zh. Prikl. Mekh. i Tekhn. Fiziki, Vol. 38, No. 5,
pp. 147-155, 1997. |
| 8. | S. A. Nazarov, "All coefficients of lower order stress
singularities can be calculated by means of invariant integrals," Vestnik
SPbGU, Ser. 1, Vol. 22, No. 4, pp. 95-99, 1996. |
| 9. | I. S. Zorin, A. B. Movchan, and S. A. Nazarov, "On the application
of the tensors of elastic capacity, polarization and associated
deformation," in Studies in Elasticity and Plasticity [in Russian], Vol. 16,
Izd-vo LGU, Leningrad, pp. 75-91, 1990. |
| 10. | I. S. Zorin, A. B. Movchan, and S. A. Nazarov, "On applications
of the elastic polarization tensor in problems of the mechanics of
cracks," Izv. AN. MTT [Mechanics of Solids]old, No. 6, pp. 128-134, 1988. |
| 11. | S. A. Nazarov, "Elastic capacity and polarization of defects in
an elastic layer," Izv. AN. MTT [Mechanics of Solids]old, No. 5, pp. 57-65, 1990. |
| 12. | S. A. Nazarov, "Weight functions and invariant integrals," in
Computational Mechanics of Solids [in Russian], Vol. 1, pp. 17-31, 1990. |
| 13. | N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in
Periodic Media. Mathematical Problems of the Mechanics of Composites [in Russian],
Nauka, Moscow, 1984. |
| 14. | E. Sanchez-Palencia, Inhomogeneous Media and Vibration Theory
[Russian translation], Mir, Moscow, 1984. |
| 15. | B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd-vo
MGU, Moscow, 1984. |
| 16. | S. A. Nazarov, "A general homogenization scheme for self-adjoint
elliptic systems in multi-dimensional and thin domains," Algebra i Analiz,
Vol. 7, No. 5, pp. 1-92, 1995. |
| 17. | S. A. Nazarov, "Nonlinear effects in deformation of composites
with a regular array of microcracks," Mekh. Kompozit. Materialov, No. 6,
pp. 1052-1059, 1988. |
| 18. | V. V. Bolotin, "Stochastic models of crack initiation and
development," in Nonlinear Models in Mechanics of Solids [in Russian],
Nauka, Moscow, pp. 166-179, 1984. |
| 19. | N. B. Romalis and B. P. Tamuzh, Fracture of Structurally
Inhomogeneous Bodies [in Russian], Zinatne, Riga, 1989. |
| 20. | S. K. Kanaun and V. M. Levin, Effective Field Methods in the
Mechanics of Composites" [in Russian], Izd-vo Petrozavodsk. Un-ta, Petrozavodsk,
1989. |
| 21. | A. B. Movchan and S. A. Nazarov, "Cracks in Composite
Materials," Parts 1 and 2, Mekh. Kompozit. Materialov, No. 5,
pp. 842-851; No. 6, pp. 1038-1046, 1990. |
| 22. | A. M. Il'in, Matched Asymptotic Expansions of Solutions of
Boundary Value Problems [in Russian], Nauka, Moscow, 1989. |
| 23. | W. G. Mazja, S. A. Nazarov, and B. A. Plamenewski, `Asymptotische
Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten,"
Akademischer Verlag, Berlin, 1990. |
| 24. | S. A. Nazarov and B. A. Plamenevsky, Elliptic Problems in Domains
with Piecewise Smooth Boundaries, Walter de Gruyter, Berlin, 1994. |
|
| Received |
16 November 1998 |
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