 | | 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
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 45, Issue 2 / 2010 | Next article >> |
| K.B. Ustinov, "Computation of the Energy of an Inhomogeneity: Asymptotics and Their Scope," Mech. Solids. 45 (2), 238-246 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
2 |
Pages |
238-246 |
| DOI |
10.3103/S0025654410020093 |
| Title |
Computation of the Energy of an Inhomogeneity: Asymptotics and Their Scope |
| Author(s) |
K.B. Ustinov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, ustinov@ipmnet.ru) |
| Abstract |
By passing to the limit in the general solution, we obtain several exact asymptotic formulas for the energy of an inhomogeneity in a body located in an external stress field. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-matrix elastic modulus ratio. In the case of a large simultaneous deviation of the parameters from unity, we distinguish seven regions corresponding to various successive passages to the limit as these parameters approach zero (or infinity). |
| Keywords |
elasticity, inhomogeneity, Eshelby tensor, small parameter |
| References |
| 1. | J. D. Eshelby,
"The Determination of the Elastic Field of an Ellipsoidal Inclusion,
and Related Problems,"
Proc. Roy. Soc. London. Ser. A
241 (1226), 376-396 (1957). |
| 2. | J. D. Eshelby,
"Elastic Inclusions and Inhomogeneities,"
in Progress in Solid Mechanics, Vol. 2,
Ed. by I. N. Sneddon and R. Hill
(North-Holland, Amsterdam, 1961),
pp. 89-140. |
| 3. | T. Mura,
Micromechanics of Defects in Solids
(Martinus Nijhoff Publ., Hague, 1982). |
| 4. | J. R. Bristow,
"Microcracks and the Static and Dynamics Elastic Constants
of Annealed and Heavily Coldworked Metals,"
British J. Appl. Phys.
11, 81-85 (1960). |
| 5. | R. L. Salganik,
"Mechanics of Bodies with Many Cracks,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 4, 149-158 (1973)
[Mech. Solids (Engl. Transl.)
8 (4) 135-143 (1973)]. |
| 6. | T. T. Wu,
"The Effort of Inclusion Shape on the Elastic Moduli
of a Two-Phase Material,"
Int. J. Solids Struct.
2, 1-8 (1966). |
| 7. | Yu. F. Kovalenko and R. L. Salganik,
"Fractured Inhomogeneities and Their Influence on
Effective Mechanical Characteristics,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 5, 76-86 (1977)
[Mech. Solids (Engl. Transl.)]. |
| 8. | R. L. Salganik,
"Transport Processes in Bodies with a Large Number of Cracks,"
Inzh. Fiz. Zh.
27 (6), 1069-1075 (1974)
[J. Engng Phys. Thermophys. (Engl. Transl.)
27 (6), 1534-1538 (1974)]. |
| 9. | W. B. Russel and A. Acrwos,
"On the Effective Moduli of Composite Materials:
Slender Rigid Inclusions at Dilute Concentrations,"
ZAMP
23 (3), 434-463 (1972). |
| 10. | W. B. Russel,
"On the Effective Moduli of Composite Materials:
Effect of Fiber Length and Geometry at Dilute Concentrations,"
ZAMP
24 (4), 581-600 (1973). |
| 11. | I. Sevostianov and M. Kachanov,
"Compliance Tensors of Ellipsoidal Inclusions,"
Int. J. Fract.
96 (1), L3-L7 (1999). |
| 12. | K. B. Ustinov and R. V. Goldstein,
"On Application of Classical Eshelby Approach
to Calculating Effective Elastic Moduli of Dispersed Composites,"
Int. J. Fract.
147 (1-4), 55-66 (2007). |
| 13. | L. J. Walpole,
"On the Overall Elastic Moduli of Composite Materials,"
J. Mech. Phys. Solids
17 (4), 235-251 (1969). |
| 14. | S. G. Lekhnitskii,
Theory of Elasticity of an Anisotropic Body
(Nauka, Moscow, 1977; Mir Publishers, Moscow, 1981). |
|
| Received |
28 October 2008 |
| Link to Fulltext |
|
| << Previous article | Volume 45, Issue 2 / 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