| ||Mechanics of Solids|
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936
Archive of Issues
|Total articles in the database:|| ||9179|
|In Russian (Èçâ. ÐÀÍ. ÌÒÒ):|| ||6485|
|In English (Mech. Solids):|| ||2694|
|D.V. Semenova and K.B. Ustinov, "Asymptotic Computation of the Inhomogeneity Energy in a Body in an External Stress Field," Mech. Solids. 46 (3), 400-415 (2011)|
||Asymptotic Computation of the Inhomogeneity Energy in a Body in an External Stress Field|
||D.V. Semenova (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 Russia, email@example.com)|
K.B. Ustinov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, firstname.lastname@example.org)
||We consider a problem on an ellipsoidal inhomogeneity in an infinitely extended homogeneous isotropic elastic medium. The inhomogeneity differs from the ambient body in the elastic moduli (Poisson's ratio ν and shear modulus μ) and in that it has intrinsic strains. We use the equivalent inclusion method to write out expressions for the Helmholtz and Gibbs free energy of the inhomogeneity as quadratic forms in the intrinsic strains and strains at infinity. The general expressions for the coefficients of these quadratic forms are written out as three rank four tensors characterizing the contribution to the energy by the plastic strain (εp2), by the strain at infinity (ε02), and (only for the Gibbs energy) by the cross term ε0 εp.|
The solutions for some important particular cases are written out by asymptotically expanding the general solution in small parameters. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-to-matrix elastic modulus ratio. We consider various physical situations arising when studying needle- and disk-shaped inclusions and characterized by various order of passage to the limit. We analyze the applicability domains of the asymptotics by reduction to a single small parameter. For the case in which the parameters considerably differ from unity simultaneously, we single out seven domains corresponding to various relations between these parameters. We construct the diagrams of relative error isolines for the resulting tensors corresponding to the energy contribution from various strain tensor components.
||elasticity, inhomogeneity, inclusion, energy, concentration, Eshelby tensor, small parameter|
|1. ||J. D. Eshelby,
"The Determination of the Elastic Fields of an Ellipsoidal Inclusion, and Related Problems,"
Proc. Roy. Soc. London. Ser. A. 241 (1226), 376-396 (1957).|
|2. ||T. Mura,
Micromechanics of Defects in Solids
(Martinus Nijhoff Publ., Hague, 1982).|
|3. ||S. K. Kanaun and V. M. Levin,
Self-Consistent Methods for Composites, Vol. 1,
(Springer, New York, 2008).|
|4. ||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.)].|
|5. ||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)].|
|6. ||W. B. Russel and A. Acrwos,
"On the Effective Moduli of Composite Materials: Slender Rigid Inclusions at Dilute Concentrations,"
23 (3), 434-463 (1972).|
|7. ||W. B. Russel,
"On the Effective Moduli of Composite Materials: Effect of Fiber Length and Geometry at Dilute Concentrations,"
24 (4), 581-600 (1973).|
|8. ||K. B. Ustinov, "On the determination of effective elastic
characteristics of two-phase media. The case of isolated
inhomogeneities having the shape of an ellipsoid of revolution,"
Usp. Mekh. 2 (2), 126-168 (2003).|
|9. ||I. Sevostianov and M. Kachanov,
"Compliance Tensors of Ellipsoidal Inclusions,"
Int. J. Fract.
96, L3-L7 (1999).|
|10. ||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).|
|11. ||K .B. Ustinov,
"Computation of the Energy of an Inhomogeneity: Asymptotics and Their Scope,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 103-113 (2010)
[Mech. Solids. (Engl. Transl.)
45 (2), 238-246 (2010)]|
|12. ||L. J. Walpole,
"On the Overall Elastic Moduli of Composite Materials,"
J. Mech. Phys. Solids
17 (4), 235-251 (1969).|
|13. ||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).|
|14. ||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).|
||20 June 2009|
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