Mechanics of Solids (about journal) Mechanics of Solids
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in January 1966
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IssuesArchive of Issues2011-3pp.400-415

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Total articles in the database: 9179
In Russian (. . ): 6485
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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)
Year 2011 Volume 46 Number 3 Pages 400-415
DOI 10.3103/S0025654411030071
Title Asymptotic Computation of the Inhomogeneity Energy in a Body in an External Stress Field
Author(s) D.V. Semenova (Moscow Institute of Physics and Technology (State University), Institutskii per.9, Dolgoprudny, Moscow Region, 141700 Russia,
K.B. Ustinov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia,
Abstract 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.
Keywords elasticity, inhomogeneity, inclusion, energy, concentration, Eshelby tensor, small parameter
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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)]
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Received 20 June 2009
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