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IssuesArchive of Issues2007-5pp.823-840

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Total articles in the database: 11223
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E. N. Vilchevskaya and A. B. Freidin, "On phase transitions in a domain of material inhomogeneity. I. Phase transitions of an inclusions in a homogeneous external field," Mech. Solids. 42 (5), 823-840 (2007)
Year 2007 Volume 42 Number 5 Pages 823-840
Title On phase transitions in a domain of material inhomogeneity. I. Phase transitions of an inclusions in a homogeneous external field
Author(s) E. N. Vilchevskaya (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr-t 61, St. Petersburg, 199178, Russia, ven@itcwin.com)
A. B. Freidin (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr-t 61, St. Petersburg, 199178, Russia, freidin@mechanics.ipme.ru)
Abstract We pose and study the problem on an inclusion experiencing a phase transition in a homogeneous external stress field transferred by a matrix. The matrix is formed by a linear-elastic material. The inclusion material admits phase transitions under strain, and the passage from one phase state into another, as well as two-phase states, is determined by the energy preference considerations and the possible existence of two-phase states. For the simplest problem we consider the problem of phase transitions in a cylindrical inclusion under homogeneous plane strain conditions. In the space of strains, we construct the domains of existence of the inclusion one-phase states and the switching surfaces between the one-phase states. We study the possibility of the inclusion two-phase states, prove the characteristic properties of axisymmetric two-phase strains, and examine their stability. We also demonstrate the scale effect, namely, the influence of the relative dimensions of the inclusion and the body on the inclusion phase state. In the second part of the paper, we study the interaction between an inclusion experiencing phase transitions and a crack.
References
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2.  E. N. Vilchevskaya and A. B. Freidin, "On the Phase Transformations of an Inclusion in an External Strain Field," in Proc. XXXII Summer School APM-2004, St. Petersburg (IPME RAS, 2004), pp. 447-454.
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15.  A. B. Freidin and A. M. Chiskis, "Phase Transition Zones in Nonlinearly Elastic Isotropic Materials. Part 1. Basic Relations," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 91-109 (1994) [Mech. Solids (Engl. Transl.)].
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18.  A. A. Vakulenko, "On Micro and Macro Kinetics of Martensitic Transformations," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 43-62 (2001) [Mech. Solids (Engl. Transl.)].
19.  A. B. Freidin, E. N. Vilchevskaya, and L. L. Sharipova, "Two-Phase Deformations within the Framework of Phase Transitions Zones," Theoret. and Appl. Mech. 28-29, 149-172 (2002).
20.  A. B. Freidin, "On New Phase Inclusions in Elastic Solids," ZAMM 87 (2), 102-116 (2007).
21.  V. A. Eremeev, A. B. Freidin, and L. L. Sharipova, "On the Stability of Two-Phase Equilibrium Elastic Bodies," Prikl. Mat. Mekh. 71 (1), 66-92 (2007) [J. Appl. Math. Mech. (Engl. Transl.)].
22.  V. A. Eremeev, A. B. Freidin, and L. L. Sharipova, "Nonuniqueness and Stability in Problems of Equilibrium of Elastic Two-Phase Bodies," Dokl. Ross. Akad. Nauk 391 (2), 189-193 (2003) [Russian Acad. Sci. Dokl. Math. (Engl. Transl.)].
23.  V. A. Eremeev, A. B. Freidin, and L. L. Sharipova, "On Centrally Symmetric Two-Phase Strain Fields," in Problems of Mechanical Strains of Solids, Intervuz. Collection of Papers Dedicated to Academician N. F. Morozov on the Occasion of His 70th Birthday (Izd-vo St. Petersburg Univ., St. Petersburg, 2002), pp. 111-122 [in Russian].
24.  A. B. Freidin, "HHeterogeneous Deformation of Elastic Solids due to Multiple Appearance of New Phase Layers," in Scientific Proc. of Intern. V. A. Likhachev Seminar "Actual Problems of Strength" (Novgorod, 1997), Vol. 1, Part 2, pp. 236-240.
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27.  A. B. Freidin, Y. B. Fu, L. L. Sharipova, and E. N. Vilchevskaya, "Spherically Symmetric Two-Phase Deformations and Phase Transition Zones," Int. J. Solids and Struct. 43, 4484-4508 (2006).
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34.  A. B. Freidin, "Silver Cracks and Shear Strips in Glasslike Polymers as New Phase Layers," Mekh. Komp. Mater., No. 1, 3-10 (1989).
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