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IssuesArchive of Issues2005-2pp.51-57

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I. Yu. Tsvelodub, "Inverse problems of inelastic deformation of inhomogeneous media," Mech. Solids. 40 (2), 51-57 (2005)
Year 2005 Volume 40 Number 2 Pages 51-57
Title Inverse problems of inelastic deformation of inhomogeneous media
Author(s) I. Yu. Tsvelodub (Novosibirsk)
Abstract A spatial elastic domain containing an inelastic inclusion is considered. Inverse problems of determining external loads ensuring the prescribed current or residual (after the elastic unloading) inclusion shape are formulated and studied. These problems are a generalization of those considered previously by the author for inelastic homogeneous bodies [1] and for plane elastic domains containing inclusions with nonlinear physical properties [2]. Issues of the well-posedness and those of the construction of approximate solutions are studied. The case of an inclusion with the boundary displacements which are nonlinear functions of the coordinates of boundary points is considered. For this case, a closed-form solution is obtained. A number of examples is presented.
References
1.  I. Yu. Tsvelodub, "Inverse problems of inelastic deformation," Izv. RAN. MTT [Mechanics of Solids], No. 2, pp. 81-92, 1995.
2.  I. Yu. Tsvelodub, "On an inverse problem for an elastic medium containing an inclusion with nonlinear physical properties," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 3, pp. 424-430, 2000.
3.  I. Yu. Tsvelodub, "Inverse elastoplastic problem," Izv. RAN. MTT [Mechanics of Solids], No. 1, pp. 35-43, 1998.
4.  A. A. Shvab, "Ill-posed static problems of elasticity," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 98-106, 1989.
5.  A. A. Vakulenko and I. B. Sevost'yanov, "An inclusion with nonlinear properties in elastic medium," in Investigations in Mechanics of Building Structures [in Russian], LISI, Moscow, 1991, pp. 8-16.
6.  J. Eshelby, The Continuum Theory of Dislocations [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1963.
7.  I. Yu. Tsvelodub, "A physically nonlinear inclusion in a linearly elastic medium (plane problem)," Izv. RAN. MTT [Mechanics of Solids], No. 5, pp. 72-84, 2000.
8.  I. Yu. Tsvelodub, "Some inverse problems for a viscoelastic solid containing an inclusion with nonlinear physical properties," PMM [Applied Mathematics and Mechanics], Vol. 65, No. 6, pp. 983-994, 2001.
9.  Yu. N. Rabotnov, Creep of Structural Members [in Russian], Nauka, Moscow, 1966.
Received 21 February 2005
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