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On the correctness of a phenomenological model of equilibrium phase transitions in a deformable elastic medium

Published online by Cambridge University Press:  16 July 2009

A. M. Meirmanov  and
N. V. Shemetov
A. M. Meirmanov
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk 630090, USSR
N. V. Shemetov
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk 630090, USSR
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Abstract

In this paper we investigate the mathematical model of the equilibrium of a finite volume in ℝn (n = 1,2, 3) of a two-phase continuous medium, under the assumption that each pure phase is an isotropic elastic solid. The main results in this paper are:

(i) the existence and uniqueness of a solution of this mathematical model;

(ii) a discussion of the stress-strain law associated with the free energy of this two-phase continuous medium, which is multiple-valued due to the non-smoothness of the Gibbs potential (complementary energy);

(iii) a description of the structure of solutions in plane strain.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 2 , June 1992 , pp. 181 - 191
Copyright
Copyright © Cambridge University Press 1992

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References

Götz, I. G., Meirmanov, A. M. & Shemetov, N. V. 1987 A phenomenological model of phase transitions of the first kind in a deformable elastic medium. Prikl. Mekh. Tekhn. Fiz. (6), 43–50 (in Russian).Google Scholar
Landau, L. D. & Lifshitz, E. M. 1964 Statistical physics. Nauka Publishers (in Russian).Google Scholar
Luckhaus, S. & Visintin, A. 1983 Phase transition in multi-component systems. Manuscript Math. 43, 261–288.CrossRefGoogle Scholar
Wainberg, M. M. 1972 The variational method and the method of monotonous operators. Nauka Publishers (in Russian).Google Scholar