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Phase transitions in non-simple bodies

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Abstract

This paper deals with the thermostatics of bodies whose equilibrium stress and free energy depend on the higher gradients of deformation. The bodies considered are fully compatible with continuum thermodynamics based on the Clausius-Duhem inequality and on the balance equations in their conventional forms. Stable equilibrium states are studied that model phase transitions as smooth solutions to the equations of mechanical equilibrium with zero body forces. The following results are obtained for them:

(i) A generalization of the classical chemical potential is constructed which is constant over a stable phase transition. (ii) A qualitative description is given of the graph of the non-homogeneous equilibrium free energy function of a body that admits a stable phase transition. (iii) It is shown that with each stable phase transition are associated unstable homogeneous equilibrium states: except possibly for a small set of exceptional states all homogeneous equilibrium states with deformation gradients that lie between the deformation gradients of the coexistent phases are unstable.

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Authors and Affiliations

  1. Mathematical Institute, Czechoslovak Academy of Sciences, Žitná 25, 11567, Praha 1, Czechoslovakia

    M. Šilhavý

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  1. M. Šilhavý
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Communicated by D. R. Owen

Part of this work was carried out at the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis. The results of this paper were presented at the conference “Mathematical Theories of Fluids” in Oberwolfach, January 1984. I thank Professor Elias Aifantis for many discussions of the subject of phase transitions and Professor David Owen for valuable suggestions concerning the manuscript of the paper.

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Šilhavý, M. Phase transitions in non-simple bodies. Arch. Rational Mech. Anal. 88, 135–161 (1985). https://doi.org/10.1007/BF00250908

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  • DOI: https://doi.org/10.1007/BF00250908

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