In this paper we describe a class of phase transitions with thermal memory using a dual approach with respect to the energy functionals. More precisely, we use as state variables the phase parameter, the entropy (in place of the absolute temperature), and the history contribution of the entropy flux. The equations are recovered from a generalization of the principle of virtual power (to describe the evolution of the phases), including the effects of micro-motions responsible for the phase transition, and a rescalation of the internal energy balance (to describe the evolution of the entropy). We discuss thermodynamical consistency in terms of the properties of the involved energy functionals: the internal energy (in place of the free energy) and the pseudo-potential of dissipation. Hence, we prove existence of a solution (in a proper functional framework) for the resulting nonlinear integrodifferential PDE system. Finally, we discuss the long-time behaviour of solutions holding on (0, + ∞) characterizing the -limit of trajectories. 2007 Elsevier Masson SAS. All rights reserved.

Bonetti, E., Fremond, M., Rocca, E. (2007). A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions, 88(5), 455-481 [10.1016/j.matpur.2007.09.005].

A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions

FREMOND, MICHEL;
2007-01-01

Abstract

In this paper we describe a class of phase transitions with thermal memory using a dual approach with respect to the energy functionals. More precisely, we use as state variables the phase parameter, the entropy (in place of the absolute temperature), and the history contribution of the entropy flux. The equations are recovered from a generalization of the principle of virtual power (to describe the evolution of the phases), including the effects of micro-motions responsible for the phase transition, and a rescalation of the internal energy balance (to describe the evolution of the entropy). We discuss thermodynamical consistency in terms of the properties of the involved energy functionals: the internal energy (in place of the free energy) and the pseudo-potential of dissipation. Hence, we prove existence of a solution (in a proper functional framework) for the resulting nonlinear integrodifferential PDE system. Finally, we discuss the long-time behaviour of solutions holding on (0, + ∞) characterizing the -limit of trajectories. 2007 Elsevier Masson SAS. All rights reserved.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
-limit of trajectories; conjugate functions; dual formulation; entropy equation; existence results; nonlinear integrodifferential phase-field system; thermal memory
Bonetti, E., Fremond, M., Rocca, E. (2007). A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions, 88(5), 455-481 [10.1016/j.matpur.2007.09.005].
Bonetti, E; Fremond, M; Rocca, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23610
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