A thermodynamic approach to nonisothermal phase-field models

Tom 42 / 2015

Irena Pawłow Applicationes Mathematicae 42 (2015), 269-331 MSC: 74A30, 35K25, 35Q74, 35L20. DOI: 10.4064/am2282-12-2015 Opublikowany online: 19 January 2016


The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers.

As the main result we obtain a general scheme of phase-field models which involves an arbitrary extra vector field. We explain the presence of such a field in the light of Edelen’s decomposition theorem asserting a splitting of a solution of the dissipation inequality into a dissipative and a nondissipative part. For particular choices of this extra vector field we obtain known schemes with either modified entropy equation or modified energy equation. A detailed comparison with several known phase-field models, in particular Cahn–Hilliard and Allen–Cahn models in the presence of deformation and heat conduction, will be presented in another publication. The Müller–Liu thermodynamic approach will be extended there also to thermoelastic phase-field models for shape memory materials.


  • Irena PawłowSystems Research Institute
    Polish Academy of Sciences
    Newelska 6
    01-447 Warszawa, Poland
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    S. Kaliskiego 2
    00-908 Warszawa, Poland

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