The goal of this paper is to work out a thermodynamical setting for phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law 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 Part II of the paper.
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.
May 10, 2021
Apr 11, 2021
|RB-2007-06 : Pawłow, Irena : A Thermodynamic Approach of Phase-Field Modeling of Thermoelastic Materials.Part I: Theory||May 10, 2021|
Chudzikiewicz, Andrzej (1949– ) Myśliński, Andrzej
Koniarski, Konr Myśliński, Andrzej