A thermodynamic approach to nonisothermal phase-field models

Irena Pawłow. "A thermodynamic approach to nonisothermal phase-field models." Applicationes Mathematicae 42.4 (2015): 269-331. <http://eudml.org/doc/279238>.

@article{IrenaPawłow2015,
abstract = { 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. },
author = {Irena Pawłow},
journal = {Applicationes Mathematicae},
keywords = {phase-field models; thermoelastic materials; order parameters; conserved and nonconserved dynamics},
language = {eng},
number = {4},
pages = {269-331},
title = {A thermodynamic approach to nonisothermal phase-field models},
url = {http://eudml.org/doc/279238},
volume = {42},
year = {2015},
}

TY - JOUR
AU - Irena Pawłow
TI - A thermodynamic approach to nonisothermal phase-field models
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 4
SP - 269
EP - 331
AB - 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.
LA - eng
KW - phase-field models; thermoelastic materials; order parameters; conserved and nonconserved dynamics
UR - http://eudml.org/doc/279238
ER -