𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Phase-Field Models with Hysteresis

✍ Scribed by Pavel Krejčı́; Jürgen Sprekels

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
163 KB
Volume
252
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Phase-field systems as mathematical models for phase transitions have drawn increasing attention in recent years. However, while capable of capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical theory of hysteresis operators developed in the past 15 years. In particular, they have proved well-posedness and thermodynamic consistency for hysteretic phase field models which are related to the Caginalp and Penrose᎐Fife models. In this paper, these results are extended into different directions: we admit temperaturedependent relaxation coefficients and relax the growth conditions for the hysteresis operators considerably; also, a unified approach is used for a general class of systems that includes both the Caginalp and Penrose᎐Fife analogues.

📜 SIMILAR VOLUMES

A Phase-Field Model with Temperature Dep
A Phase-Field Model with Temperature Dependent Constraint
✍ Pierluigi Colli; Nobuyuki Kenmochi; Masahiro Kubo 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 139 KB

This paper is concerned with a phase-field model with temperature dependent constraint for the order parameter. In the kinetic equation of the order parameter, we take account of diffusion as well as the undercooled/superheated state which is modelled by means of a hysteresis input-output relation;