Phase-field models for transition phenomena in materials with hysteresis

Claudio Giorgi

doi:10.3934/dcdss.2015.8.693

Article Contents

2015, Volume 8, Issue 4: 693-722. Doi: 10.3934/dcdss.2015.8.693

This issue Previous Article Rate-independent memory in magneto-elastic materials Next Article The Souza-Auricchio model for shape-memory alloys

Phase-field models for transition phenomena in materials with hysteresis

Claudio Giorgi^1,

1.
DICATAM, Università di Brescia, Via Valotti 9, 25133 Brescia

Received: March 2014

Revised: July 2014

Published: August 2015

Abstract / Introduction Related Papers Cited by

Abstract

Non-isothermal phase-field models of transition phenomena in materials with hysteresis are considered within the framework of the Ginzburg-Landau theory. Our attempt is to capture the relation between phase-transition and hysteresis (either mechanical or magnetic). All models are required to be compatible with thermodynamics and to fit well the shape of the major hysteresis loop. Focusing on uniform cyclic processes, numerical simulations at different temperatures are performed.

Keywords:

First and second order phase transitions,
austenite-martensite transition,
ferromagnetic transition,
Ginzburg-Landau theory,
hysteresis loops,
free energy potentials.

Mathematics Subject Classification: Primary: 74N30, 74C05, 74F05, 80A17, 80A22, 82C26, 82D40.

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