Premium
Analysis of a thermomechanical phase transition model
Author(s) -
Chełmiński Krzysztof,
Hömberg Dietmar,
Kern Daniela
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700440
Subject(s) - phase transition , quasistatic process , cauchy stress tensor , nonlinear system , plasticity , infinitesimal strain theory , tensor (intrinsic definition) , momentum (technical analysis) , transformation (genetics) , phase (matter) , work (physics) , mechanics , stress (linguistics) , mathematics , materials science , mathematical analysis , physics , thermodynamics , finite element method , geometry , chemistry , biochemistry , linguistics , philosophy , finance , quantum mechanics , gene , economics
Subject of this work is a macroscopic thermomechanical model of phase transitions in steel. Effects like transformation strain and transformation plasticity induced by the phase transitions are considered and used to formulate a consistent thermomechanical model. The resulting system of state equations consists of a quasistatic momentum balance coupled with a nonlinear stress‐strain relation, a nonlinear energy balance equation and a system of ODEs for the phase volume fractions. We prove the existence of a unique weak solution using fixed‐point arguments. A key issue is a regularity analysis for the mechanical subsystem to obtain continuity of the stress tensor. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)