Analysis of a thermomechanical phase transition model

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)