Solid-solid phase transitions in steel: modeling, simulation and optimal control

Prof. Dietmar Hoemberg (Technische Universitat Berlin & WIAS-Berlin, Germania)


Abstract:

Subject of the  talk is a  macroscopic thermomechanical model of phase 
transitions.
Effects like transformation strain and transformation plasticity induced 
by the phase transitions are considered and used to formulate a 
consistent thermomechanical model. The physical parameters are allowed 
to depend on the respective phase volume fractions by a mixture ansatz.

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 weak solution to the problem and depict some 
results of numerical simulations. Then we investigate the respective 
control problem neglecting the transformation induced plasticity term.

The last part of the talk is devoted to some practical considerations 
concerning the interplay of numerical optimal control and machine based 
control in the case of laser surface hardening.