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The heat treatment of steel - a mathematical control problem
2009, Hömberg, Dietmar, Kern, Daniela
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.
On a thermomechanical model of phase transitions in steel
2007, Chełminski, Krzysztof, Hömberg, Dietmar, Kern, Daniela
We investigate a thermomechanical model of phase transitions in steel. The strain is assumed to be additively decomposed into an elastic and a thermal part as well as a contribution from transformation induced plasticity. The resulting model can be viewed as an extension of quasistatic linear thermoelasticity. We prove existence of a unique solution and conclude with some numerical simulations.