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Author: Hömberg, Dietmar × Author: Lasarzik, Robert × End date: 2022 × Start date: 2020 × End date: 2019 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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    Modelling and simulation of flame cutting for steel plates with solid phases and melting
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Arenas Jaén, Manuel J.; Hömberg, Dietmar; Lasarzik, Robert; Mikkonen, Pertti; Petzold, ThomasFlame cutting, finite element method, heat equation, phase transitions, transport equation
    The goal of this work is to describe in detail a quasi-stationary state model which can be used to deeply understand the distribution of the heat in a steel plate and the changes in the solid phases of the steel and into liquid phase during the flame cutting process. We use a 3D-model similar to previous works from Thiebaud [1] and expand it to consider phases changes, in particular, austenite formation and melting of material. Experimental data is used to validate the model and study its capabilities. Parameters defining the shape of the volumetric heat source and the power density are calibrated to achieve good agreement with temperature measurements. Similarities and differences with other models from literature are discussed.
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    Topology optimization subject to additive manufacturing constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Ebeling-Rump, Moritz; Hömberg, Dietmar; Lasarzik, Robert; Petzold, Thomas
    In Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem.
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    Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Hömberg, Dietmar; Lasarzik, Robert
    In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weak-strong uniqueness of these solutions, i.e., that a weak entropy solutions coincides with a classical solution emanating form the same initial data as long as the classical one exists. The weak entropy solution concept has advantages in comparison to the previously introduced weak solutions, e.g., it allows to include free energy functions with low regularity properties corresponding to phase transitions.