Thermomechanical models are the basis for the description of numerous technological processes. The consideration of phase transitions and of inelastic constitutive laws leads to coupled new systems of partial differential equations. Up to now a qualitative solution theory for these systems is available only in special cases.

A further important question is the identification of unknown materials parameters. Typically, quantities like heat conductivity or the latent heat released or consumed during phase transitions do not only depend on temperature but also on the respective phase. In stock removal processes modelling and identification of tool-induced heating of the workpiece come along.

These tasks are dealt with in collaboration with partners from engineering sciences and from industry. An important challenge is the further interdisciplinary development of measurement techniques based on the mathematical investigations.


Symmetric cooling of a roller bearing ring based on a thermoelastic model with solid-solid phase change (top: temperature evolution, bottom: phase evolution)


Publications

  Monographs

  • P. Colli, G. Gilardi, D. Hömberg, E. Rocca, eds., Special Issue dedicated to Jürgen Sprekels on the Occasion of his 65th Birthday, 35, no. 6 of Discrete Contin. Dyn. Syst. Ser. A, American Institute of Mathematical Sciences, Springfield, 2015, 472 pages, (Collection Published).

  • P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON -- Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

  • B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279--299, (Chapter Published).

  Articles in Refereed Journals

  • CH. Heinemann, Ch. Kraus, E. Rocca, R. Rossi, A temperature-dependent phase-field model for phase separation and damage, Archive for Rational Mechanics and Analysis, 225 (2017) pp. 177--247.
    Abstract
    In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature (cf., e.g., [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface models describing phase separation and damage. European J. Appl. Math. 24 (2013), 179--211]), we encompass in the model thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More in particular, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in [E. Feireisl: Mathematical theory of compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53 (2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then recently employed in [E. Feireisl, H. Petzeltová, E. Rocca: Existence of solutions to a phase transition model with microscopic movements. Math. Methods Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to a thermodynamically consistent PDE system for phase transitions and damage. SIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

  • Y. Guo, D. Hömberg, G. Hu, J. Li, H. Liu, A time domain sampling method for inverse acoustic scattering problems, Journal of Computational Physics, 314 (2016) pp. 647--660.
    Abstract
    This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally ``direct'' involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations.

  • K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016) pp. 557--588.
    Abstract
    We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.

  • D. Hömberg, Q. Liu, J. Montalvo-Urquizo, D. Nadolski, Th. Petzold, A. Schmidt, A. Schulz, Simulation of multi-frequency-induction-hardening including phase transitions and mechanical effects, Finite Elements in Analysis and Design, 121 (2016) pp. 86--100.
    Abstract
    Induction hardening is a well known method for the heat treatment of steel components. With the concept of multi-frequency hardening, where currents with two different frequency components are provided on a single inductor coil, it is possible to optimize the hardening zone to follow a given contour, e.g. of a gear. In this article, we consider the simulation of multi-frequency induction hardening in 3D. The equations to solve are the vector potential formulation of Maxwell's equations describing the electromagnetic fields, the balance of momentum to determine internal stresses and deformations arising from thermoelasticity and transformation induced plasticity, a rate law to determine the distribution of different phases and the heat equation to determine the temperature distribution in the workpiece. The equations are solved using adaptive finite element methods. The simulation results are compared to experiments for discs and for gears. A very good agreement for the hardening profile and the temperature is observed. It is also possible to predict the distribution of residual stresses after the heat treatment.

  • G. Hu, M. Yamamoto, Hölder stability estimate of the Robin coefficient in corrosion detection problems with a single boundary measurement, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 31 (2015) pp. 115009/1--115009/20.

  • TH. Petzold, D. Hömberg, D. Nadolski, A. Schulz, H. Stiele, Adaptive Finite-Elemente-Simulation des Mehrfrequenz-Induktionshärtens, HTM Journal for Heat Treatment and Materials, 70 (2015) pp. 33--39.

  • R. Rossi, M. Thomas, From an adhesive to a brittle delamination model in thermo-visco-elasticity, ESAIM. Control, Optimisation and Calculus of Variations, 21 (2015) pp. 1--59.
    Abstract
    We address the analysis of a model for brittle delamination of two visco-elastic bodies, bonded along a prescribed surface. The model also encompasses thermal effects in the bulk. The related PDE system for the displacements, the absolute temperature, and the delamination variable has a highly nonlinear character. On the contact surface, it features frictionless Signorini conditions and a nonconvex, brittle constraint acting as a transmission condition for the displacements. We prove the existence of (weak/energetic) solutions to the associated Cauchy problem, by approximating it in two steps with suitably regularized problems. We perform the two consecutive passages to the limit via refined variational convergence techniques.

  • CH. Heinemann, E. Rocca, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, Mathematical Methods in the Applied Sciences, 38 (2015) pp. 4587--4612.
    Abstract
    In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the ones already present in the literature consists in the possibility of taking into account a damage-dependent thermal expansion coefficient. This term implies the presence of nonlinear couplings in the PDE system, which make the analysis more challenging.

  • D. Hömberg, Th. Petzold, E. Rocca, Analysis and simulations of multifrequency induction hardening, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 22 (2015) pp. 84--97.
    Abstract
    We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system.

  • W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014) pp. 1328--1333.
    Abstract
    In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.

  • D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in non-isothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014) pp. 035003/1--035003/24.
    Abstract
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.

  • K. Chełminski, D. Hömberg, O. Rott, On a thermomechanical milling model, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 12 (2011) pp. 615--632.
    Abstract
    This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.

  • A. Fasano, D. Hömberg, D. Naumov, On a mathematical model for laser-induced thermotherapy, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems. Elsevier Science Inc., New York, NY. English, English abstracts., 34 (2010) pp. 3831--3840.
    Abstract
    We study a mathematical model for laser-induced thermotherapy, a minimally invasive cancer treatment. The model consists of a diffusion approximation of the radiation transport equation coupled to a bio-heat equation and a model to describe the evolution of the coagulated zone. Special emphasis is laid on a refined model of the applicator device, accounting for the effect of coolant flow inside. Comparisons between experiment and simulations show that the model is able to predict the experimentally achieved temperatures reasonably well.

  • A. Fasano, D. Hömberg, L. Panizzi, A mathematical model for case hardening of steel, Mathematical Models & Methods in Applied Sciences, 19 (2009) pp. 2101--2126.
    Abstract
    A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations.

  • D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009) pp. 438--442.
    Abstract
    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.

  • D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009) pp. 669--681.
    Abstract
    The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solid-solid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results.

  • K. Chełminski, D. Hömberg, D. Kern, On a thermomechanical model of phase transitions in steel, Advances in Mathematical Sciences and Applications, 18 (2008) pp. 119--140.

  • P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008) pp. 793--799.
    Abstract
    The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations.

  • H. Alder, D. Hömberg, W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, HTM Zeitschrift für Werkstoffe. Wärmebehandlung. Fertigung, 61 (2006) pp. 103--108.

  • D. Hömberg, W. Weiss, PID control of laser surface hardening of steel, IEEE Transactions on Control Systems Technology, 14 (2006) pp. 896--904.

  • D. Hömberg, A. Khludnev, A thermoelastic contact problem with a phase transition, IMA Journal of Applied Mathematics, 71 (2006) pp. 479--495.

  • D. Hömberg, M. Yamamoto, On an inverse problem related to laser material treatments, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 22 (2006) pp. 1855--1867.

  • D. Hömberg, A mathematical model for induction hardening including mechanical effects, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 5 (2004) pp. 55--90.

  • D. Hömberg, S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003) pp. 1003-1028.

  Contributions to Collected Editions

  • G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics, in: MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, pp. 012009/1--012009/20.
    Abstract
    This note deals with the analysis of a model for partial damage, where the rate-independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from [Roubíček M2AS'09, SIAM'10] with the methods from Lazzaroni/Rossi/Thomas/Toader [WIAS Preprint 2025]. The present analysis encompasses, differently from [Roubíček SIAM'10], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [WIAS Preprint 2025], a nonconstant heat capacity and a time-dependent Dirichlet loading.

  • Q. Liu, Th. Petzold, D. Nadolski, R. Pulch, Simulation of thermomechanical behavior subjected to induction hardening, in: Scientific Computing in Electrical Engineering, SCEE 2014, Wuppertal, Germany, July 2014, A. Bartel, M. Clemens, M. Günther, E.J.W. TER Maten, eds., 23 of Mathematics in Industry, Springer International Publishing Switzerland, Cham, 2016, pp. 133--142.

  • C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C -- Production, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151--153.

  • M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4 -- PDE-constrained optimization with industrial applications, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207--222.

  • D. Hömberg, E. Rocca, Th. Petzold, Multi-frequency induction hardening -- A challenge for industrial mathematics, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 257--264.

  • D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227--243.

  • P. Krejčí, E. Rocca, J. Sprekels, Liquid-solid phase transitions in a deformable container, in: Continuous Media with Microstructure, B. Albers, ed., Springer, Berlin/Heidelberg, 2010, pp. 285-300.

  • L. Panizzi, A. Fasano, D. Hömberg, Modeling, analysis and simulations of case hardening of steel, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 965--970.

  • D. Hömberg, O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 493--498.

  • O. Rott, P. Rasper, D. Hömberg, E. Uhlmann, A milling model with thermal effects including the dynamics of machine and work piece, B. Denkena, ed., Proceedings, 1st International Conference on Process Machine Interactions, Hannover, September 3--4, 2008, PZH Produktionstechnisches Zentrum GmbH, Garbsen, 2008, pp. 369--378.
    Abstract
    This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.

  • D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering -- IDE 2008, 17--19 September 2008, Bremen, Germany, H.-W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201--209.

  • D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, in: Distortion Engineering -- Verzugsbeherrschung in der Fertigung III --, 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 39--55.

  • M. Anthonissen, D. Hömberg, W. Weiss, Real-time control of surface remelting, in: Progress in Industrial Mathematics at ECMI 2004, A. Di Bucchianico, R.M.M. Mattheij, M.A. Peletier, eds., 8 of Mathematics in Industry, Springer, 2005, pp. 356--360.

  • D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325--335.

  Preprints, Reports, Technical Reports

  • D. Hömberg, O. Rott, K. Sturm, Discretisation and error analysis for a mathematical model of milling processes, Preprint no. 2364, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2364 .
    Abstract, PDF (565 kByte)
    We investigate a mathematical model for milling where the cutting tool dynamics is considered together with an elastic workpiece model. Both are coupled by the cutting forces consisting of two dynamic components representing vibrations of the tool and of the workpiece, respectively, at the present and previous tooth periods. We develop a numerical solution algorithm and derive error estimates both for the semi-discrete and the fully discrete numerical scheme. Numerical computations in the last section support the analytically derived error estimates.

  • D. Hömberg, F.S. Patacchini, K. Sakamoto, J. Zimmer, A revisited Johnson--Mehl--Avrami--Kolmogorov model and the evolution of grain-size distributions in steel, Preprint no. 2283, WIAS, Berlin, 2016.
    Abstract, PDF (4023 kByte)
    The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.

  • B. Albers, P. Krejčí, E. Rocca, Solvability of an unsaturated porous media flow problem with thermomechanical interaction, Preprint no. 2211, WIAS, Berlin, 2016.
    Abstract, PDF (259 kByte)
    A PDE system consisting of the momentum balance, mass balance, and energy balance equations for displacement, capillary pressure, and temperature as a model for unsaturated fluid flow in a porous viscoelastoplastic solid is shown to admit a solution under appropriate assumptions on the constitutive behavior. The problem involves two hysteresis operators accounting for plastic and capillary hysteresis.

  Talks, Poster

  • TH. Petzold, The MIMESIS project -- An example for an interdisciplinary research project, Leibniz-Kolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9 - 11, 2016, Leibniz-Gemeinschaft, Berlin, November 9, 2016.

  • D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

  • D. Hömberg, Math for steel production and manufacturing, MACSI10 -- Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8 - 9, 2016, University of Limerick, Ireland, December 9, 2016.

  • M. Heida, Modeling of fluid interfaces, Jahrestagung der Deutschen Mathematiker-Vereinigung, Minisymposium ``Mathematics of Fluid Interfaces'', September 21 - 25, 2015, Universität Hamburg, Fakultät für Mathematik, Informatik und Naturwissenschaften, Hamburg, September 23, 2015.

  • CH. Heinemann, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, 3rd Workshop of the GAMM Activity Group Analysis of Partial differential Equations, September 30 - October 2, 2015, Universität Kassel, Institut für Mathematik, October 1, 2015.

  • D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

  • D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

  • TH. Petzold, Adaptive Finite-Elemente-Simulation des Mehrfrequenz-Induktionshärtens in 3D, Härterei-Kongress, October 22 - 24, 2014, Köln, October 23, 2014.

  • TH. Petzold, Finite element simulations and experiments for multifrequency induction hardening, IUTAM Symposium on Thermomechanical-Electromagnetic Coupling in Solids: Microstructural and Stability Aspect, June 16 - 18, 2014, Paris, France, June 18, 2014.

  • TH. Petzold, Modelling and simulation of multi-frequency induction hardening of steel parts, 7th International Scientific Colloquium ``Modelling for Electromagnetic Processing'' (MEP 2014), September 16 - 19, 2014, Leibniz Universität Hannover, September 19, 2014.

  • TH. Petzold, Modelling and simulation of multifrequency induction hardening for gear components, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium ``Recent Trends in Modelling, Analysis, and Simulation of Induction Heat Treatments'', June 9 - 13, 2014, Taormina, Italy, June 13, 2014.

  • M. Thomas, Rate-independent systems with viscosity and inertia: Existence and evolutionary Gamma-convergence, Workshop ``Variational Methods for Evolution'', December 14 - 20, 2014, Mathematisches Forschungsinstitut Oberwolfach, December 18, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials, 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems (MURPHYS-HSFS-2014), April 7 - 11, 2014, WIAS Berlin, April 8, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, International Workshop ``Variational Modeling in Solid Mechanics'', September 22 - 24, 2014, University of Udine, Department of Mathematics and Informatics, Italy, September 23, 2014.

  • M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, Oberseminar ``Analysis und Angewandte Mathematik'', Universität Kassel, Institut für Mathematik, December 1, 2014.

  • D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25 - 28, 2014, University of Warwick, UK, March 26, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

  • D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

  • D. Hömberg, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

  • J. Sprekels, Prandtl--Ishlinskii operators and elastoplasticity, Spring School on ``Rate-independent Evolutions and Hysteresis Modelling'', May 27 - 31, 2013, Politecnico di Milano, Università degli Studi di Milano, Italy.

  • D. Kern, Analysis and simulation of a thermomechanical model of phase transitions in steel, Universität Bremen, SFB 570 ``Distortion Engineering'', February 2, 2011.

  • N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 9. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Siegen, April 6, 2011.

  • N. Togobytska, Simulation, optimisation and control of microstructure evolution and mechanical properties during hot rolling of multiphase steels, 10. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Freiberg, November 8, 2011.

  • D. Hömberg, Optimal control problems in thermomechanics, Schwerpunktskolloquium ``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, January 20, 2011.

  • N. Togobytska, An inverse problem for laser-induced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23 - 24, 2010, September 24, 2010.

  • N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Aachen, November 10, 2010.

  • D. Hömberg, Modelling, simulation and control of phase transformations in steel, Nippon Steel Corporation, Chiba, Japan, September 10, 2010.

  • D. Hömberg, Multiphase steels, heat treatment and distortion --- Mathematical challenges in steel production and manufacturing, Summer School ``High Performance Computing'' (organizer: TU Ilmenau), September 29 - October 2, 2010, Upstalsboom Hotel Friedrichshain, Berlin, September 30, 2010.

  • D. Kern, Optimal control of a thermomechanical model including transformation induced plasticity, SIAM Conference on Control and its Applications, July 6 - 8, 2009, Denver, USA, July 8, 2009.

  • N. Togobytska, Parameter identification for the phase transformations in steel, Conference on Applied Inverse Problems 2009, July 20 - 24, 2009, University of Vienna, Austria, July 21, 2009.

  • N. Togobytska, Parameter identification from dilatometric investigations, SIAM Conference on Control and its Applications, July 6 - 8, 2009, Denver, USA, July 8, 2009.

  • N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', WIAS Berlin, June 23, 2009.

  • D. Hömberg, Coupling of process, machine, and work-piece in production processes --- A challenge for industrial mathematics, Workshop ``Industrial Mathematics and its Practice'', February 23 - 24, 2009, University of Tokyo, Japan, February 23, 2009.

  • D. Hömberg, Die Wärmebehandlung von Stahl --- Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

  • D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multi-phase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9 - 11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

  • D. Hömberg, Distortion compensation --- An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27 - 31, 2009, Buenos Aires, Argentina, July 27, 2009.

  • D. Hömberg, Interactions between machine, work-piece, and process dynamics in milling machines, SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09), October 9 - 10, 2009, San Francisco, USA, October 9, 2009.

  • D. Hömberg, Optimal control of heat treatments and stability of milling processes --- Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

  • D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

  • O. Rott, A milling model with thermal effects including the dynamics of machine and workpiece, 1st International Conference on Process Machine Interactions (PMI 2008), September 3 - 4, 2008, Leibniz Universität Hannover, September 3, 2008.

  • O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, The European Consortium for Mathematics in Industry (ECMI 2008), June 30 - July 4, 2008, University College, London, UK, July 3, 2008.

  • O. Rott, Numerical solution of a milling model including thermoelastic workpiece effects, Universität Dortmund, Fachbereich für Mathematik, June 23, 2008.

  • O. Rott, Parameter für ein MKS-Modell einer Fräsmaschine, DFG SPP 1180 Workshop ``Parameteridentifikation bei Werkzeugmaschinen'', February 21 - 22, 2008, WIAS Berlin, February 22, 2008.

  • O. Rott, Semiimplizite Zeitintegration eines gekoppelten Systems aus partiellen und gewöhnlichen Differentialgleichungen mit Retardierung, DFG SPP 1180 Workshop ``Modellierungstechnologien'', May 29 - 30, 2008, Dresden, May 30, 2008.

  • N. Togobytska, On the evaluation of the dilatometer experiments, Chemnitz Symposium on Inverse Problems 2008, September 25 - 26, 2008, September 25, 2008.

  • N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Antragskolloquium zum DFG Schwerpunktprogramm 1204/2, Bonn, May 20, 2008.

  • W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26 - 28, 2008.

  • D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

  • D. Hömberg, On a mathematical model for high-speed milling including the dynamics of machine and work-piece, Conference ``Direct, Inverse and Control Problems for PDE's'' (DICOP 08), September 22 - 26, 2008, Cortona, Italy, September 26, 2008.

  • D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

  • D. Hömberg, Solid-solid phase transitions --- Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

  • D. Hömberg, The heat treatment of steel --- A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17 - 19, 2008, Bremen, September 19, 2008.

  • D. Kern, Optimal control of a thermo-mechanical model of phase transitions in steel, 13th Czech-French-German Conference on Optimization, September 17 - 21, 2007, Heidelberg, September 20, 2007.

  • W. Weiss, Control of laser surface hardening, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

  • W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, Ruhr-Universität Bochum, Institut für Werkstoffe, May 30, 2007.

  • D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

  • D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

  • D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

  • D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

  • D. Hömberg, Phase transition models for multiphase steels, Industrial and Interdisciplinary Workshop ``Problems Related to the Manufacture of Multiphase Steels'', University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, November 2, 2007.

  • D. Hömberg, Solid-solid phase transitions in steel --- modeling, simulation and optimal control, Universitá di Pavia, Dipartimento di Matematica, Italy, March 27, 2007.

  • D. Hömberg, Thermomechanical phase transition models --- analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

  • D. Hömberg, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

  • D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

  • D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28 - 31, 2006, Miedzyzdroje, Poland, August 29, 2006.

  • D. Hömberg, Optimal control of thermomechanical phase transitions, Workshop ``Inverse and Control Problems for PDE's'', March 13 - 17, 2006, Rome, Italy, March 13, 2006.

  • D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14 - 18, 2006, Föhr.

  • D. Hömberg, Thermomechanical models of phase transitions --- modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

  • D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7 - 12, 2005, Coimbra, Portugal, June 11, 2005.

  • D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24 - 26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

  • D. Hömberg, Die Laserhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

  • D. Hömberg, Entwicklung eines Prognosetools zur Identifizierung von stabilen Fräsprozessen, DFG SPP 1180, Garbsen, May 19, 2005.

  • D. Hömberg, Laser material treatments --- modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

  • D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

  • D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25 - 29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

  • D. Hömberg, Optimal control of solid-solid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17 - 23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

  • D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie --- Simulations- und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3 - 4, 2005, Frankfurt am Main, November 3, 2005.

  • D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

  • D. Hömberg, Modelling, simulation and control issues in laser-induced thermotherapy, 13-th European Conference on Mathematics for Industry (ECMI 2004), June 21 - 25, 2004, Eindhoven University of Technology, Eindhoven, Netherlands, June 22, 2004.

  • D. Hömberg, On a thermomechanical model of phase transitions in steel, INdAM Workshop ``Dissipative Models in Phase Transitions'', September 5 - 11, 2004, Cortona, Italy, September 10, 2004.

  • D. Hömberg, On a thermomechanical model of surface heat treatments, University of Tokyo, Department of Mathematical Sciences, Japan, October 14, 2004.

  • D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

  • D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

  • D. Hömberg, Thermoelastische Phasenübergänge in Stahl, Humboldt-Universität zu Berlin, Institut für Mathematik, May 13, 2004.

  • D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

  • D. Hömberg, A mathematical model for capacitor resistance welding, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7 - 11, 2003, Sydney, Australia, July 10, 2003.