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Modelling and simulation of flame cutting for steel plates with solid phases and melting
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 Thiébaud (J. Mater. Process. Technol. 214(2):304–310, 2014) 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. © 2020, The Author(s).
A model for resistance welding including phase transitions and Joule heating
In this paper we introduce a new model for solid-liquid phase transitions triggered by Joule heating as they arise in the case of resistance welding of metal parts. The main novelties of the paper are the coupling of the thermistor problem with a phase field model and the consideration of phase dependent physical parameters through a mixture ansatz. The PDE system resulting from our modelling approach couples a strongly nonlinear heat equation, a non-smooth equation for the the phase parameter (standing for the local proportion of one of the two phases) with quasistatic electric charge conservation law. We prove existence of weak solutions in the 3D case, while the regularity result and the uniqueness of solution is stated only in the 2D case. Indeed, uniqueness for the three dimensional system is still an open problem.
1D symmetry for semilinear pdes from the limit interface of the solution
We study bounded, entire, monotone solutions of the Allen-Cahn equation. We prove that under suitable assumptions on the limit interface and on the energy growth, the solution is 1D. In particular, differently from the previous literature, the solution is not assumed to have minimal properties. We think that this approach could be fruitful in concrete situations, where one can observe the phase separation at a large scale and whishes to deduce the values of the state parameter in the vicinity of the interface. As a simple example of the results obtained with this point of view, we mention that monotone solutions with energy bounds, whose limit interface does not contain a vertical line through the origin, are 1D, at least up to dimension 4.
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity $k$ are allowed to depend both on the order parameter $chi$ and on the absolute temperature $theta$ of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.