𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A model for resistance welding including phase transitions and Joule heating

✍ Scribed by Dietmar Hömberg; Elisabetta Rocca

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
383 KB
Volume
34
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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 modeling 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 a quasistatic electric charge conservation law. We prove the existence of weak solutions in the three-dimensional (3D) case, whereas the regularity result and the uniqueness of solution is stated only in the two-dimensional case. Indeed, uniqueness for the 3D system is still an open problem.

📜 SIMILAR VOLUMES

A mathematical model for impulse resista
A mathematical model for impulse resistance welding
✍ F. Duderstadt; D. Hömberg; A. M. Khludnev 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 282 KB

## Abstract We present a mathematical model of impulse resistance welding. It accounts for electrical, thermal and mechanical effects, which are non‐linearly coupled by the balance laws, constitutive equations and boundary conditions. The electrical effects of the weld machine are incorporated by a

A sharp interface model for phase transi
A sharp interface model for phase transitions in crystals with linear elasticity
✍ T. Blesgen; U. Weikard 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 153 KB

## Abstract A model describing phase transitions coupled with diffusion and linear elasticity in crystals under isothermal conditions is introduced. The elastic deformation as well as the phase parameter are obtained directly by the minimization of the free energy. After stating the model, the exis

A fast convergent and accurate temperatu
A fast convergent and accurate temperature model for phase-change heat conduction
✍ Víctor D. Fachinotti; Alberto Cardona; Alfredo E. Huespe 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 300 KB

This work proposes a temperature-based ÿnite element model for transient heat conduction involving phasechange. Like preceding temperature-based models, it is characterized by the discontinuous spatial integration over the elements a ected by the phase-change. Using linear triangles or tetrahedrals,