WIAS Preprint No. 638, (2001)

A mathematical model for impulse resistance welding


  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Duderstadt, Frank
  • Khludnev, Alexander M.

2010 Mathematics Subject Classification

  • 35D05 35Q72 74F15


  • Joule heating, resistance welding, thermo-viscoelasticity




We present a mathematical model of impulse resistance welding. It accounts for electrical, thermal and mechanical effects, which are nonlinearly coupled by the balance laws, constitutive equations and boundary conditions. The electrical effects of the weld machine are incorporated by a discrete oscillator circuit which is coupled to the field equations by a boundary condition. We prove the existence of weak solutions for a slightly simplified model which however still covers most of its essential features, e.g. the quadratic Joule heat term and a quadratic term due to non-elastic energy dissipation. We discuss the numerical implementation in a 2D setting, present some numerical results and conclude with some remarks on future research.

Appeared in

  • Math. Methods Appl. Sci. 26 (2003), pp. 717--737

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