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A cell method‐based numerical model for resistance welding

P. Alotto (Dipartimento di Ingegneria Elettrica, Università di Padova, Padova, Italy)
M. Guarnieri (Dipartimento di Ingegneria Elettrica, Università di Padova, Padova, Italy)
F. Moro (Dipartimento di Ingegneria Elettrica, Università di Padova, Padova, Italy)
A. Stella (Dipartimento di Ingegneria Elettrica, Università di Padova, Padova, Italy)



The purpose of this paper is to simulate in the time domain three‐dimensional electrical, thermal, mechanical coupled contact problems arising in electric resistance welding (ERW) processes.


A three‐dimensional multiphysical numerical model for analyzing contact problems is proposed. Electrical and thermal field equations in bulk domains are discretized with the cell method (CM). Welding resistance at contact interfaces is described locally by synthetic statistic parameters and contacting domains are matched together by a non‐overlapping domain decomposition method. Contact pressure distribution is resolved by a finite‐element procedure. The model is validated with 3D FEM software package.


The semi‐analytical model describing the electric and thermal resistances at contact interfaces can be easily embedded in CM formulations, where problem variables are expressed directly in integral form. Compatibility conditions between contact members are enforced by a domain decomposition approach. System conditioning and computing time are improved by a solution strategy based on the Schur complement method.

Research limitations/implications

The electrical‐thermal analysis is not coupled strongly with the mechanical analysis and contact pressure distribution is assumed to be not depending on thermal stresses, which can be considerable near the contact area where localized joule heating occurs.

Practical implications

Resistance welding processes involve mechanical, electrical, and thermal non‐linear coupled effects that cannot be simulated by standard commercial software packages. The proposed numerical model can be used instead for designing and optimizing ERW processes.


The paper shows that numerical modeling of ERW processes requires a careful prediction of the localized joule heating occurring at the electrode‐material interface. This effect is reconstructed by the proposed approach simulating coupled electrical, thermal, and mechanical effects on different spatial scales.



Alotto, P., Guarnieri, M., Moro, F. and Stella, A. (2011), "A cell method‐based numerical model for resistance welding", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 5, pp. 1479-1486.



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