This paper presents a finite element method approach for modeling a thermal-electrical-mechanical coupled-field contact comprised of an elastic hemisphere and an elastic half space. The goal of this model is to develop a fundamental understanding of the behavior of a multi-physics contact with a particular interest in the contact area. The results from the model illustrate a clear difference in contact behavior between force control and displacement control in the presence of an applied electrical potential. It is shown that, while Hertzian contact theory can be used to accurately predict the behavior of the contact under force control, a new relationship must be established to accurately predict the behavior of the contact under displacement control. This relationship can be applied to RF MEMS switch contact bumps as well as macro scale electrical contacts.

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