A contact model with Tresca's friction law is considered, the behavior of the material being modeled by the subdifferential of a convex constitutive map. Using a separable bipotential defined by means of the constitutive map and its Fenchel conjugate we deliver a two-field weak formulation of the model under consideration. This formulation allows us to deliver existence and uniqueness results based on minimization arguments. Subsequently, we study some properties of the solution and the data dependence. An alternative one-field formulation, in displacements, is also discussed focusing on the connections between formulations. Finally, we consider a regularization of the Tresca law and we deliver convergence results.
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