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A 3-D domain decomposition method for fully coupled electrothermomechanical contact problems is presented. The formulation is based on the cell method. Contacting domains are linked together by introducing a new reference frame (i.e., the mortar surface). Field discontinuities across contact interfaces are simulated by suitable constitutive operators. It is shown that the same coupling strategy can be adopted for the electrical, thermal, and mechanical contact problems. Compatibility constraints are imposed by means of dual Lagrange multipliers defined on the mortar surface. Coupled nonlinear algebraic equations are finally cast into a saddle-point problem, which is resolved by combining the Schur complement method with the Newton-Raphson method. The proposed mortar approach is validated with a commercial 3-D finite-element method multiphysics software package.